COMBINING RESEARCH IN PHYSICAL CHEMISTRY AND
CHEMICAL EDUCATIONPart A:The Femtosecond Molecular Dynamics Of Small Gas-Phase Anion Clusters
Part B:
Surveying Student Beliefs About Chemistry And The Development Of Physical
Chemistry Learning Tutorials

byJack Barbera

B.S. (Honors), University of Colorado at Denver, 2000

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of Philosophy
Department of Chemistry and Biochemistry
2007

ii

This thesis entitled:
Combining research in physical chemistry and chemical education
Written by Jack Barbera
has been approved for the
Department of Chemistry and Biochemistry___________________________
W. Carl Lineberger___________________________
Carl E. Wieman

Date: ______________

HRC Protocol # 0603.08
The final copy of this thesis has been examined by both the signatories, and we find that boththe content and the form meet acceptable presentation standards of scholarly work in theabove mentioned discipline.

iii
Barbera, Jack. (Ph.D. Physical Chemistry)
Combining research in physical chemistry and chemical education.
Part A: The Femtosecond Molecular Dynamics Of Small Gas-Phase Anion Clusters
Part B: Surveying Student Beliefs About Chemistry And The Development Of Physical
Chemistry Learning Tutorials
Thesis directed by Professors W. Carl Lineberger and Carl E. Wieman

This dissertation combines work in the areas of experimental physical chemistry andchemical education.

In the area of physical chemistry, femtosecond pump-probe

spectroscopy is used to interrogate the time-dependence for energy redistribution, solvent
reorientation, and dissociation dynamics in small gas-phase anion clusters. The chemical
education research addressed in this manuscript include the development and validation of asurvey to measure students’ beliefs about chemistry and the learning of chemistry and thedevelopment and testing of learning tutorials for use in undergraduate physical chemistrycourses in thermodynamics and kinetics.
In the first part of this dissertation, the Cu(CD3OD) dynamics are investigated using a
combination of femtosecond pump-probe experiments and ab initio calculations.
Dissociation of this complex into Cu and CD3OD occurs on two distinct time scales: 3 and 30
ps, which arise, respectively, from the coupling of intermolecular solvent rotations andexcited methyl rotor rotation into the Cu–O dissociation component upon electron
photodetachment of the precursor anion.
In the second part of this dissertation, the time-resolved recombination ofphotodissociated IBr−(CO2)n (n = 5 – 10) cluster anions is investigated. Upon excitation to
the A′ 2Π1/2 state of the chromophore, the bare anion results in I− and Br products, uponsolvation with CO2, the IBr− chromophore regains near-IR absorption after recombination andvibrational relaxation on the ground electronic state. The recombination times vary with theivnumber of solvent molecules from 12 ps for n = 5 to 900 ps for n = 10. Extensive electronic
structure and non-adiabatic molecular dynamic simulations provide a framework tounderstand this behavior.
In the third part of this dissertation, the modification and validation of the Colorado
Learning Attitudes about Science Survey (CLASS) for use in chemistry is presented in detail.
The CLASS survey is designed to measure student beliefs about chemistry and the learningof chemistry. This instrument is a modification of the original CLASS-Phys survey designed
for use in physics. Statements on the chemistry version (CLASS-Chem) are validated usingchemistry students with a broad range of experience levels to ensure clarity in wording andmeaning. The chemistry version addresses additional belief areas important in learningchemistry but not physics, specifically, beliefs about reactions and molecular structure.
Statements are grouped into statistically robust categories using reduced basis factor analysis.
The final part of this dissertation addresses the development and testing of learning
tutorials for use in undergraduate physical chemistry. The tutorials are designed to promote
the active mental engagement of students in the process of learning. Questions within the
pencil-paper format guide students through the reasoning needed to apply concepts to realworld situations. Each tutorial is connected to a physical model or computer simulation
providing students with additional hands-on investigations to strengthen their connection withthe concepts addressed in the tutorial. Currently tutorials connected with the First andSecond Laws of Thermodynamics as well as Kinetics have been developed and tested.

v

This thesis is dedicated to my grandmother, for all her love and support.
Mary C. Amarante(1921 – 2002)

vi
Acknowledgements

The list of those to thank is long, however, there are a few people (and two dogs) thatmust be mentioned first and foremost. Carl Lineberger has been a great advisor and mentor.
Despite his vast travel schedule and many commitments, I found his door was always open
for discussions about science, personal issues, and about my future in academia. For this I
am truly grateful! I value our interactions and look forward to carrying on with them ascolleagues. If there is any one person in JILA that is busier than Carl Lineberger it is Carl
Wieman. Despite Carl’s meeting/travel schedule, he agreed to be my co-advisor, allowing
me to gain invaluable research skills in science education. Carl Wieman’s transformationfrom being a Nobel Prize winning physicist to being a top-notch physics education researcher
was very inspirational to me. I valued the opportunity to work with him on several chemical
education projects and look forward to fruitful collaborations during my academic career.
Outside the realm of academics and science, my mother has had the greatest impact
on my life. Her continued loved and support throughout the MANY phases of my life haveallowed me to explore the world around me and never fear I was letting her down or not
living up to some pre-determined standard. I always have and always will feel like I can doanything because of her!
Next on the list are my dogs Basil (Full Name: Basil Cesario Copernicus) and Dotti.
How do you thank a dog? Well, lots of belly rubs and cookies seem to work well, along witha warm spot on the couch. Basil’s enthusiastic whines and whimpers of joy when I walk inthe door at the end of a long day make even the worst days great. Dotti’s consistent“dancing” and following me around the house at the end of a day always made me feel like
all was well.
Last on this short list is my wife, Mischel. We began dating right after I made thedecision to attend CU for my doctoral work in 2002. I wonder what would have happened if

vii
I decided on Purdue instead? Mischel is my best friend and I value her as my partner in life.
Without her support throughout my graduate tenure I would certainly have never made it tothis point. She was always willing to talk about my frustrations as well as my successes andconsistently provided a gauge of the important things in life. For all but the first five monthsof our relationship I have been in school, I look forward to the additional time I will get tospend with my best friend now that I an finally done with school. I promise to learn Italian
now so we can take another trip to Milan and stay for more than 12 hours!
I feel fortunate to have had wonderful people to work with during my time at CU.
From the day I walked into B1B30 (Lineberger Femtosecond Lab) both Mark Taylor andFelician Muntean were welcoming and helpful. I could not have asked for better lab partners
to aid in my scientific pursuits. Collaborations with Robert Parson and Matt Thompson haveprovided valued theoretical insight to enhance a large portion of my experimental findings.
Outside the walls of JILA I was fortunate to collaborate with Anne McCoy and her graduate
student Samantha Horvath, of the Ohio State University.

Their talent, hard work, andfriendly demeanor made for a great scientific experience. On the education side of things, I
owe a great big THANK YOU to Kathy Perkins for all her help and guidance. Kathy isanother one of those people who, no matter how busy, always seemed to make time to talkand help. I have also worked closely with Joshua Martin and Vladimir Dribinski in my lab
work as well as Linda Koch on my education projects, I thank all of them for theircontributions and comments throughout the past few years.
There are many people who I did not directly work with on projects but who, without
there support or assistance my life would have been much harder. First on this list has to be
the other physical chemistry students in my incoming class. I spent more time with themduring our first year, both studying and complaining, than I spent with Mischel. I still feel tothis day that I would not have made it through that first year without them.

On theexperimental side there is a vast list of people in the “ion-molecule” groups to thank:

viiiVeronica Bierbaum, Barney Ellison, Mathias Weber, Jeff Rathbone, Todd Sanford, Adam
Gianola, and Django Andrews. I also owe a debt of gratitude to the Physics Education groupand most notably Wendy Adams and Noah Finkelstein. Outside of my two research groups
there are also a wealth of people to thank. These include the many folks who comprise the
JILA support staff. Without there help in the machine shop, electronics shop, or with the
Keck cluster most of my experiments would have never worked.
Lastly I need to thank all of the wonderful friends I have made while at CU, theirfriendships have kept me sane both in and out of school. Tom Baker and Tom Reilly quickly
became my core study partners during our first year and are now considered as my goodfriends. I enjoy taking breaks to talk about bikes with Tom Baker or to grab a cup of coffeewith Tom Reilly, I am sure our friendship will continue on after we all leave graduate school.
While I have never actually worked with or studied with Brad Perkins or Kendra (Redin)
Fraze they have both become good friends who were always available to talk about school oranything else. Lastly I need to thank my long standing friend Stephanie Villano, she and I
did our undergraduate work together at UCD. Since her arrival at CU the year after me, wehave become better friends and I will miss our daily interactions when I am gone. Having
lunch with her and Nicole has kept me going through these last few years.

ix
Contents

Solute Dynamics in Size Selected Solvents .............................................................................................1
1.1

Motivation ..............................................................................................................................1

1.2

The femtosecond dynamics of Cu(CD3OD)...........................................................................2

1.3

The time-resolved solvent induced recombination of IBr−(CO2)n ..........................................5

1.4

Dissertation overview Part A: Experimental Physical Chemistry .........................................7

References for Chapter I ......................................................................................................................8
Experimental Apparatus.........................................................................................................................14
2.1

Overview ..............................................................................................................................14

2.2

Cluster ion and discharge sources ........................................................................................14

2.3

Mass spectrometer................................................................................................................17

2.4

Laser System ........................................................................................................................20

2.5

Data Aquisition ....................................................................................................................24

References for Chapter II ...................................................................................................................29
Femtosecond Dynamics of Cu(CD3OD) ................................................................................................31
3.1

Introduction ..........................................................................................................................31

3.2

Experimental ........................................................................................................................31

3.3

Theory ..................................................................................................................................33

3.3.1

Ab initio calculations ............................................................................................................34

3.3.2

Vibrational Coordinates and Hamiltonian............................................................................36

3.4

Results and Discussion.........................................................................................................38

3.4.1

Initial State Characterization ................................................................................................38

3.4.1.1 Calculations..........................................................................................................................38
3.4.1.2 Photoelectron Spectra...........................................................................................................41
3.4.2

Time Evolution of the Cu+ and Cu+(CD3OD) signals ..........................................................43

x
3.4.3

Dissociation Time Components ...........................................................................................47

3.4.3.1 Direct Dissociation...............................................................................................................47
3.4.3.2 Energy Redistribution...........................................................................................................51
3.5

Conclusions ..........................................................................................................................52

References for Chapter III..................................................................................................................54
The Time-Resolved Solvent Induced Recombination of IBr−(CO2)n .....................................................56
4.1

Introduction ..........................................................................................................................56

4.2

Experimental ........................................................................................................................56

4.3

Theoretical Methods.............................................................................................................59

4.4

Results and Analysis ............................................................................................................62

4.5

Discussion ............................................................................................................................68

4.6

Conclusion............................................................................................................................71

References for Chapter IV..................................................................................................................73
Chemical Education Introduction...........................................................................................................76
5.1

Towards an understanding of student learning.....................................................................76

5.2

Measuring student beliefs about chemistry and learning chemistry.....................................77

5.3

Tutorials for undergraduate physical chemistry ...................................................................78

5.4

Dissertation overview: Chemical Education ........................................................................79

References for Chapter V...................................................................................................................80
Measuring Student Beliefs About Chemistry and Learning Chemistry .................................................83
6.1

Introduction ..........................................................................................................................83

6.2

Instrument Design ................................................................................................................83

6.3

Scoring and Administration..................................................................................................86

6.4

Validation.............................................................................................................................88

6.4.1

Interviews.............................................................................................................................89

6.4.1.1 CLASS-Phys Statements......................................................................................................90

xi
6.4.1.2 Chemistry-specific Statements .............................................................................................91
6.4.2

Faculty Surveys ....................................................................................................................92

6.4.3

Categorization of Statements................................................................................................94

6.4.3.1 Categorization Philosophy and Approach ............................................................................95
6.4.3.2 Unmodified Physics Categories ...........................................................................................98
6.4.3.3 CLASS-Chem Categories.....................................................................................................99
6.4.4

Concurrent Validity............................................................................................................101

6.4.5

Test-Retest Studies.............................................................................................................102

6.5

Applications .......................................................................................................................103

6.5.1

Semester Shifts...................................................................................................................104

6.5.2

Comparison Between Chemistry and Physics ....................................................................105

6.6

Conclusions and Future Directions ....................................................................................108

References for Chapter VI................................................................................................................110
Tutorials for Undergraduate Physical Chemistry .................................................................................112
7.1

Introduction ........................................................................................................................112

7.2

Study Design ......................................................................................................................112

7.2.1

Student Observations and Interviews .................................................................................113

7.2.2

Physical Models .................................................................................................................120

7.2.3

Tutorial Design...................................................................................................................121

7.2.3.1 First Law of Thermodynamics ...........................................................................................121
7.2.3.2 Second Law of Thermodynamics.......................................................................................122
7.2.3.3 Reaction Kinetics ...............................................................................................................124
7.3

Testing................................................................................................................................126

7.3.1

Scoring Rubric....................................................................................................................127

7.3.2

Pre Tutorial Quizzes...........................................................................................................128

7.3.2.1 First Law of Thermodynamics ...........................................................................................129
7.3.2.2 Second Law of Thermodynamics.......................................................................................131

xii
7.3.2.3 Reaction Kinetics ...............................................................................................................133
7.3.3

Tutorial Worksheets and Models........................................................................................134

7.3.3.1 First Law of Thermodynamics ...........................................................................................135
7.3.3.2 Second Law of Thermodynamics.......................................................................................138
7.3.3.3 Reaction Kinetics ...............................................................................................................141
7.3.4

Post Tutorial Quiz ..............................................................................................................143

7.3.4.1 First Law of Thermodynamics ...........................................................................................143
7.3.4.2 Second Law of Thermodynamics.......................................................................................146
7.3.4.3 Reaction Kinetics ...............................................................................................................148
7.3.5

Exam Questions..................................................................................................................150

7.4

Course Implementation and Evaluation .............................................................................152

7.4.1

Pre/Post Analysis................................................................................................................153

7.4.2

Comparison with Control Group ........................................................................................157

7.4.2.1 Pre-Semester Concept Exam ..............................................................................................158
7.4.2.2 Common Exam Scores .......................................................................................................159
7.5

Conclusions and Future Directions ....................................................................................164

References for Chapter VII ..............................................................................................................167
Bibliography.........................................................................................................................................169
Appendix A ..........................................................................................................................................182
A.1

CLASS-Chem v2 Statements .............................................................................................183

A.2

Robustness data for ‘Personal Interest’ category................................................................185

A.3

Robustness data for ‘Real World Connections’ category...................................................186

A.4

Robustness data for ‘Problem Solving: General’ category.................................................187

A.5

Robustness data for ‘Problem Solving: Confidence’ category...........................................188

A.6

Robustness data for ‘Problem Solving: Sophistication’ category ......................................189

A.7

Robustness data for ‘Sense Making/Effort’ category.........................................................190

A.8

Robustness data for ‘Conceptual Connections’ category ...................................................191

xiii
A.9

Robustness data for ‘Conceptual Learning’ category.........................................................192

A.10

Robustness data for ‘Atomic-Molecular Perspective of Chemistry’ category ...................193

Appendix B ..........................................................................................................................................194
B.1

First Law Pre/Post Quiz .....................................................................................................195

B.2

First Law Tutorial Worksheet (Air Can) ............................................................................196

B.3

Second Law Pre/Post Quiz .................................................................................................198

B.4

Second Law Tutorial Worksheet (Rubber Band) ...............................................................199

B.5

Kinetics Pre/Post Quiz........................................................................................................201

B.6

Kinetics Tutorial Worksheet (PhET Sim) ..........................................................................202

B.7

Chem 4511 Concept Test ...................................................................................................205

B.8First Law Exam Questions .................................................................................................214

B.9

Second Law Exam Questions.............................................................................................215

B.10

Reaction Kinetics Exam Questions ....................................................................................216

xiv
List of Tables and Figures
Figure 1.1

Femtosecond photodetachment-photoionization scheme used to interrogate
dynamics on neutral potential energy surface. .........................................................3

Figure 1.2

Calculated potential energy curves for the lowest six electronic states of IBr−. The
arrow indicates the pump/probe transition from the ground state (X) to the firstexcited state (A′). .....................................................................................................6

Figure 2.1

Schematic diagram of the sputtering discharge ion source for generation ofCu−(CD3OD) and electron gun source for generation of IBr−(CO2)n clusters. .......15

Figure 2.2

Schematic diagram of the Wiley-McLaren time-of-flight mass spectrometer. ......17

Figure 2.3

Optical set-up for photodetachment-photoionization experiments. .......................22

Figure 2.4

Optical set-up for one color multi-photon recombination studies..........................23

Figure 2.5

Schematic diagram of data acquisition system used in both experimental
configurations. .......................................................................................................25

Figure 3.1

Radial potential energy curves and laser pump-probe schemes. Dashed curves
represent cuts in the Cu−DOCD3 Cs orientation, while solid curves represent the
Cu−ODCD3 C1 orientation. The vertical arrows represent various pump-probe
processes employed in the experiments reported here. ..........................................32

Figure 3.2

The in situ measurement of the time resolution for photodetachmentphotoionization experiments. Rising points display rising Cu+ signal as a functionof the delay between the photodetachment and photoionization pulse sequence.
Solid line represents tanh fit to points and dashed line is the derivative (sech2) ofthis fit. ....................................................................................................................33

Figure 3.3(a) Minimum energy configuration for Cu−(CD3OD), used to define coordinates
for the four 1-d slices employed in the simulations: Cu—O stretch; out-of-plane
bend, Cu-O-C-D4 dihedral angle; in-plane bend, Cu-O-C angle; and methyl grouprotation, D1-C-O-D4 dihedral angle. Also shown are the minimum energy
configurations for the neutral (b), and the cation (c)..............................................35

Table 3.1

Select geometrical parameters of all species, calculated at MP2 level of theory. ..39

Table 3.2

Calculated fundamental frequencies of the four vibrational modes corresponding to
the 1-d potential energy slices for Cu−(CD3OD) and Cu(CD3OD), which is theneutral complex in the anion configuration, i.e. the vertical detachment geometry.
40

Table 3.3

Calculated fundamental frequencies for the four vibrational modes corresponding
to the 1-d potential energy slices of Cu(CD3OD), neutral geometry......................40

Figure 3.4

Experimental and calculated Cu−(CD3OD) photoelectron spectra. The
experimental spectrum is shown as black points. The three lines represent
calculated photoelectron spectra with various Cu−O separations. The solid black
curve gives the spectrum for R(Cu−O) = 3.42 Å, the calculated minimum energy
anion geometry. The grey curves represent photoelectron spectra calculated with ±xv
0.18 Å changes in the Cu−O distance, with the dashed line representing 3.24 Åand the dash-dot line representing 3.60 Å..............................................................42
Figure 3.5

Initial experimental time dependence of cation signals. The open circles represent
Cu+ signal from Cu(CD3OD), while the filled circles represent the Cu+(CD3OD)
signal from Cu(CD3OD). The Cu+ signal rise from Cu− (grey triangles) indicatesthe instrument time resolution................................................................................44

Figure 3.6

Experimental time dependence of cation signals resulting from photodetachmentphotoionization of Cu−(CD3OD). The rising Cu+ signal (open circles) results fromphotodetachment (398 nm) followed by two-color (327 nm + 265 nm) resonant
ionization. The decaying Cu+(CD3OD) signal (filled circles) results fromphotodetachment (398 nm) followed by one-color (265 nm) resonant multiphoton
ionization. Solid lines represent exponential fits to data used to extract timecomponents. ...........................................................................................................45

Table 3.4

Parameters of double exponential fit to the functions given in Eqs. (4) and (5); theindicated errors are ± 1σ of the least squares fit parameters. .................................47

Figure 3.7

Radial [R(Cu–O)] potential energy curves for Cu−(CD3OD) (i), Cu(CD3OD) withother coordinates frozen at the anion configuration (ii), and fully relaxedCu(CD3OD) (iii). The insets show the various solvent orientations for the threeminima. ..................................................................................................................48

Figure 3.8

Radial potential energy curves for the anion (i) and neutral at the vertical
detachment geometries (ii) of Cu(CD3OD) and Cu(H2O). The solid curves
represent the Cu(CD3OD), while the dashed curves represent Cu(H2O). The
vertical line is drawn at the Cu–O distance corresponding to the minimum energy
configuration of both anions. The horizontal line at 1.23 eV indicates thedissociation limit of the neutral complexes............................................................49

Figure 4.1

Calculated potential energy curves for the lowest six electronic states of IBr−. The
arrow indicates the pump/probe transition from the ground state (X) to the firstexcited state (A'). ...................................................................................................57

Table 4.1

One-photon8 (pump only) and expected two-photon (pump/probe) ionic products
for selected IBr−(CO2)n clusters, following 790 nm excitation. Only significant (>5% of total) secondary products are shown. For each parent cluster size, thosesecondary products recorded in our experiments and used for determination ofrecombination time scales are shown in bold.........................................................58

Figure 4.2

Minimum energy structures of IBr− with various numbers of CO2 solvent
molecules, indicating asymmetric solvation around Br end...................................60

Figure 4.3

Calculated potential energy curves for the lowest six electronic states ofIBr−(CO2)8. The arrow indicates the pump/probe transition from the ground state(X) to the first excited state (A′). ...........................................................................61

Figure 4.4

The IBr−(CO2)5 (closed circle) and IBr−(CO2)6 (open circle) recombination
fractions as a function of time following excitation to the A′ state. Solid lines
represent single exponential fits which yield recombination times of 12 ± 0.5 ps(n=5) and 30 ± 5 ps (n=6). .....................................................................................63

Figure 4.5

Short time recombination fractions of IBr−(CO2)5 (triangle) and IBr−(CO2)6 (circle)
showing symmetry in data due to identical pump/probe wavelengths. The

xvi
coherence peak at t=0 arises due to enhancement of two-photon background.
Rising signal delayed by ~0.7 ps (n=5) and ~2 ps (n=6)........................................64
Figure 4.6

The IBr−(CO2)7 recombination fraction as a function of time following excitation
to the A′ state. The solid line represents a single exponential fit which yields a
recombination time of 140 ± 20 ps.........................................................................66

Figure 4.7

The IBr−(CO2)8 (closed circle) and IBr−(CO2)10 (open circle) recombination
fractions as a function of time following excitation to the A′ state. The solid line
represents a single exponential fit which nicely describes both data sets and yields
a recombination time of 900 ± 100 ps. The n=10 data exhibit more noise due tovery low ion signals. ..............................................................................................67

Figure 4.8

The IBr−(CO2)12 recombination fractions as a function of time following excitation
to the A′ state. The solid line represents a single exponential fit which yields a
recombination time of 9 ± 0.7 ps. ..........................................................................68

Figure 4.9

Comparison of absorption recovery times for experiment (closed circle) andmolecular dynamics simulations (closed triangle). Dashed lines are provided to
guide the eye. .........................................................................................................71

Table 5.1

Contrast of novice and expert beliefs on several dimensions of science (adaptedfrom David Hammer27)........................................................................................77

Table 6.1

Chemistry statements added to the CLASS-Chem v2............................................86

Figure 6.1% Favorable vs % Unfavorable plot of faculty responses......................................93

Figure 6.2

Flow chart depicting reduced basis factor analysis. ...............................................96

Table 6.2

Data from optimized ‘Real World’ Category.........................................................98

Figure 6.3

Scree plots from a good category (A) and a poor category (B)..............................98

Table 6.3

Comparison of robustness values for the eight categories of the CLASS-Phys
survey with both physics and chemistry students. .................................................99

Table 6.4

CLASS-Chem v2 categories, statement numbers, and robustness values. Bold
indicates added statements to v2. .........................................................................100

Figure 6.4

Comparison of percent favorable scores for ‘Personal Interest’ and ‘Overall’categories for a range of courses and majors including faculty. ..........................102

Table 6.5

Correlation of percent favorable, neutral, and unfavorable scores from fall 2005 to
fall 2006 general chemistry I courses and fall 2004 to spring 2005 algebra-based
physics I. ..............................................................................................................103

Table 6.6

General chemistry I: Results show decline in percent favorable scores over one
semester. ..............................................................................................................104

Table 6.7

Demographics of introductory courses surveyed. ................................................105

Figure 6.5

CLASS survey scores for biology majors at the start (pre) of Phys I (solid) and
Chem I (hollow). The students were consistently more expert-like in their view ofxvii
physics, with differences beings statistically significant (p<0.01) for both ‘Overall’and the 3 categories shown. .................................................................................107
Figure 6.6

Pre-post shift for CLASS-Chemistry and CLASS-Physics scores where there is astatistically significant difference in the shifts (p<0.01). .....................................108

Figure 7.1

Typical reaction energy profile showing potential energies for the reactant,product, and transition state. ................................................................................119

Figure 7.2

Student sketch of how potential energy of transition state varies with temperature.
120

Figure 7.3

Screen image of reversible reaction simulation showing a potential energy plot
with several reactant molecules. Kinetic energy and speed distributions are alsoplotted for the molecules shown. .........................................................................125

Table 7.1

Grading rubric used for introductory quiz questions............................................127

Table 7.2

Grading rubric used for detailed quiz questions...................................................128

Table 7.3

First Law of Thermodynamics pre-quiz results. Data reflects percentage ofstudents with each individual rubric score. Questions 1a and 1b are scored using
Table 7.1, question 2 is scored using Table 7.2. ..................................................130

Table 7.4

Second Law of Thermodynamics pre-quiz results. Data reflects percentage ofstudents with each individual rubric score. Question 1 is scored using Table 7.1,
questions 2 and 3 are scored using Table 7.2. ......................................................132

Table 7.5

Reaction Kinetics pre-quiz results. Data reflects percentage of students with eachindividual rubric score. Questions 1 and 2 are scored using Table 7.1, question 3
is scored using Table 7.2......................................................................................134

Table 7.6

First Law of Thermodynamics post-quiz results and pre-post gains. Data reflects
percentage of students with each individual rubric score. Questions 1a and 1b arescored using Table 7.1, question 2 is scored using Table 7.2. Average gain is
calculated for question 2 only. .............................................................................144

Table 7.7

Second Law of Thermodynamics post-quiz results and pre-post gains. Data
reflects percentage of students with each individual rubric score. Questions 1 isscored using Table 7.1, questions 2 and 3 are scored using Table 7.2. Averagegain is calculated for questions 2 and 3 only. ......................................................147

Table 7.8

Reaction Kinetics post-quiz results and pre-post gains. Data reflects percentage ofstudents with each individual rubric score. Questions 1 and 2 are scored using
Table 7.1, question 3 is scored using Table 7.2. Average gain is calculated forquestion 3 only. ....................................................................................................149

Table 7.9

First Law of Thermodynamics pre/post-quiz results and pre-post gains. Data
reflects percentage of students with each individual rubric score. Questions 1a and1b are scored using Table 7.1, question 2 is scored using Table 7.2. Average gainis calculated for question 2 only...........................................................................154

Table 7.10

Second Law of Thermodynamics pre/post-quiz results and pre-post gains. Data
reflects percentage of students with each individual rubric score. Questions 1 is

xviiiscored using Table 7.1, questions 2 and 3 are scored using Table 7.2. Averagegain is calculated for questions 2 and 3 only. ......................................................155
Table 7.11

Reaction kinetic pre/post-quiz results and pre-post gains. Data reflects percentage
of students with each individual rubric score. Questions 1 is scored using Table
7.1, questions 2 and 3 are scored using Table 7.2. Average gain is calculated forquestion 3 only. ....................................................................................................156

Table 7.12

Comparison of average scores on pre-semester concept exam for control and test
groups. Question statements can be found in Appendix B7.................................159

Figure 7.4

Comparison of average scores for control and test groups on common questions.
Rubric score reflects average score on conceptual question using scoring rubric
presented in Table 7.2. The difference in the Conceptual scores and Rubric scores
are statistically significant at the p<0.01 level. ....................................................160

Figure 7.5

Comparison of average scores for control and test groups on common questions.
Rubric score reflects average score on conceptual question using scoring rubric
presented in Table 7.2. The difference in the Conceptual scores and Rubric scores
are statistically significant at the p<0.01 level. ....................................................161

Figure 7.6

Comparison of average scores for control and test groups on common questions.
Rubric score reflects average score on conceptual question using scoring rubric
presented in Table 7.2. The difference in the Conceptual scores and Rubric scores
are statistically significant at the p<0.05 level. ....................................................163

______________
Chapter I
Solute Dynamics in Size Selected Solvents________________
1.1

Motivation
Solvated ions are ubiquitous in chemical and biological systems. Understanding theinteractions between solvent and solute is important in determining the outcome of chemical
reactions. Detailed analyses of these interactions are hindered by several factors. First,
solvent-solute systems traditionally contain many molecules which make it impossible toconsider individual molecular interactions. The molecular dynamics that take place within
and between these molecules occurs on extremely fast time scales. Finally, each solvent andsolute molecule is different due to its local environment. An alternative approach to gain
insight on the nature of these interactions is to look at a simplified problem with a known
number of solvent molecules. Gas-phase ionic complexes can be combined with mass andoptical spectroscopies to probe the nature of solvation in charged solvent-solute systems.1-11
The work presented here uses the combination of gas-phase anionic clusters andfemtosecond pump-probe spectroscopy to gain insight to the nature of molecular dynamics insmall clusters. Gas-phase clusters provide a controllable, well-defined solvent environment
which allows for the study of detailed interactions between solvent and solute.12-19 These
details are lost in condensed phase studies due to the statistical averaging needed in
describing these systems. An additional benefit of investigations using gas-phase clusters
comes with the use of easily generated charged species. The use of ionic species allows thesestudies to be performed within an ion mass spectrometer20 providing easy control ofmolecular speeds and product separation.

2
Coupling these ionic species with femtosecond laser techniques allows step-wisemonitoring of dynamics occurring within these systems.

Femtosecond time-resolved

methods for the study of gas-phase molecular dynamics have a long history and haveprovided breakthroughs in understanding fundamental chemical processes.13,21-23

These

studies involve a pump-probe scheme where first an ultrafast pump pulse initiates a reaction,
creates a nonstationary state or wave packet, and the evolution of this reaction is monitored asa function of time using a probe pulse.
1.2

The femtosecond dynamics of Cu(CD3OD)
In this study, time-resolved pump-probe laser spectroscopy is used to examine thedissociation dynamics initiated upon electron photodetachment of Cu−(CD3OD). This group
has previously used similar pump-probe techniques to examine the dynamics ofCu−(H2O)n,24,25 and such anion-water complexes have been the subject of numerous
theoretical and experimental investigations.10,11,26-35
Our studies employ photodetachment-photoionization (PDPI) spectroscopy inprobing the neutral dynamics of the clusters of interest. In this method, the neutral dynamics
are initiated when an ultrafast laser pulse photodetaches electrons from a mass selected anion
cluster, as shown in figure 1.1. The nascent neutral is interrogated by resonance enhanced
multiphoton

ionization(REMPI)36,37

atvarious

times

(∆t)

following

electronphotodetachment; this probe results in a time dependent cation signal which, following adetailed analysis, provides insight to the state of the neutral complex.

3

cationhν3∆texcitedstatehν2
neutralhν1Figure 1.1

anion

Femtosecond photodetachment-photoionization scheme used to interrogate
dynamics on neutral potential energy surface.

The PDPI method combines many techniques which aid in the investigation ofneutral molecular dynamics. First, complexes prepared as negative ions can be carefully
mass selected providing careful studies on known cluster sizes. Because photodetachment
occurs rapidly compared to the time of nuclear motion, photodetachment of these anioniccomplexes provides a neutral molecule with a well defined initial nuclear configuration. The
dynamics of this neutral complex are initiated upon photodetachment to the electronic groundstate (Fig. 1.1). The time-delayed REMPI probe not only allows a sensitive determination of
the instantaneous geometry of the neutral but also allows mass separation of the various
cationic photoproducts. Our method of PDPI spectroscopy is a modified version of that
introduced by Wöste and co-workers in 1995.38 The employment of a pulsed supersonic
expansion in our instrument allows for the production of colder negative ions.

The

simultaneous detection of both neutral and charged photoproducts allows us to account forany signal drifts due to ion production or laser intensity.

4
In previous studies of Cu−(H2O),24,39 electron photodetachment was shown to lead tolarge-amplitude H2O reorientation within and dissociation from Cu(H2O), due to thedifference in topology between the anion and neutral potential energy surfaces.

The

Cu−(H2O) complex has a hydrogen-bonded, Cu––HOH, minimum energy configuration,
while neutral Cu(H2O) has a Cu–O interaction, favoring Cu–OH2, that determines its
minimum energy configuration.

Electron photodetachment from Cu–(H2O) produces anensemble of vibrationally excited Cu(H2O) complexes with an average internal energy near
the dissociation threshold of the complex.

For the Cu(H2O) study, following electron

photodetachment from Cu−––HOH, dissociation of Cu(H2O) occurred on three different
timescales, each separated by an order of magnitude. Some 30% of the nascent Cu(H2O)
complexes directly dissociated. The remaining bound complexes dissociated on a 10 pstimescale via coupling of H2O internal rotation to the Cu–H2O dissociation coordinate and on
a 100 ps timescale by coupling of the H2O intramolecular bend vibrations with the Cu–H2O
dissociation coordinate.24,39,40
Hydrogen and methyl substituents, and functional groups in general, play pivotal
roles in a wide array of chemical reactions. Substitutions of CH3 for H, and vice versa, caninfluence reactivity, especially due to steric interactions. Methyl groups have been shown toaffect the structure and binding energy in I−(ROH) complexes, (R = H, CH3),41 and haverecently been part of an investigation of infrared spectral features in Cl−(ROH) complexes, (R= H, CH3, CH3CH2).42

In this thesis, the effects of a methyl group addition on the

dissociation dynamics of a metal-ligand complex are investigated. We are interested indetermining how the methyl group affects the solvent reorientation and dissociation dynamics
in a Cu−(ROH) (R = H, CH3), complex. For experimental reasons, the spectroscopic studies
are carried out using fully deuterated methanol. Reports from previous investigations24,25 on
Cu−(H2O)n show no significant difference in the time-evolution of the dissociating neutral
complexes upon deuteration.

5
1.3

The time-resolved solvent induced recombination of IBr−(CO2)nIn this study, femtosecond pump-probe spectroscopy is used to examine therecombination and relaxation of an excited IBr− chromophore. This process is highly
influenced by the interaction of the chromophore with its surrounding solvent molecules.
The stepwise investigation of this influence provides insight not available in condensed phasestudies. The utilization of anions as a tool to probe chemical dynamics of this nature has
recently been discussed by Neumark13.
Although it may seem surprising that a small cluster can serve as an adequate
prototype of a much larger condensed phase system, it has been demonstrated that certain
solvent-induced phenomena require very few solvent molecules to occur. Examples of suchphenomena are the “cage” effect,43-65 and the solvent-induced recombination, which in somecases can be observed with as few as only one solvent molecule present.66,67
The investigation in this chapter continues an extensive experimental study ofdihalide ion clusters XY−Ln (X,Y = I, Br, Cl; L = CO2, OCS, Ar) that display the profoundeffects of the solvent on the dissociation dynamics of the XY− core.2,7,67-76 In the present
work we investigate dependence of the rate of solvent-induced recombination in size-selected
IBr−(CO2)n, n = 5-10 clusters excited to the A’ 2Π1/2 state of the IBr− chromophore, as afunction of number of solvent molecules. The investigation encompasses a range of solvation
where the recombination has been shown to be nearly complete,77 and where pastexperience7,75,78,79 indicates the likelihood both of very rapid recombination rates and of rates
that increase with increasing solvation.
Potential energy curves of the unsolvated IBr− anion are shown in Fig. 1.2.77
Excitation of this unsolvated anion with 790 nm radiation produces only I− and Br fragments,
indicating that the A′ 2Π state is the only state excited at this wavelength. Our earlier
investigation of IBr− showed77 that the addition of a single CO2 solvent results in the6appearance of the Br− ion, indicating a solvent-induced non-adiabatic process. The first“caged” product, IBr−, appears from excitation of IBr−(CO2)2. The cage fraction rises to 90 %for IBr−(CO2)5, and, for clusters with n ≥ 8, only recombined ionic products are detected.
This behavior is very similar to that observed for I2−(CO2)n,79 and, consequently, trends in thetimescales of the recombination processes for IBr−(CO2)n and I2−(CO2)n were expected to becomparable. However, a preliminary measurement of the recombination time for IBr−(CO2)8
found a nanosecond recombination time, some two orders of magnitude

Energy, eV

2.0

1.0

B 2Σ+1/2

Br− + I*A′ 2Π1/2

I− + Br*I− + BrA 2Π3/2

0.0

X 2Σ+1/2

Br− + I

-1.0
3.0

4.0

5.0

R(I−Br), Å
Figure 1.2

Calculated potential energy curves for the lowest six electronic states of IBr−.
The arrow indicates the pump/probe transition from the ground state (X) to
the first excited state (A′).

slower than that of I2−(CO2)n clusters.77

Such a drastic discrepancy must reflect afundamental difference between IBr−(CO2)n and I2−(CO2)n. In order to help understand thisdifference, we have carried out a more thorough experimental measurement of recombination
times for a number of IBr−(CO2)n clusters. When complemented by extensive calculations,80
these experiments provide the likely explanation for the anomalous recombination of

7
IBr−(CO2)n as arising from a solvent–induced trap on the IBr− A′ 2Π1/2 surface, a trap thatarises from the solvent asymmetry, and is deepest for 5-10 CO2 solvent molecules.
1.4

Dissertation overview Part A: Experimental Physical Chemistry
The work presented in this section of the dissertation is divided into three chapters.

Chapter II presents the experimental setup and laser system configurations for both studies.
Chapter III presents the femtosecond photodetachment-photoionization investigation ofCu(CD3OD). Chapter IV presents the time resolved recombination studies on CO2 solvatedIBr−. Due to the diverse nature of the work presented in this dissertation, each individual
chapter will present conclusions and outline future directions depending on the investigation.

8

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________________
Chapter II
Experimental Apparatus________________
2.1

Overview
Both sets of experiments described in this portion of the dissertation involve the

combination of femtosecond pump-probe laser pulses with mass selected anions in a tandem
time-of-flight (TOF) mass spectrometer. Following this interaction, either anionic or cationicphotoproducts are detected. This experimental apparatus section first describes the two typesof cluster ion sources used in each experiment; second, the mass spectrometer is described indetail; next, the laser system and optical components for each experiment are presented; andfinally, the data acquisition procedures are outlined.
2.2

Cluster ion and discharge sources
Cluster anions are created in one of two different sources (Fig. 2.1) depending on thenature of the starting materials. The Cu−(CD3OD) anion experiment requires the generationof gas-phase copper metal, this is achieved via a high pressure pulsed sputtering discharge ion
source. Solid IBr crystals have a high enough vapor pressure to produce IBr−(CO2)n cluster
ions by crossing a neutral supersonic expansion perpendicularly with a high energy beam ofelectrons.

15

Ar + Ne + CD3OD

general valve

ceramic blockcopper cathodestainless steel
anode

conical expansion
channelCO2 + IBrelectron gun

general valve

focused electron beam

faraday cup

Figure 2.1

Schematic diagram of the sputtering discharge ion source for generation ofCu−(CD3OD) and electron gun source for generation of IBr−(CO2)n clusters.

To generate copper-methanol anions a mixture of 80% Ne and 20% Ar at stagnationpressures between 6–8 atm, flows through a small stainless steel vial containing liquidmethanol-d4 (CD3OD, Aldrich, CAS# 811-98-3) at room temperature and is expanded into
vacuum through a pulsed (200 Hz) General Valve (0.8 mm orifice). Copper anions areproduced when the carrier gas flows past a 1 mm gap between a copper rod cathodemaintained at negative 2–3 kV and a stainless steel anode maintained at ground, as seen in

16
Fig. 2.1. Immediately following the discharge, cluster anions form in the expanding gas. The
gas enters a 40° cone used to cool and stabilize clusters upon introduction into the ~ 5 x 10-5
Torr pressure of the source chamber.

Along with Cu−(CD3OD)n ions, the source generates

Cu−n, Cu−(D2O)n, Cu−Dn, Cu−OD, Cu−(CD3O), and CD3O−(CD3OD)n anions. In order toavoid mass contamination of 63Cu−(CD3OD) with 65Cu−(CD3O), the less abundant, butisotopically pure, m/z 101 ion packet is studied, 65Cu−(CD3OD).

Photodetachment-

photoionization experiments on 65Cu−(CH3OH) were not performed due to the congestion of
the mass spectrum in that region.
While evaporative cooling1,2 allows estimates of anion cluster temperatures,rotational and vibrational temperatures of the anions produced in our sputtering dischargesource have not been well characterized.

Previous anion cluster studies estimate thetemperature of (H2O)−18 and I2−(CO2)16 cluster ions3,4 and indicate these cluster temperatures
to be ~ 150 K and ~ 50 K, respectively. These studies are used to estimate the temperaturefor our smaller Cu−(CD3OD) clusters (m/z = 101) to be greater than 150 K. For the purposeof calculations in this study, a vibrational temperature of 200 K is used. The qualitative
conclusions, however, do not depend on the exact temperature.
The IBr−(CO2)n cluster ions are formed5 in the supersonic expansion of a gas mixture
obtained by passing 2-3 atm of CO2 through a glass reservoir containing crystals of IBr(Aldrich, 98% purity, CAS# 7789-33-5) at room temperature. The time required to passivate
the supply gas line was reduced from a week6 to less than a day by replacing stainless steellines with Teflon tubing.7 The mixture enters a source chamber through the 0.8 mm diameter
nozzle of a General Valve operating at 100 Hz repetition rate and is immediately intersectedby a 300 µA, 1 keV electron beam. Attachment of slow secondary electrons produces IBr−,from which IBr−(CO2)n clusters grow via ion-neutral collisions. Based on prior modeling of

17
the expansion conditions,8,9 we estimate the resultant cluster ion internal energy to correspondto a temperature of 40-70 K.
2.3

Mass spectrometer
The time-of-flight (TOF) mass spectrometer has been described in detailpreviously,5,10,11 only relevant details will be given here. After ions are produced in either
source, negative ions are extracted into a differentially-pumped Wiley-McLaren12 TOF mass
spectrometer (Fig 2.2) by a pulsed transverse electric field located 10 cm below the expansion
nozzle. This extraction field provides the first acceleration stage in theion source(discharge and verticale− gun not shown)deflector

horizontal
deflector

off-axis
detectorpotential
switcheinzellensdap h u gh
ot te
op r
ro
du
c

mass-gate

reflectronts

inlinedetectorneutralspump

0V+/-3.6 kV

deflected
photoproducts

∆t
probe

0V

0 V 2.55 kV-1 kV

Figure 2.2

one or two photon
depending on experiment

1 kV 2.55 kV
0V

Schematic diagram of the Wiley-McLaren time-of-flight mass spectrometer.

mass spectrometer with a pulse risetime of 10 ns and a 1 ms duration, the voltage varies
between -500 and -1000 V depending on the ion focusing conditions.

In the second

acceleration region, the ions are further accelerated to a total energy of ~3.5 keV, and brought
to a spatial and temporal focus at the laser interaction region, 1.5 m downstream.
Immediately after the acceleration region, horizontal and vertical deflectors are used to steer
the ions. An einzel lens, operating in decelerating mode, is used to focus the ion packet.

18
After the einzel lens, the ions are deflected around a 1.5° bend in the flight path which
separates neutral particles from the ion beam. Ions in the mass spectrometer enter a field-free‘potential switch’ region,13 which switches the reference potential of the ions from +2.55 kV
to ground. This relieves the need to float the detector region of the instrument at +2.55 kV.
The potential switch is a 40 cm long cylindrical mesh with 2.5 cm diameter apertures at bothends. This mesh is electrically isolated from the rest of the flight tube. The ions enter thecylinder, which is initially biased at the same +2.55 kV potential as the final element of thesecond acceleration region. Once inside the field-free cylinder, a pulse generator (Directed
Energy, model PVX-4140) switches its potential to ground (∆t ≤ 25 ns), and the ions present
in the switch exit into the detector region referenced to ground. In the m/e = 100 amu range,
this potential switch provides an effective transmission window of ∆ m/e ≈ 80 amu.
The field free region of the mass spectrometer is 1.5 m in length, after traveling thisdistance; ions are separated by mass into discrete packets. For example, the two isotopes ofcopper (m/e = 63 and 65) are separated by ∆t ≈ 200 ns. This separation is sufficient enough toallow a pulsed mass gate to transmit the ion packet of interest while deflecting all other ions.
This serves in reducing noise arising from scattered ions. The mass gate is operated at adeflecting potential of -1 kV, with a field-free transmission window of width ∆t ≈ 200–500
ns. Deflected anions are collected by a tube mounted on the front aperture of the reflectron inorder to reduce scatter into the detector mounted above. To further reduce noise, a horizontal
plate is extended from the off-axis detector housing to the front face of the reflectron, thisprevents anion scatter from the front faces of the mass gate or the reflectron, from striking theoff-axis detector. The addition of this horizontal plate reduced background counts from ~ 30
counts in 800 laser shots to less than 5 counts. Approximately 5 cm after the ion packet of
choice exits the mass gate, the packet is intersected by the laser beams. At this point, the ion
packet has a ~3 mm waist and ~3 mm length and is estimated to contain 103 – 104 ions. The

19
pump-probe process which takes place at this intersection varies depending on the experimentbut ultimately produces daughter ion fragments.
In the copper-methanol experiment a pump pulse produces neutral clusters which arethen resonantly ionized via a two-photon probe pulse. The packet of anions, neutrals andcations enter a single field reflectron mass spectrometer.14 In this experiment, the reflectron
serves two purposes. First, it separates the anions from the neutral and cation photoproducts:
reflecting and spatially focusing either anions or cations onto an off-axis detector whiletransmitting the undeflected neutrals to an in-line detector. Second, it provides secondary
mass analysis of the parent and photofragment ions. The reflecting potential varies fromground, at the entrance, to typically ±3.6 kV at the exit of the reflectron. The reflecting
potential is set either negative or positive to decelerate, reflect and focus the trajectories ofanions or cations, respectively, while deflecting the ions of opposite charge. The small massdifference between the parent cation, Cu+(CD3OD), and the cation photofragment, Cu+, does
not necessitate variation of the reflectron potential to separately optimize their spatial foci at,and positions on the off-axis detector.
For the IBr−(CO2)n studies, both pump and probe photons have enough energy topromote the chromophore to a low-lying dissociative excited state. Recombination andrelaxation from this excited state produces various daughter fragments based on the size ofthe parent.

The ion packet containing both parent and daughter cluster ions enters thereflectron where they are mass separated. The mass of the parent and daughter clusters varies
by more than 200 amu on average. This large mass difference requires variation of thereflectron voltage in order to allow transmission of either the parent anionic cluster or the
dissociation products. Typical reflectron voltages range from -1 kV for the smaller clusters to-3.5 kV for the parent clusters.
Ions which exit the reflectron impinge upon a detector displaced 10° above theprimary axis of the ion beam. The off-axis detector is a dual microchannel (MCP) plate pair

20
(Burle Electro-Optics 31558, diameter = 25 mm), located ~20 cm from the reflectron exit.
The entrance housing of the off-axis detector contains a mesh grid biased at -200 V, thispotential eliminates low energy electrons from the ion beam reducing detector noise. In orderto enhance the detector efficiency, the ions receive an additional 3 keV of energy before
striking the first MCP plate. The off-axis detector is operated in one of two modes. Whendetecting parent negative ions the detector is operated at low gain, in analog mode. The frontof the first MCP is maintained at the flight potential of +3.00 kV, the front of the second
MCP at +4.35 kV, and the MCP anode at +4.55 kV. When employed to detect daughter ions,the detector is operated at a higher voltage in a gain saturated (particle counting) mode. For
example in the IBr anion cluster experiments, the front of the first MCP is maintained at theflight potential of +3.00 kV, the front of the second MCP at +4.90 kV, and the MCP anode at+5.10 kV.
Neutral products which pass through the reflectron are collected on an in-line
channeltron detector (Burle Electro-Optics, 32685) situated approximately 20 cm
downstream from the last element of the reflectron. Any ionic products which pass all theway to the end of the reflectron are deflected away from the channeltron by a pair of parallel
plate deflectors mounted on the rear of the reflectron. The dual charged-neutral collector
arrangement enables the normalization of the time-dependent off-axis signal to the timeindependent neutral signal. This dual detection allows for the reduction of fluctuations in thetime-dependent ion signal due to fluctuations in the negative ion intensity or timing jitter
between the ion packet and laser pulses.
2.4

Laser System
The femtosecond laser system used in these experiments has been in operation in ourgroup for over a decade. It has therefore been fully described in previous publications,9,15 abrief description is provided here. A Ti:sapphire oscillator (Coherent Mira Basic), pumped

21
by a Nd:VO4 laser (Coherent Verdi V5, λ = 532 nm), produces ~85 fs pulses at 750–850 nm,
with a repetition rate of ~76 MHz and pulse energy of 7–8 nJ. Since the present experiments
require higher photon fluxes than are provided by the Ti:sapphire oscillator, the pulses areamplified by a regenerative, multi-pass Ti:sapphire amplifier (Quantronix Titan), which is
pumped by a Nd:YLF laser (Quantronix, model 527 DQ, λ = 527 nm). The amplifier output
has a pulse energy of ~3 mJ at a repetition rate of 400 Hz. The temporal pulsewidth ismeasured to be ~120 fs by optical autocorrelation (INRAD, model 5-14BX) and thespectrum, centered at λ = 800 nm, has a bandwidth ∆λ ≈ 10 nm.
The photodetachment-photoionization experiments utilize the optical set-up shown in
Fig. 2.3. In this configuration two-thirds of the 800 nm pulse from the amplifier is diverted
into a commercial harmonic generator (CSK Optronics Supertripler, model 8315A). Second
harmonic (400 nm) and third harmonic (267 nm) pulses are generated using 1 mm lithium
triborate (LBO) and 1 mm β-barium borate (BBO) crystals, respectively. The remaining onethird of the 800 nm pulse pumps an optical parametric amplifier (OPA, Light Conversion,
TOPAS), whose fourth harmonic output provides tunable radiation between 300 and 400 nm.
The OPA and second harmonic beams passes through independent delay stages. A
micrometer stage provides a fixed delay of 0.3 ps between the OPA beam and the third
harmonic beam. This slight delay ensures that OPA beam comes before the third harmonic.
The second harmonic beam passes through a computer controlled stage (Parker, 008-9129)
providing delays up to 800 ps with a resolution of 100 fs. All the beams are combined
collinearly using dichroic beamsplitters, and pass though a fused silica window into the mass
spectrometer. The beams are focused to a spot of ~1 mm diameter, at the point of interaction
with the ion packet, using independent telescopes. At this point, the typical pulse energies
are 100 µJ for 400 nm, 60 µJ for 267 nm, and 10–12 µJ for the OPA.

22

Nd:VO4 pump

Nd:YLF pump

λ=532 nm

λ=527 nm, 400 Hz

Ti:sapphire oscillator

Ti:sapphire amplifier

λ=800 nm, ∆t=85 fs

λ=800 nm, ∆t=120 fs,

76 MHz, 7 nJ/pulse

400 Hz, 3 mJ/pulse

optical parametric amplifier
λ=300-400 nm, 25 µJ/pulse

doubler / tripler

opticalλ=267 nm, 100 µJ/pulse

autocorrelator

λ=400 nm, 200 µJ/pulse

267 nm

400 nm

300-400 nm
fibre optic
spectrometertelescope

computer
controlled
delay stage

telescope

micrometerdelay stage

anion beam

telescopelaser interaction
regionFigure 2.3

Optical set-up for photodetachment-photoionization experiments.

The one color multi-photon experiments on solvated IBr− clusters utilize the opticalconfiguration depicted in Fig. 2.4. In this configuration half of the 795 nm output from theamplifier passes through a computer controlled delay stage (Parker, 008-9129) with a rangeof 800 ps, and a time resolution of ~100 fs. The remaining amplifier output travels throughan optical rail delay stage with a range of 3.5 ns. Manual positioning along the optical rail

23
leads to a precision of ~20 ps. The two beams are recombined collinearly and focused using
a single telescope before passing through the fused silica window into the mass spectrometer.
At the point of intersection with the ion packet the beams have a spot of ~1 mm diameter andpulse energy of ~500 µJ each.
Nd:VO4 pump

Nd:YLF pump

λ=532 nm

λ=527 nm, 400 Hz

Ti:sapphire oscillator

Ti:sapphire amplifier

λ=795 nm, ∆t=85 fs

λ=795 nm, ∆t=120 fs,

76 MHz, 7 nJ/pulse

400 Hz, 3 mJ/pulse

opticalautocorrelator
795 nm
795 nm

50% beam splittercomputer
controlled
delay stage

telescope

3.5 ns range

800 ps range

manualdelay stage

anion beamlaser interaction
regionFigure 2.4

Optical set-up for one color multi-photon recombination studies.

24
Daily set-up for both optical configurations involves optimization of the power,
shape, and overlap of the pump and probe beams. Clean homogenous beam shapes areneeded in order to provide consistent overlap over the range of delays scanned during either
experiment.

Pulse power optimization mainly consists of daily optimization within theamplifier itself, although some power is gained through careful optimization within the OPA
for the photodetachment-photoionization experiments. The optical configuration in Fig. 2.3
contains many non-linear crystals, the alignment and focusing of the beams into the crystals
is critical to produce consistent beam profiles. The set-up in Fig. 2.4 only utilizes thefundamental output from the amplifier making beam shape optimization facile. Optimal
pump-probe overlap is achieved in a two-step process.

First, one beam is carefully

overlapped with the ion beam in order to maximize the one photon signal. The remaining
beam is then overlapped with the first. In this second step, carefully attention is paid to theoverlap of the beams over the entire range of the computer controlled delay. Remaining
beams are then overlapped using the same procedure.
2.5

Data Aquisition
A schematic diagram of the signal processing electronics for both experiments ispresented in Fig. 2.5. Because the collector anode of the off-axis MCP detector is floated athigh voltage, the ion signal is capacitively coupled to the signal processing electronics. Thisconfiguration allows the transient signal spikes to pass through to the amplifiers while
isolating the high voltage.

The signal is amplified in two stages, first by a fast 10x

preamplifier (Ortec, model 9301) directly connected to the output capacitor, this stage isfollowed by a rack mounted bipolar amplifier (Phillips Scientific, model 771) providing an
additional 10x amplification. The resulting signal is split (Minicircuits, model ZSC-2-2),
with one half monitored on an oscilloscope and the other half proceeding to the particle
counting electronics. Negative ion mass spectra are recorded using a 100 MHz transient

25
recorder/signal averager (TRANSIAC, models 2101/4100), and accessed by a PC through a
GPIB interface to the CAMAC crate (Kinetic Systems, model 1510-P2C), which is controlled
by a GPIB crate controller (DSP, model 6001).
off-axis detector(microchannel plates)

10x
pre ampoff-axis ions
neutrals

ion beam trajectory

10x
pre amp

refl
ect
ron

10x
amp

in-line detector(channeltron)
10x
amp

oscilloscopeions
neutralsplitterneutral channel

ion channel
digital delay
generator

discriminator

ion gate
generator

quad scaler

neutralgate
generator

gatedintegrator

ion channel

neutral channel

GPIB

GPIB

computerFigure 2.5

Schematic diagram of data acquisition system used in both experimental
configurations.

When the experiment is being operated in ion counting mode, a 300 MHz
discriminator (Phillips Scientific, model 6904, discrimination threshold ≈ 150 mV) separates
detector noise from the ion signal. The ion signal is input into a quad scaler (DSP, model
QS-450), which counts the pulses associated with individual ions. The quad scaler counts

26
only the ions that arrive in one of four time-gates positioned around the arrival times of thedesired photoproducts. The timing of the gates is controlled by a digital delay generator(Stanford Research Systems model DG 535). A PC acquires the signal from the quad scaler
via the previously described GPIB interface and CAMAC crate.
The neutral products give rise to an analog signal at the in-line channeltron detector.
This signal is amplified by a fast 10x preamplifier (Ortec, model 9301) connected in close
proximity to the channeltron collector. A 10x bipolar amplifier (Phillips Scientific, model
6950) increases the total amplification to 100x, the amplified signal is split between an
oscilloscope and a gated integrator (LeCroy, model 2249SG). The neutral signal is integrated
in a time-gate generated by a pulse generator (Tektronix, model PG502) and timed by adigital delay generator (Stanford Research Systems model DG 535). The PC acquires thesignal from the gated integrator via the previously described GPIB interface and CAMAC
crate.
Two digital delay generators (Stanford Research Systems, model DG 535) control thetiming of the experiments, while the master clock of the experiments is provided by the pulse
train from the Ti:sapphire oscillator.

A small fraction of this ~76 MHz pulse train iscontinuously monitored by a photodiode, and the resulting signal, divided to ~400 Hz, is usedby a Pockels cell driver (Medox Electro-Optics, model DR85-A) to trigger the Ti:sapphire
regenerative amplifier and the Nd:YLF pump laser. The ~400 Hz signal from the Pockels
cell driver is divided down (Modulo-N divider, JILA LC022-2) to match the repetition rate
needed to produce the best ionic clusters, and used to trigger the two digital delay generators.
The timing of the sequence of events in the experiments is critical for optimal ion
production and detection.

The first event is the relative timing between the gas pulse

produced by the general valve and extraction field pulse. This timing is adjusted so that thehighest density of anions is accelerated into the mass spectrometer. Once extraction has
occurred, the next event is the timing of the pulsed potential switch; this timing is adjusted so27that the mass range of interest is referenced to ground potential and proceeds on to the massgate.

Next in line is the mass-gate timing itself; this is adjusted to allow maximum

transmission of the parent anion packet. Timing between the extraction pulse and the laser
pulse is optimized in order to ensure that the photons interact with the densest portion of theion packet selected by the mass-gate. The last timing involves the time-gates used in the
integration of the neutral and ion photoproduct signals, these gates are adjusted to collectsignal corresponding to the parent anion as well as the photoproducts and neutral signal.
The photodetachment-photoionization data acquisition procedure consists ofscanning a range of time delays between the pump pulse and the probe pulses, while
simultaneously integrating the analog neutral signal and the individual cation photoproductsignals. One single scan consists of sweeping the entire range of time-delays while data is
accumulated during 800 laser shots per time delay.

Many back and forth scans are

performed, for a total of ~4 x 104 laser shots per time delay.

The final signal (after

appropriate background corrections) is given by the cation signal divided by the neutral
signal. Background cation and neutral signals arising from each of the one and two color
combinations are measured, at a range of pump-probe time delays, using computer controlled
shutters (Uniblitz, model VS14S2T0) in each of the beam paths. These measurements areused for two purposes. First, they enable analysis of the contribution that each of the threelaser pulses makes to the cation signals.

Second, these background measurements are

typically recorded at the beginning and end of data acquisition.

Subtraction of theappropriate background signals from the raw time dependent cation/neutral signal furnishes
the final two or three-color signals, depending on the channel. Typical cation signals are ~0.5
cations/laser shot. Error bars for the experimental data are obtained by comparing the scatterpresent in multiple data sets.
The IBr− recombination data acquisition procedure consists of scanning a range oftime delays between the pump and probe pulses. One single scan consists of sweeping the28
entire range of time-delays while data is accumulated during 1000 laser shots per time delay.
Many back and forth scans are performed, for a total of ~4 x 104 laser shots per time delay.
Background signals arising from each of the beams are measured, at a range of pump-probe
time delays using computer controlled shutters (Uniblitz, model VS14S2T0) in each of thebeam paths. These measurements are used for two purposes. First, they enable analysis of
the contribution that each of the laser pulses makes to the ion signals.

Second, thesebackground measurements are typically recorded at the beginning and end of data acquisition.
Subtraction of the appropriate background signals from the raw time dependent ion signal
furnishes the final two photon time-dependent signal. Typical two-photon ion signals are 0.2– 0.5 ions/laser shot. The number of ions per laser shot is heavily dependent on the size ofthe parent anion cluster. Error bars for the experimental data are obtained by comparing thescatter present in multiple data sets.

29

References for Chapter II
1

W. H. Robertson and M. A. Johnson, Annu. Rev. Phys. Chem. 54, 173 (2003).

2

W. H. Robertson, J. A. Kelley, and M. A. Johnson, Rev. Sci. Instrum. 71, 4431
(2000).

3

P. J. Campagnola, L. A. Posey, and M. A. Johnson, J. Chem. Phys. 95, 7998 (1991).

4

J. M. Papanikolas, J. R. Gord, N. E. Levinger, D. Ray, V. Vorsa, et al, J. Phys. Chem.
95, 8028 (1991).

5

M. A. Johnson and W. C. Lineberger, in Techniques for the Study of Ion Molecule
Reactions, edited by J. M. Farrar and J. W. Saunders (Wiley, New York, 1988), pp.
591.

6

T. Sanford, S.-Y. Han, M. A. Thompson, R. Parson, and W. C. Lineberger, J. Chem.
Phys. 122, 054307 (2005).

7

E. Wrede, S. Laubach, S. Schulenburg, A. Brown, E. R. Wouters, et al, J. Chem.
Phys. 114, 2629 (2001).

8N. E. Levinger, D. Ray, M. L. Alexander, and W. C. Lineberger, J. Chem. Phys. 89,
5654 (1988).

9

V. Vorsa, P. J. Campagnola, S. Nandi, M. Larsson, and W. C. Lineberger, J. Chem.
Phys. 105, 2298 (1996).

10

M. L. Alexander, Ph.D., University of Colorado, 1987.

11

N. E. Levinger, Ph.D. Thesis, University of Colorado, 1990.

12

W. C. Wiley and I. H. McLaren, Rev. Sci. Instrum. 26, 1150 (1955).

13

L. A. Posey, M. J. Deluca, and M. A. Johnson, Chem. Phys. Lett. 131, 170 (1986).

30
14

B. A. Mamyrin, V. I. Karataev, D. V. Shmikk, and V. A. Zagulin, Sov. Phys. JETP.
37, 45 (1973).

15

D. W. Boo, Y. Ozaki, L. H. Andersen, and W. C. Lineberger, J. Phys. Chem. A 101,
6688 (1997).

________________
Chapter III
Femtosecond Dynamics of Cu(CD3OD)________________
3.1

Introduction
As described in detail in Chapter I, the dynamics of the Cu(CD3OD) neutral complex

are initiated upon photodetachment of an electron from Cu−(CD3OD). This process produces
a vibrationally excited complex which dissociates through a variety of mechanisms. In thischapter the experimental and theoretical investigation of these mechanisms is presented in thelight of previous investigations of the similar Cu(H2O) complex.1-4
The remainder of this chapter is structured as follows. Section 3.2 describes theexperimental measurement techniques.

In Section 3.3 details of the ab initio electronic

structure calculations and vibrational wave function determination are described. Section 3.4
presents the results and discussion of the experimental and theoretical work in light of theprevious Cu(H2O) results. Conclusions are presented in Section 3.5.
3.2

Experimental
This

sectionofthe thesis

describes

thephotodetachment-photoionization

measurements used to investigate the dynamics of the Cu(CD3OD) van der Waals cluster.
The experimental apparatus and data acquisition corresponding to this experiment werepreviously presented in Chapter II. The various laser pulse sequences used in the present
photodetachment-photoionization experiments have been previously presented in detail,1-3
and therefore, only a brief summary will be presented here. The radial potential energy
curves in Fig. 3.1 show that neutral Cu(CD3OD) complexes are formed by electron
photodetachment from Cu−(CD3OD) using a 398 nm pulse. Monitoring the time evolution of

32
the neutral cluster is accomplished by photoionizing Cu(CD3OD) and its fragments in various
pump-probe schemes. Figure 3.1 shows the two different pump-probe schemes used to detect
the cation photoproducts. Scheme one in Fig. 3.1 is used to monitor the Cu+ evolution as afunction of the delay between the photodetachment and the excitation/ionization pulses;
similarly, scheme two in Fig. 3.1 is used to monitor the Cu+(CD3OD) evolution. TypicalCu+(CD3OD) and Cu+ signals are ~ 0.5 cations per laser shot.
The time resolution of the experimental apparatus is determined in situ, using threecolor, three-photon photodetachment-photoionization of Cu− (Fig. 3.1, scheme 1).

The

400 nm pulse photodetaches an electron from Cu− and a sequence of 327 and 265 nm photons
resonantly ionize the 2S1/2 Cu atom through the 2P1/2 intermediate state.

2

1

10

Cu+
265

327

6

Cu*
327

327

4

398

Energy (eV)

8

398

2

0
2

3

4

5

Cuº
Cu−

6

R(Cu−O) (Å)
Figure 3.1

Radial potential energy curves and laser pump-probe schemes. Dashedcurves represent cuts in the Cu−DOCD3 Cs orientation, while solid curves
represent the Cu−ODCD3 C1 orientation. The vertical arrows represent
various pump-probe processes employed in the experiments reported here.

33
The delay between the excitation (327 nm) and the ionization (265 nm) pulses is fixed at
0.3 ps. As the photodetachment - excitation delay time (∆t) is varied, the Cu+ signal exhibitsa step function increase at ∆t = 0 (Fig. 3.2) and the rise-time of this step provides a direct
measure of the time resolution of the apparatus. The solid line in Fig. 3.2 is a fit of the data
to the form A(1+ tanh(t/τ)), and the derivative of this fit (dashed line) has a sech2 form. The
width (FWHM) of this sech2 function provides the effective time resolution of theexperimental apparatus, 260 fs.

Normalized Cation Internsity

1.0

0.5

260 fs

0.0
-0.5

0.0

0.5

Pump-Probe Delay (ps)Figure 3.2

3.3

The in situ measurement of the time resolution for photodetachmentphotoionization experiments. Rising points display rising Cu+ signal as afunction of the delay between the photodetachment and photoionization pulse
sequence. Solid line represents tanh fit to points and dashed line is thederivative (sech2) of this fit.

TheoryPrevious experiments on the dynamics of Cu(H2O)1,4 focused on a three-dimensional,

fully-coupled treatment that included the three intramolecular degrees of freedom of H2O.
Although the full-dimensional treatment gave useful information, it was found that many of

34these insights could also be borne out in analyses of three separate one-dimensional slices.
Since carrying out quantum dynamics simulations on Cu(CD3OD) in full dimensionality isimpractical, we draw from our experiences with Cu(H2O) and expect that the onedimensional decoupled picture should hold as well for Cu(CD3OD) as it did for Cu(H2O). It is
for this reason that we coupled the four one-dimensional motions to produce the full, fourdimensional representation.
The calculations used to characterize the Cu(CD3OD) complex fall into two generalcategories. First we determine the minimum energy configurations for the anion, neutral, andcation complexes and then evaluate a series of one-dimensional slices through the potential
energy surfaces, starting from these geometries. These one-dimensional potential energy
surfaces are used to calculate vibrational wave functions and energies using a sinc-discretevariable representation (DVR).5,6 The resulting energies and wave functions are used toinvestigate the regions of the potential surface that are sampled by Cu(CD3OD) upon electron
photodetachment. In particular we focus on the partitioning of energy among the internal
coordinates and how this is reflected in the time-dependent signal and Cu(CD3OD)
photoelectron spectrum.
3.3.1

Ab initio calculations
All electronic structure calculations are performed using the GAUSSIAN 98 or

GAUSSIAN 03 program packages.7,8The basis sets and level of theory used in thesecalculations have been described in a previous study,2,4 and therefore, only brief details will
be given here. The basis set used to represent the copper atom is an augmented form of the
Stuttgart-Dresden-Bonn (SDB) relativistic core potential developed by Preuss and coworkers,9 referred to as aug-SDB. The aug-SDB basis was developed by Wang and coworkers10 during their investigation of anion and neutral CuX2 (X = Cl, Br). Hydrogen,oxygen, and carbon are each represented by aug-cc-pVTZ11,12 basis sets.

Second-order

35
Møller-Plesset perturbation theory (MP2) was used to optimize all geometries, as well as incalculation of various potential energies. The minimum energy configurations for the anion,
neutral, and cation complexes are shown in Fig. 3.3(a), (b), and (c) respectively.

(a)

−

(b)
4

1

1
3

2

(c)

+
Figure 3.3

4

3

2

4
1

2

3

(a) Minimum energy configuration for Cu−(CD3OD), used to define
coordinates for the four 1-d slices employed in the simulations: Cu—O
stretch; out-of-plane bend, Cu-O-C-D4 dihedral angle; in-plane bend, Cu-O-C
angle; and methyl group rotation, D1-C-O-D4 dihedral angle. Also shown are
the minimum energy configurations for the neutral (b), and the cation (c).

Both radial and angular one-dimensional potential slices are calculated at theMP2 level of theory, beginning from the minimum energy configuration of the anion
and neutral. We also calculated one-dimensional cuts starting from the vertical
detachment geometry (VDG), i.e. cuts through the Cu(CD3OD) potential based on theminimum energy configuration of the anion. For example, the anion surface iscalculated as a function of the Cu–O distance, R, ranging from 1.6 – 7.6 Å inincrements of 0.1 Å. The energy of the neutral surface is calculated over a range of
1.5 – 7.0 Å while the VDG surface ranges from 1.8 – 7.2 Å; both are evaluated inincrements of 0.2 Å. In all scans the O–D bond length and the Cu-O-C-D4 dihedral
angle are relaxed at every step, while all other bond lengths and angles are held
constant.

36
Three types of angular scans were carried out, the molecular coordinates for theseone-dimensional surfaces are based on the structures shown in Fig. 3.3. The electronicenergy is calculated as a function of out-of-plane (OOP) motion by varying the Cu-O-C-D4dihedral angle over a range of ± 60° for the anion and ± 180° for the flatter, neutral and VDG
surfaces. For all three surfaces, the OOP motion is evaluated in increments of 2°, and the O–
D and Cu–O distances are allowed to relax at each step along the path. Variation of the CuO-C angle produces in-plane (IP) motion. The electronic energy as a function of this motion
is calculated over a ± 60° range in 2° increments for the anion surface and from –180° to 180°in increments of 10° for the VDG surface; the O–D and Cu–O bond lengths are optimized ateach step. For all three complexes, the electronic energy is calculated as a function of methyl
torsion over a ± 60° range of the D1-C-O-D4 dihedral angle in 5° increments. In this cut, allthree C–D bond lengths and O-C-D bond angles are relaxed. The ranges for each of the onedimensional potentials are chosen such that they span the angular regions sampled by thevibrational wave functions for the states of interest.
3.3.2

Vibrational Coordinates and Hamiltonian
One-dimensional variational calculations were carried out using a discrete variable

representation (DVR) technique. For the Cu–CD3OD distance coordinate, R, we use thereduced mass of the complex. The effective masses, beff, for the angular motions are derived
from the rotational constants for the associated molecular motions. In the case of the IP
rotation, this corresponds to the rotation of CD3OD about its C rotation axis, coupled torotation of the complex about its center of mass. The OOP motion corresponds to rotation of
the O–D bond about the C–O bond axis, while the methyl torsion is simply the three-foldrotation of the CD3 group about its symmetry axis. Based on the above definitions, the valuesof beff for these three motions are 0.6687 cm-1 (IP), 9.9512 cm-1 (OOP), and 4.5172 cm-1
(CD3), and the effective Hamiltonians for the radial and angular motions are respectively

37

h2 d 2Hˆ = −+ V ( R)2 µ dR 2(1)

Hˆ = beff Jˆ 2 + V (θ ) .

(2)

Here J2 is the angular momentum operator associated with the one-dimensional motions, andas such it has eigenvalues that are proportional to j2. The potential surfaces, V, are acquired
using spline interpolations of the energies obtained from the electronic structure calculations
described above. For the stretch coordinate, grid points used for the DVR calculations range
from 0.5 to 15.0 Å with a grid spacing of 0.0181 Å. For the bend and torsion coordinates, thegrid ranges from –180° to 180° with a spacing of 0.5°. For the stretch coordinate, grid points
beyond those from ab initio calculations were necessary, and the ab initio data are
extrapolated using
extrp

V (r ) =C 6 C8
+
,
r6 r8

(3)

where the values of C6 and C8 are chosen to ensure that the potential and its first derivative
are continuous.
Within the Condon approximation, the photoelectron spectrum can be generated fromoverlaps between eigenstates on the anion and neutral surfaces.

Since the low-lying

vibrational states on the anion surface are localized near the potential minimum, we focus on
those eigenstates on the neutral surface that are evaluated using cuts near the equilibrium
structure of the anion, e.g. the VDG surface. Within this treatment, the four-dimensional
wave functions are approximated by products of four one-dimensional functions.

The

overlap integrals between the eigenstates on the anion and VDG surfaces are evaluated foreach thermally populated state of the anion using the 200 K vibrational temperature as was
mentioned above. The resulting spectra are summed and convolved with a Gaussian with a
FWHM of 50 cm-1 (0.0062eV).
experiment.

This width is chosen to facilitate comparison with

38
3.4

Results and Discussion
In this section of the thesis, results from both the calculations and experiments arepresented independently. Following this presentation, both sets of data are combined topresent a cohesive discussion of the molecular dynamics taking place upon photodetachmentof the Cu−(CD3OD) cluster.
3.4.1

Initial State Characterization
Electron photodetachment from Cu−(CD3OD) produces an ensemble of neutral

Cu(CD3OD) complexes far from their equilibrium geometry, resulting in large amplitude
solvent rearrangement and dissociation.

In order to investigate the nature of thisrearrangement and dissociation, we must characterize the initial state of the ion-molecule
complex.
3.4.1.1 Calculations
The anion complex has a distinctly different minimum energy configuration from theneutral and cation complexes, select structural information is listed in Table 3.1. The anion
structure, seen in Fig. 3.3(a), has Cs symmetry with the Cu− positioned in the symmetry planeof methanol. We note that the interaction of methanol with the copper anion lengthens theO–D bond from 0.96 Å in isolated methanol to 0.99 Å in the cluster, and compresses the
C-O-D angle from 107.98° in methanol to 105.82° in the cluster. This minimum energy
configuration corresponds to a primary interaction between the copper anion and thepermanent electric dipole moment of methanol molecule. In fact Cu− interacts so strongly
with the methanol that it lowers the CD3 torsional barrier by nearly 75%. The barrier torotation for the neutral complex is 421 cm-1, but the anion has a significantly lower barrier of
110 cm-1. This anion minimum energy configuration corresponds to Cu−–DOCD3. As shownin the previous study,1,4 the Cu−(H2O) minimum energy geometry corresponds to a Cs

39
configuration with Cu− lying in the plane of the water molecule and oriented ~ 33° off the C2v
axis of H2O.
Table 3.1

Select geometrical parameters of all species, calculated at MP2 level oftheory.
CD3OD

Cu−(CD3OD)

Cu(CD3OD)

Cu+(CD3OD)

R (Cu—O)—

3.23 Å

2.04 Å

1.86 Å

R (O—D)

0.96 Å

0.99 Å

0.96 Å

0.96 Å

R (C—O)

1.42 Å

1.41 Å

1.44 Å

1.47 Å

θ (C-O-D)

107.98˚

105.82˚

108.85˚

109.64˚Calculations of the neutral Cu(CD3OD) cluster at the MP2 level result in a minimum
energy structure with C1 symmetry, as seen in Fig. 3.3(b). In the minimum energy structure,
the neutral copper atom resides 116° off of the methanol symmetry plane at a Cu–O distanceof 2.04 Å. In comparing the neutral species to methanol itself we see that the O–C bondlength increases, while the O–D bond length remains unchanged, and the C-O-D angle
expands slightly.

In nice agreement with Cu(CD3OD), the previous characterization ofCu(H2O) shows that the minimum energy neutral geometry corresponds to a Cs Cu–OH2
configuration.
Upon electron photodetachment of Cu−(CD3OD), the resulting neutral complex is
produced with an initial geometry corresponding to the minimum energy structure of theanion. Comparing figures 3.3(a) and 3.3(b) we note that this configuration is far from theminimum energy geometry of the neutral complex, described above. Given the difference inthe structural parameters, it is not surprising that the frequencies are also very dissimilar
between the anion and neutral complexes. The anion complex has much higher vibrationalfrequencies, suggesting that the Cu−–D interaction is much stronger than that of the Cu–O
interaction found in the neutral complex. Tables 3.2 and 3.3 provide the harmonic andanharmonic fundamental frequencies of several modes of interest for the anion and neutral

40complexes. The anharmonic frequencies were obtained from the DVR calculations describedabove, while the one-dimensional harmonic frequencies were obtained by replacing thepotential term in Eqs. (1) and (2) with a quadratic expansion of the potential about a local
minimum. In contrast, the fifteen-dimensional harmonic frequencies were obtained from anormal mode analysis at the potential minimum. There are obvious differences among thefrequencies, and these frequency discrepancies arise from several sources. The contrast
between the two one-dimensional results reflects the anharmonicity of the potentials. As canbe seen, the stretch, IP, and OOP potentials are nearly harmonic, while anharmonicity plays alarger role in the torsion potential.

The variation between the two sets of harmonicfrequencies reflects the difference between the coordinates that are used to define the onedimensional potential cuts and the normal mode coordinates.
Table 3.2
Calculated fundamental frequencies of the four vibrational modes
corresponding to the 1-d potential energy slices for Cu−(CD3OD) and Cu(CD3OD), which isthe neutral complex in the anion configuration, i.e. the vertical detachment geometry.
Cu(CD3OD)
Cu−(CD3OD)
15-d
1-d
1-d
1-d
1-d
Vibration
Harmonic Anharmonic
Harmonic
Anharmonic
Harmonic
Cu–O stretch
138 cm-1
102 cm-1
104 cm-1
54 cm-1
57 cm-1-1-1-1-1
IP bend
83 cm
119 cm119 cm
24 cm
32 cm-1-1-1-1-1423 cm495 cm
66 cm
212 cm-1
OOP bend
489 cm-1-1a-1-1
CD3 rotation
44cm
53 cm
69 cm
105 cm118 cm-1a
Due to the near degeneracy of the three lowest energy states of the torsion, this value
reflects the energy difference between the third excited state and the ground state.
Table 3.3
Calculated fundamental frequencies for the four vibrational modes
corresponding to the 1-d potential energy slices of Cu(CD3OD), neutral geometry.
Vibration

15-d Harmonic
230 cm-1

1-d Anharmonic
183 cm-1

1-d Harmonic
193 cm-1

Cu—O stretch
OOP bend
298 cm-1
246 cm-1
265 cm-1-1-1a
CD3 rotation
82 cm
116 cm123 cm-1a
Due to the near degeneracy of the three lowest energy states of the torsion, this value
reflects the energy difference between the third excited state and the ground state.
It should also be noted that no fifteen-dimensional harmonic calculations arepresented for the VDG in Table 3.2. This stems from the fact that the vertical detachment

41
geometry is not a stationary point on the neutral surface. However, the VDG does manifest
itself in the one-dimensional cuts as local minima on the neutral potential energy surfaces.
Therefore the one-dimensional calculations are shown in Table 3.2 for comparison to theanion and neutral frequencies.
Since the VDG is not the global minimum on the neutral surface, determining whichof the calculated vibrational energy levels correspond to the ground and first excited states of
the complex in the VDG can be difficult. For the OOP bend, the lowest energy state that isstrongly localized in the VDG minimum is easily assigned, whereas the first excited state ismore difficult to isolate. This complication reflects the fact that the barrier to free rotation of
the copper atom around the OD group of methanol is only 70 cm-1 above this lowest energy
state. As the harmonic frequency for this mode is 212 cm-1, it is not surprising that the statethat we identify as the first excited state has a frequency much lower than the harmonic value.
In fact its energy is close to the barrier to free rotation, and it is rather delocalized over thefull range for the OOP angle. The IP motion also exhibits similar difficulties, albeit to a lesser
extent. We also calculated the minimum energy structure of Cu+(CD3OD), shown in Fig.
3.3(c); key structural parameters for all three charge states are summarized in Table 3.1.
3.4.1.2 Photoelectron Spectra
The Cu−(CD3OD) photoelectron imaging spectrum reported here was obtained using
a similar instrument to that described in the experimental section. Modifications include theuse of tunable radiation produced by a Coherent Infinity Nd:YAG-pumped optical parametricoscillator and the addition of a photoelectron imaging device.13 As this spectrometer has
been described previously,14,15 only relevant details will be given here. The imaging systemis operated in the velocity map imaging16,17 mode. This photoelectron imaging spectrometeris very similar to that described by Sanov and co-workers.17,18 Photoelectrons are accelerated
onto a microchannel plate detector coupled to a phosphor screen; images are collected on a

42
CCD camera. The two-dimensional photoelectron images are reconstructed into the threedimensional photoelectron velocity and angular distributions using the BASEX image
reconstruction method developed by Reisler and co-workers.19
The Cu−(CD3OD) photoelectron spectrum is displayed in Fig. 3.4.20 For comparison,
we also plot the calculated Cu−(CD3OD) photoelectron spectrum, shown as a solid line. Theenergy scale of the calculated spectrum has been adjusted by 91 meV, such that the maxima
of the calculated and experimental spectra coincide. Both the magnitude and direction of thisadjustment correspond to the error found in our comparable calculation of the electron
affinity of Cu atom.

Normalized Intensity

1.0
0.8
0.6
0.4
0.2
0.0
1.80

1.75

1.70

1.65

1.60

1.55

1.50

Electron Binding Energy (eV)Figure 3.4

Experimental and calculated Cu−(CD3OD) photoelectron spectra. The
experimental spectrum is shown as black points. The three lines represent
calculated photoelectron spectra with various Cu−O separations. The solid
black curve gives the spectrum for R(Cu−O) = 3.42 Å, the calculated
minimum energy anion geometry. The grey curves represent photoelectron
spectra calculated with ± 0.18 Å changes in the Cu−O distance, with thedashed line representing 3.24 Å and the dash-dot line representing 3.60 Å.

43
The agreement between the experimental and calculated photoelectron spectra isremarkable. In particular, the calculated spectrum reproduces the width and contour of theexperimental spectrum. This provides us with confidence in our reduced dimensional modelfor the Cu(CD3OD) complex. Analysis of the calculated spectrum shows that its shape andwidth are captured by a one-dimensional calculation that includes only the Cu–O stretch
coordinate, although the torsional motion must also be taken into account to achieve the levelof agreement seen in Fig 3.4. The two dashed lines in Fig. 3.4 are spectra calculated with the
Cu–O distance in the anion shifted ± 0.18 Å from the calculated minimum energy
configuration. As described in Section 3.4.3. below, the lack of agreement between theory
and experiment with these modified geometries gives us important additional confidence inthe validity of the calculated time dependence.
3.4.2

Time Evolution of the Cu+ and Cu+(CD3OD) signals
The primary focus of this work is the time evolution of Cu+(CD3OD) and Cu+,

cations that are produced by photodetachment of an electron from Cu¯(CD3OD) followed by
two-photon resonant ionization after a specified delay time. The resulting signals, plotted asa function of pump-probe delay time, are reported in Fig. 3.5.

44

Normalized Cation Intensity

1.0

Cu−→Cu+
Cu+

0.8
0.6
0.4

Cu+CD3OD

0.2
0.0
-1

Figure 3.5

0

1
2
3
Pump-Probe Delay (ps)4

Initial experimental time dependence of cation signals. The open circles
represent Cu+ signal from Cu(CD3OD), while the filled circles represent the
Cu+(CD3OD) signal from Cu(CD3OD). The Cu+ signal rise from Cu− (greytriangles) indicates the instrument time resolution.

Before discussing these results we need to consider how these signals are obtained.
Figure 3.1 displays the photodetachment-photoionization laser schemes superimposed on aschematic of the Cu(CD3OD) radial potential energy surface. The Cu+ signal has primarily athree-color (398 nm + 327 nm + 265 nm) dependence, as seen in Fig. 3.1, scheme 1. The
major background in this scheme is produced by a two-color (327 nm + 265 nm) contribution
and is typically 10% of the maximum three-color signal. The Cu+(CD3OD) signal has
primarily a two-color (398 nm + 327 nm) dependence, as seen in Fig. 3.1, scheme 2. As in
the Cu(H2O)n experiments,1,3 background measurements indicate that the 398 nm + (2 x 327nm) contribution to the Cu+(CD3OD) signal is much larger (>90%) than the 398 nm + 327 nm+ 265 nm component. One-color backgrounds from both the 398 nm and 327 nm pulses
contribute to both the Cu+(H2O) and Cu+(CD3OD) signals.
Figure 3.5 shows the initial rise of the Cu+ and Cu+(CD3OD) signals from Cu–(CD3OD) following pump and probe pulses. As a point of reference, the instrument response,

45
measured by the rise of Cu+ from Cu−, is plotted with grey triangles and fit with a solid line.
The Cu+(CD3OD) signal rises at the same rate as the instrument response while the Cu+ signal
rises with increasing pump-probe delay. A longer time scan is plotted in Fig. 3.6. This plotshows that both signals reach their respective asymptotic values by ~ t = 100 ps. If we sum
these two signals, we find that their sum is nearly constant. Similar rise and decay features
were also observed in the Cu(H2O) studies.1,3,4

Normalized Cation Intensity

1.0

Cu+

0.8

0.6

0.4

Cu+(CD3OD)

0.2

0.0
0

Figure 3.6

10

20

30
40
50
60
70
Pump-Probe Delay (ps)8090

Experimental time dependence of cation signals resulting fromphotodetachment-photoionization of Cu−(CD3OD). The rising Cu+ signal(open circles) results from photodetachment (398 nm) followed by two-color(327 nm + 265 nm) resonant ionization. The decaying Cu+(CD3OD) signal(filled circles) results from photodetachment (398 nm) followed by one-color(265 nm) resonant multiphoton ionization. Solid lines represent exponential
fits to data used to extract time components.

In order to extract dynamical information from the experimental data, all data sets are
summed to produce total Cu+ and Cu+(CD3OD) time-dependent signals. Due to day-to-day
fluctuations in measured cation intensities as well as in the position of t = 0, special careneeds to be taken when adding multiple data sets. The following procedure is used to accountfor these fluctuations.

First, time-independent background signals are obtained at the

46
beginning and end of each data set. If the background signals changed significantly before
and after a data set, then that data set was rejected. For the accepted sets, the averagebackground signal is subtracted from the data set. For the Cu+ channel this backgroundcorrection shows that the t < 0 signal is zero, while for the Cu+(CD3OD) channel, thebackground correction shows that the signal is zero both for t < 0 and for t > 100 ps. The
uncertainty in the determination of t = 0 is ± 0.25 ps. The complementary shapes of the two
curves permits a simple multiplicative scaling of the Cu+(CD3OD) channel intensity, suchthat the sum of the Cu+ and Cu+(CD3OD) signals is essentially constant at a value of 1 for all
delay times greater than a few ps. The individual scaled and background-corrected data sets
are averaged to obtain the Cu+ and Cu+(CD3OD) data shown in Fig. 3.6. Each data point is anaverage of ~1.5×105 laser shots. Fitting of the data to single-exponential rise [Cu+] anddecay [Cu+(CD3OD)] does not produce a satisfactory fit. Consequently a two component fit
was employed. The solid lines in Fig. 3.6 were obtained by fitting the data to doubleexponential rise/decay of the following form:
t
t
−
−
⎛
⎞
⎛
⎞
x ⎟
x ⎟
⎜
⎜
I[Cu ] = a1 1 − e+ a2 1 − e
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
+

+

1

I[Cu (CD 3 OD)] = b1e

−

t
x1

+ b2 e

−

t
x2

2

(4)

.

(5)

This parameterization gave a satisfactory fit; the parameters so obtained are reported given in
Table 3.4.

Although the fits to the Cu+ and Cu+(CD3OD) data were carried out

independently, the corresponding derived parameters (a1, b1), (a2, b2), (x1, y1) and (x2, y2) areeach within 1 σ of their counterpart. This agreement strongly suggests that both Cu+ and
Cu+(CD3OD) signals arise from a common physical process. The fit parameters also showthat each component has roughly 50% contribution to the signal. The reported error in fitting
is determined by the standard deviation of the exponential fit to the averaged data sets. Theseerrors are represented graphically in Fig. 3.6 and numerically in Table 3.4.

The large

47
uncertainty present in y1 comes from the recurring oscillatory features present in the decaying
signal, as can be seen in Fig. 3.5.
Table 3.4
Parameters of double exponential fit to the functions given in Eqs. (4) and(5); the indicated errors are ± 1σ of the least squares fit parameters.

3.4.3

Cu+

Cu+(CD3OD)

x1 = 2.9 ± 0.7 ps

x1 = 5 ± 3 ps

x2 = 29 ± 4 ps

x2 = 33 ± 3 ps

a1 = 0.48 ± 0.10

b1 = 0.52 ± 0.07

a2 = 0.52 ± 0.08

b2 = 0.48 ± 0.08

Dissociation Time Components
In contrast to the present work, we found that three time scales were required to fit

the Cu+ signal in the Cu(H2O) study, and that the Cu+(H2O) signal displayed more structure
than was observed for Cu+(CD3OD).1 In Cu(H2O) the shortest timescale was ~ 1 ps. Thiswas shown to correspond to direct dissociation of the Cu(H2O) complex upon electron
photodetachment.

An intermediate timescale of ~ 10 ps was associated with coupling

between the hindered rotation of H2O in the complex to the Cu–H2O dissociation channel.
Finally the 100 ps component was attributed to vibrational predissociation driven by a small
amount of excitation in the water bend.
3.4.3.1 Direct Dissociation
As can be seen in Fig. 3.7, after photodetachment, the neutral Cu(CD3OD) complex
is in the VDG, a configuration which is far from the minimum energy configuration on thepotential surface. The motions that would take the complex to the minimum energy geometry
involve a combination of methanol rotation and a shortening of the Cu−O distance. At theequilibrium Cu−O distance in the VDG of Cu(CD3OD), the potential is relatively flat along
the coordinates corresponding to methanol rotation. If there is sufficient energy in the Cu−O
stretch coordinate, the complex should have enough time to dissociate before getting trapped

48
near the minimum energy configuration of the complex. This mechanism is responsible forthe < 1 ps, fast rise signal for Cu+ from Cu+(H2O).

1.3

(ii)

1.2

Energy (eV)

1.1
1.0

(iii)

0.0

-0.2

−

-0.4

(i)

-0.6
2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

R(Cu-O) (A)Å

Figure 3.7

Radial [R(Cu–O)] potential energy curves for Cu−(CD3OD) (i), Cu(CD3OD)
with other coordinates frozen at the anion configuration (ii), and fully relaxedCu(CD3OD) (iii). The insets show the various solvent orientations for thethree minima.

As seen in the results reported in Table 3.4, the parameters that describe the Cu+ rise
do not contain the fast (t < 1 ps) Cu+ component observed in the Cu(H2O) study.1 This direct
dissociation component was also absent in the Cu(H2O)2 rearrangement studies.3

To

understand this difference between the Cu(H2O) and Cu(CD3OD) dissociation dynamics, weturn to cuts through the potentials for the anion and neutral species, plotted in Fig. 3.8.

49

1.30

(ii)

1.25

Energy (eV)

1.20
1.15
0.00

-0.20

-0.40

(i)

-0.60
2.5

3.0

3.5

4.0

4.5

5.0

5.5

R(Cu-O) (A)Å

Figure 3.8

Radial potential energy curves for the anion (i) and neutral at the vertical
detachment geometries (ii) of Cu(CD3OD) and Cu(H2O). The solid curves
represent the Cu(CD3OD), while the dashed curves represent Cu(H2O). The
vertical line is drawn at the Cu–O distance corresponding to the minimum
energy configuration of both anions. The horizontal line at 1.23 eV indicatesthe dissociation limit of the neutral complexes.

Here the solid lines are for the Cu(CD3OD) complexes, while dashed lines provide thepotentials for the Cu(H2O) complexes. The vertical and horizontal dotted lines represent theequilibrium Cu−O distance on the anionic surface and the dissociation energy of the neutral
complex, respectively.

As these plots show, upon photodetachment, the Cu(CD3OD)

complex will be in a configuration that is close to the potential minimum in the VDG, along
the Cu−O stretch coordinate. Comparison of the well depths shows that the interactionenergy of copper in a hydrogen-bonded configuration with methanol is much larger than thecorresponding interaction energy between copper and water. These differences imply that the50copper water complex will have more energy along the copper-water dissociation coordinate
than will be the case for Cu(CD3OD).
The implications of the above analysis of the potential curves, plotted in Fig. 3.8, canbe quantified by considering the properties of the ground state wave functions, calculatedusing the lower, anionic surfaces, when they are projected onto the neutral surfaces. The
average energy of these states is 148 cm-1 below the dissociation threshold (Do(C2v) = 265 cm1 4) in the copper water system, while for Cu(CD3OD) the average energy is 586 cm-1 below

the dissociation threshold (Do = 628 cm-1). While the greater relative energy of Cu(H2O)
compared to Cu(CD3OD) supports the above observations, the complexes are initially at a
finite temperature, and this should also be taken into account. Looking at the overlaps
between the wave functions corresponding to the thermally populated states on the anion
surface at 200 K and the vibrational wave functions at the VDG on the neutral surface, 18%of the probability amplitude reflects overlaps with states in Cu(H2O) with energies above thedissociation threshold, while this value drops to less than 2% for Cu(CD3OD). This final
observation supports our inability to fit a fast time-component, analogous to the < 1 ps risetime in Cu(H2O).
The above arguments rely on the shift between the minimum energy geometries ofthe slices along the Cu-O coordinate of Cu¯(CD3OD) and Cu(CD3OD) in the VDG. The
appropriateness of this picture can be investigated by calculating the photoelectron spectrum,
as described above, with the Cu−O distance dependence of the potential shifted by ±0.18 Å.
The results of these calculations are plotted with dashed lines in Fig. 3.4. The best agreementin the width of the calculated and experimental spectra is obtained when the calculated
vertical detachment potential surface is used. This finding, along with the calculated overlaps
between the radial wave functions and the anion and VDG potential energy surfaces, supports
the fact that the direct dissociation channel that was reported for the Cu(H2O) complex is notobserved in Cu(CD3OD).

51

3.4.3.2 Energy Redistribution
While the above discussion shows that there is not enough energy deposited directlyin the Cu–O coordinate of Cu(CD3OD) to lead to direct dissociation, in most cases there ismore than sufficient excitation in several of the other vibrational degrees of freedom todissociate the complex.

An investigation of cuts through the neutral potentials,

corresponding to both the in-plane and out-of-plane motion, reveals a relatively flat landscapesimilar to that seen in Cu(H2O). In the three-dimensional simulations of the dynamics of thecopper-water system on the neutral surface, the 10 ps timescale obtained from the fits to theCu+ and Cu+(H2O) signals are attributed to energy transfer between the hindered rotation of
the water molecule and the dissociation coordinate. Comparisons of the initial internalenergy in the in-plane and out-of-plane rotation coordinates in these two systems, based on
one-dimensional calculations, shows that they differ by less than 10%. This, coupled to thesimilarity of the 3 ps time scale obtained in the present study and the 10 ps time scale forCu(H2O) leads us to conclude that the motions responsible for the 3 ps rise and decay times
are associated with energy transfer from the methanol hindered rotation to the dissociation of
the complex. The shorter timescale for methanol compared to water likely reflects thesmaller rotational constants for methanol leading to a larger density of states.
In the Cu(H2O) study, the 100 ps dissociation component stemmed frompredissociation driven by vibrationally-excited bending modes of H2O. Table 3.4 gives thelongest dissociation component as 30 ps for Cu(CD3OD). This component arises fromcoupling of the methyl rotor rotation into the Cu–CD3OD dissociation coordinate. When theoverlap between the thermally populated torsional levels for Cu¯(CD3OD) and the states on
the neutral surface are calculated, it is found that upon photodetachment, 50% of theprobability amplitude ends up in states with energy in the methyl rotor. This value of 50%
matches nicely with the values of the a2 and b2 parameters in Table 3.4. Based on this, we52
attribute the 30 ps time scale to coupling of states with methyl rotor excitation to thedissociation coordinate. The difference in the dissociation time is, compared to the 100 ps
component of Cu(H2O), is ascribed to the presence of the methyl rotor and its ability toaccelerate intramolecular vibrational energy redistribution (IVR).21-23
3.5

Conclusions
The experimental and theoretical investigations of the time-dependent dissociation

dynamics of the Cu(CD3OD) complex are reported. Experiments using photodetachmentphotoionization spectroscopy provide insight to the evolution of the nascent neutral complex
formed via electron photodetachment from Cu−(CD3OD). Ab initio calculations provide theminimum energy structures and one-dimensional potential energy surfaces used indetermining the vibrational energies and wave functions of the complex. Analysis of both theexperimental and theoretical results take place in the light of the previous detailed
investigation of the Cu(H2O) complex.
Ab initio minimum energy structures show that both Cu(H2O) and Cu(CD3OD) have
similar hydrogen bonded anion orientations as well as similar neutral Cu–O orientations.
However, the Cu(CD3OD) complex does not exhibit the direct dissociation (t < 1 ps)
observed in Cu(H2O), due to the predominantly bound-to-bound transitions upon electron
photodetachment of Cu−(CD3OD). The rising Cu+ and decaying Cu+(CD3OD) signals fromCu(CD3OD) both exhibit time components of 3 and 30 ps. The 3 ps component arises fromcoupling of CD3OD hindered rotations to the Cu–CD3OD dissociation coordinate; this timescale is comparable to the solvent reorientation coupling observed in Cu(H2O). Angular onedimensional potential energy slices and calculated excitation energies confirm the similarityof the two systems in these solvent reorientation coordinates. Excited methyl rotations
couple into the Cu–CD3OD dissociation coordinate on the 30 ps time scale, slightly fasterthan the water bend coupling of 100 ps observed in Cu(H2O).

53
It has been shown in this study, as well as in the previous work on Cu(H2O)2,3 that a
dynamical analysis of larger solvent systems, where a fully dimensional theoreticalinvestigation is impractical, is nicely interpreted using detailed results from smaller systems.
This extension is important for our future investigations with more extensively solvatedcopper anion complexes. This work also motivates studies which investigate other solvatedmetal clusters. More compelling sets of experiments come in the form of producing colder
anions by tagging complexes with rare gas atoms and utilizing an entrainment technique forneutral ligand addition.24,25

54

References for Chapter III

1

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5676 (2004).

2

M. S. Taylor, Ph.D. Thesis, University of Colorado, Boulder, 2004.

3

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M. S. Taylor, F. Muntean, W. C. Lineberger, and A. B. McCoy, J. Chem. Phys. 121,
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M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, et al,
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10

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11

R. A. Kendall, T. H. Dunning, Jr., and R. J. Harrison, J. Chem. Phys. 96, 6796
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12

T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 (1989).

13

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401, 570 (2004).

55
14

M. E. Nadal, P. D. Kleiber, and W. C. Lineberger, J. Chem. Phys. 105, 504 (1996).

15

A. Sanov, T. Sanford, S. Nandi, and W. C. Lineberger, J. Chem. Phys. 111, 664(1999).

16

A. Eppink and D. H. Parker, Rev. Sci. Instrum. 68, 3477 (1997).

17

E. Surber, R. Mabbs, and A. Sanov, J. Phys. Chem. A 107, 8215 (2003).

18

R. Mabbs, K. Pichugin, E. Surber, and A. Sanov, J. Chem. Phys. 121, 265 (2004).

19

V. Dribinski, A. Ossadtchi, V. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73,
2634 (2002).

20

D. Andrews, Ph.D. Thesis, University of Colorado, Boulder, 2006.

21

D. B. Moss and C. S. Parmenter, J. Chem. Phys. 98, 6897 (1993).

22

C. S. Parmenter and B. M. Stone, J. Chem. Phys. 84, 4710 (1986).

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P. J. Timbers, C. S. Parmenter, and D. B. Moss, J. Chem. Phys. 100, 1028 (1994).

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W. H. Robertson, J. A. Kelley, and M. A. Johnson, Rev. Sci. Instrum. 71, 4431
(2000).

________________
Chapter IV
The Time-Resolved Solvent Induced Recombination of IBr−(CO2)n________________
4.1

Introduction
As described in detail in Chapter I, excitation of IBr− to the A' 2Π1/2 state produces I−

and Br fragments. This process is altered upon addition of CO2 solvent molecules which canlead to charge transfer products or recombination of the IBr− core. The results of several
experimental and theoretical investigations are presented and compared to similar work on
the I2− chromophore.1-4
The remainder of this chapter is structured as follows. Section 4.2 explains thetechnique used to determine the recombination times. Section 4.3 outlines the theoreticalmethods used in determining minimum energy structures, radical potential energy surfaces,
and molecular dynamics simulations. Section 4.4 presents the experimental results and theiranalysis. These results are explained in Section 4.5 using a physical picture that is based on
the results of ab initio calculations and compared to the molecular dynamics simulations.
Section 4.6 summarizes our experimental findings and suggested explanations.
4.2

Experimental

This section of the thesis describes the pump-probe technique used to investigate the solvent
induced recombination of the IBr− chromophore.

The experimental apparatus and dataacquisition corresponding to this experiment were previously presented in Chapter II. The
methodology used to determine the recombination dynamics of IBr− (CO2)n clusters after
excitation to the A' 2Π1/2 state (Fig. 4.1) is based on the fact that the dissociated IBr−
chromophore regains near-IR absorption only after recombination and57

Energy, eV

2.0

1.0

B 2Σ+1/2

Br− + I*A′ 2Π1/2

I− + Br*I− + BrA 2Π3/2

0.0

X 2Σ+1/2

Br− + I

-1.0
3.0

4.0

5.0

R(I−Br), Å
Figure 4.1

Calculated potential energy curves for the lowest six electronic states of IBr−.
The arrow indicates the pump/probe transition from the ground state (X) to
the first excited state (A').

substantial vibrational relaxation on the ground electronic surface. Previous studies of IBr−
(CO2)n A' 2Π1/2 photofragmentation5 at 790 nm demonstrated that, for clusters with n ≥ 5, therecombination efficiency exceeds 90%, and is 100% for n ≥ 8. The energy released in theprocess of bond re-formation results in evaporation of 4-6 CO2 molecules, in accordance withthe solvent binding energetics.5

Therefore, absorption of another photon at the same

wavelength by these smaller clusters leads to the formation of distinct secondary products. In
order to follow the recombination process, the number of these secondary product ions ismonitored as a function of the pump–probe delay time to follow the recombination process.
There are considerable background signals present at delay times corresponding to small
recombination signals, and these contributions were accounted for by data acquisition
sequences that have been previously described in detail.1,6,7

58
The expected distribution of pump–probe product ions was obtained from sequential
application of the measured5,8 distribution of one photon ionic photoproducts, and issummarized in Table 4.1. The observed secondary product
Table 4.1
One-photon8 (pump only) and expected two-photon (pump/probe) ionicproducts for selected IBr−(CO2)n clusters, following 790 nm excitation. Only significant (>5% of total) secondary products are shown. For each parent cluster size, those secondary
products recorded in our experiments and used for determination of recombination timescales are shown in bold.
Parent cluster

Primary (one-photon) products

IBr−(CO2)5

3% Br−(CO2)2
6% Br− (CO2)3
49% IBr−
36% IBr−(CO2)
6% IBr− (CO2)2
4% Br− (CO2)3
6% IBr−58% IBr− (CO2)
30% IBr− (CO2)2
2% IBr− (CO2)3
3% Br− (CO2)4
16% IBr− (CO2)
51% IBr− (CO2)2
22% IBr− (CO2)3
8% IBr− (CO2)4
2% IBr− (CO2)
26% IBr− (CO2)2
49% IBr− (CO2)3
20% IBr− (CO2)4
3% IBr− (CO2)5
12% IBr− (CO2)3
38% IBr−(CO2)4
38% IBr− (CO2)5
12% IBr− (CO2)6

IBr−(CO2)6

IBr−(CO2)7

IBr−(CO2)8IBr−(CO2)10

Secondary (two-photon)
products
69% I−
28% I-(CO2)
3% Minor products

30% I−
58% I−(CO2)
12% Minor products
9% I−
55% I−(CO2)
10% Br−(CO2)
16% IBr−
10% Minor products
42% I−(CO2)
11% Br−(CO2)
30% IBr−
17% Minor products
7% I−(CO2)
8% Br−(CO2)2
50% IBr−
21% IBr−(CO2)
6% IBr−(CO2)2
8% Minor products

branching ratios differ only slightly from the ratios reported in Table 4.1. This, however,should be expected, since the one-photon products used to estimate the two-photon ratios
were obtained at cluster temperatures of 40-70 K.8 While parent clusters in our experiments

59
are expected to have similar temperatures, the internal energy of the recombined products
may be substantially higher leading to variation in the number of solvent molecules
evaporated. As the product ions are mass selected, it is possible to obtain potentially different
recombination signals from each secondary product ion, as has previously been observed.9 In
the present studies, the time dependence of several different secondary products arising froma single parent ion was investigated, and no substantial differences were detected.
Consequently, the time dependent data for each parent ion reported in the next section arise
from the sum of those most intense secondary two photon products that are shown in bold
face in Table 4.1.
4.3

Theoretical Methods
The IBr− potential energy surfaces and associated electronic properties needed for themolecular dynamics (MD) simulations were obtained using MOLPRO 2002.6.10 This work
was performed by Matt Thompson, and a detailed description of his methods can be foundelsewhere.11,12 The energy-consistent effective core potential (ECP) of the Stuttgart-Bonngroup13 was used; specifically, the calculations employed large-core MDF ECPs based upon
multi-configuration Dirac-Hartree-Fock calculations of the neutral atom. This potential also
includes a core polarization potential that models the charge-induced dipole interaction of thecore. The basis sets used are an augmented form, (7s7p3d2f)/[5s5p3d2f], of the stock(6s6p)/[4s4p] basis sets included with the ECPnMDF ECPs.13,14 These calculations used theinternally-contracted multi-reference configuration interaction methods developed by
Knowles and Werner.15-17 The reference orbitals and configurations were obtained from state
averaged complete active-space self-consistent field calculations18,19 that consisted of the 15
electrons in the lowest two Σ, Πx, and Πy states that arise from the 2P and 1S states of theseparated atomic components. A spin-orbit calculation of all six states was then performed

60
using spin-orbit ECPs.20 This was performed at 42 points along the PES corresponding tobond lengths ranging from 4.5 to 100 a0.

Figure 4.2

n=5

n=6

n=7

n=8

n = 10n = 14

Minimum energy structures of IBr− with various numbers of CO2 solvent
molecules, indicating asymmetric solvation around Br end.

The minimum-energy IBr−(CO2)n structures were constructed by sampling 201
configurations from a molecular dynamics simulation of a 1-ns trajectory on the IBr−(CO2)nground state having an average temperature of 80 K.11 These configurations were thenquenched to local minima using Newton-Raphson minimization.21 A representative sampleof the resulting minimum-energy structures for relevant numbers of solvent molecules is61presented in Fig. 4.2. The solvent asymmetry that leads to strong modification of the IBr−electronic states is readily seen.
In order to more quantitatively investigate the effect of the solvent molecules on theIBr− potential curves (Fig. 4.1), the IBr−(CO2)8 minimum energy structure was used toconstruct a radial cut through the IBr−(CO2)8 potential energy surface (Fig. 4.3) using the MD
program described below. To generate the potential plot (Fig. 4.3), the iodine atom is“pulled” away from the minimum-energy configuration of IBr−(CO2)8, and the energies of thesix spin-orbit states are obtained as a function of the I−Br distance with the solvent fixed atinitial configuration. This slice through the IBr−(CO2)8 surface can rapidly change with

Energy, eV

solvent configuration.

Br− + I*2.0

B 2Σ+1/2

1.0

A′ 2Π1/2

I− + Br

0.0

A 2Π3/2

Br− + I

I− + Br*

X 2Σ+1/2
3.0

4.0

5.0

R(I−Br), Å
Figure 4.3

Calculated potential energy curves for the lowest six electronic states ofIBr−(CO2)8. The arrow indicates the pump/probe transition from the groundstate (X) to the first excited state (A′).

62
The MD simulations for IBr−(CO2)n are based on the effective Hamiltonian method
developed by Maslen, Faeder, and Parson22 previously applied to I2− (CO2)n.23-28 Briefly, theIBr−-CO2 interaction is based on an operator including electrostatic and induction terms forthe solute and solvent. For the solute, distributed multipole analysis (DMA)29 is performed
during the ab initio calculations detailed above.

More importantly, transition DMA is

performed. This technique allows for calculation of the polarization response of the solute to
the solvent. The solvent charge distribution and polarization is based on a condensed-phasemodel.30

The short-range dispersion-repulsion interactions are described by atom-atom

Lennard-Jones potentials based on high resolution photoelectron spectra31 and from fits of
CR-CCSD[T] calculations performed in GAMESS32,33 of Br− · · ·CO2 . At each time step inthe simulation, the Hamiltonian is diagonalized to yield the energies, forces, and nonadiabatic
transition probabilities needed for the next step. On a single state, motion is computed using
the velocity Verlet algorithm,34 while nonadiabatic transitions are performed according to amodified24 version of Tully’s surface-hopping method.35,36
4.4

Results and Analysis
The only previous measurement of the recombination time in IBr−(CO2)n was

conducted for the n = 8 cluster.5,8 Although no well-defined time dependence was recordedin that study, unambiguous evidence for recombination on a nanosecond scale was obtained.
This finding was different from our expectation of rapid, picosecond-scale recombination
based on studies of the similar I2−(CO2)n system, in which the recombination times decreased
from 16 ps to 5 ps as the cluster size increased from n = 8 to n = 17.1,2,6,9

IBr (CO2)n Recombination Fraction

63

1.0

0.8
0.6
0.4
n = 5
n = 6
sin g le exp o n en tial fit

0.2
0.0
0

20

40

60

80

100

P um p-P robe D elay (ps)Figure 4.4

The IBr−(CO2)5 (closed circle) and IBr−(CO2)6 (open circle) recombination
fractions as a function of time following excitation to the A′ state. Solid lines
represent single exponential fits which yield recombination times of 12 ± 0.5
ps (n=5) and 30 ± 5 ps (n=6).

Figure 4.4 shows time dependent pump/probe signal obtained from the excitation ofIBr−(CO2)5 and IBr−(CO2)6 at 797 nm. It is immediately apparent that the absorption recovery
time is much shorter than that previously observed for the larger IBr−(CO2)8 anion. In
addition, the recovery time increases with additional solvation, in marked contrast to ourprevious experience. 1,2,6,9 Over the 100 ps time shown in this figure, there appears to be asimple functional form to the recovery, and we could fit the data to the single-exponential
t
− ⎤
⎡
τ
form N ( t ) = ⎢1 − e ⎥ , with a high-quality fit and with no statistical indications for the⎣⎦necessity to include a second time constant. The resulting fits yield recovery times (τ) of 12± 0.5 ps and 30 ± 5 ps for IBr−(CO2)5 and IBr−(CO2)6, respectively, and are displayed as solid

64
lines in Fig. 4.4. Unlike the previously obtained value for IBr−(CO2)8,5 the magnitude ofthese times is in qualitative agreement with those measured previously for I2−(CO2)nrecombination,1,2,6,9 although the cluster size dependence is opposite to that observed forI2−(CO2)n.

IBr-(CO2)n Recombination Fraction

0.4

0.3

0.2
n=5
n=6
0.1

0.0
-4

-2

0

2

4

Pump-Probe Delay (ps)Figure 4.5

Short time recombination fractions of IBr−(CO2)5 (triangle) and IBr−(CO2)6(circle) showing symmetry in data due to identical pump/probe wavelengths.
The coherence peak at t=0 arises due to enhancement of two-photon
background. Rising signal delayed by ~0.7 ps (n=5) and ~2 ps (n=6).

An interesting observation is emphasized in Fig. 4.5, where more detailed
recombination signals at early times are presented. One can see that there is a noticeable
delay in the appearance of time-dependent signal. For n = 5 this delay is ~ 0.7 ps while for n= 6 it is ~2 ps. One consequence of the long recovery times observed for the larger clusters isthat the very low recombination signals at early times preclude our concluding that this
delayed onset persists to larger cluster ions. However, there is no a priori reason to expect
otherwise.

65
Due to the fact that both pump and probe laser pulses have the same wavelengths andcomparable energies, the pump/probe signal in our experiment must have a symmetric shapeabout t = 0, although the unequal pump and probe intensities mean that the intensity for somet<0 can be different from the corresponding t>0 signal. Moreover, since time-independent
background results from the two-photon absorption of either pump or probe radiation alone,
this background doubles when pump and probe pulses overlap in time giving rise to a“coherence peak.” This peak is used to determine the exact location of t = 0.
As more CO2 solvent molecules are added we obtain longer recombination times, incontrast to those measured for I2−(CO2)n.1,2,6,9 The addition of just one more solvent molecule
to IBr−(CO2)6 results in a very large change in the recombination timescale. Figure 4.6 shows
the absorption recovery signal for IBr−(CO2)7. A single-exponential fit of this data gives atime-constant of 140 ± 20 ps. Increasing the cluster size to n=8 and n=10 results in evenlonger recombination times.

Figure 4.7 shows a single-exponential fit for n = 8 and n=10.

Both of these data sets are equally well represented by the same single-exponential rise. Thisfit yields a recombination time of 900 ± 300 ps, in good agreement with the previous estimate
for n=8.5 Due to very low intensity of the IBr−(CO2)10 parent cluster, the corresponding
pump/probe signal is noisier than that of IBr−(CO2)8.

66

0.8

0.6

0.4

0.2

-

IBr (CO2)n Recombination Fraction

1.0

n = 7
single exponential fit
0.0
0

100

200

300

400

500

600

Pum p-Probe D elay (ps)Figure 4.6

The IBr−(CO2)7 recombination fraction as a function of time following
excitation to the A′ state. The solid line represents a single exponential fit
which yields a recombination time of 140 ± 20 ps.

-IBr (CO2)n Recombination Fraction

67

1.0

0.8

0.6

0.4
n = 8
n = 10sin g le exp o n en tial fit

0.2

0.0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

P um p-P robe D elay (ns)Figure 4.7

The IBr−(CO2)8 (closed circle) and IBr−(CO2)10 (open circle) recombination
fractions as a function of time following excitation to the A′ state. The solidline represents a single exponential fit which nicely describes both data sets
and yields a recombination time of 900 ± 100 ps. The n=10 data exhibit
more noise due to very low ion signals.

Preliminary experimental data shows that the trend of recombination times
lengthening with the addition of CO2 molecules ends when we reach the n = 12 level. Figure
4.8 shows a single exponential rise for n = 12 with a time-constant of 9 ± 0.7 ps. This
recombination time is faster than that seen for the n = 5 case and is on par with the I2−(CO2)nrecombination measurements.

Experiments are underway to confirm this n = 12

measurement as well as to obtain a recombination time for n = 14.

68-

IBr (CO2)n Recombination Fraction

1.0

0.8

0.6

0.4

n = 12
single exponential fit

0.2

0.0
0

20

40

60

80

Pump-Probe Delay (ps)Figure 4.8

4.5

The IBr−(CO2)12 recombination fractions as a function of time following
excitation to the A′ state. The solid line represents a single exponential fit
which yields a recombination time of 9 ± 0.7 ps.

Discussion
The experimental results obtained in this study and presented in previous sections canbe rationalized using a physical picture based on calculations37 and on comparisons to similarI2−(CO2)n and ICl−(CO2)n systems.6,38

According to ab initio calculations and otherexperimental investigations, there is a major qualitative difference between the shape of theA' 2Π1/2 curve in I2− 1,9,39,40 and those in IBr− 37and ICl−.38 While the A' state of I2− isessentially repulsive,41 the corresponding state of IBr− exhibits a detectable well42 at aninternuclear separation of ~ 4.5 – 5 Å (see Fig. 4.1). Addition of asymmetrically placed
solvent molecules increases the depth of this well until it reaches a maximum depth forIBr−(CO2)8 and changes its radial location (Fig. 4.3). According to our structure calculations,69
this is the most asymmetric solvent configuration, based on the solvent electric field at thecenter of the solute ion. In this solvent size range, the well depth is comparable to thebinding energy of a single solvent molecule and could readily slow the evaporative coolingprocess, the mechanism whereby the recombined solute anion returns to near its initialenergy. We will argue that this well is responsible for “trapping” the IBr− solute on the A'
surface and leads to the slow recombination observed over a small range of partial solvation.
Nonadiabatic MD simulations of IBr−(CO2)5−13 were carried out to obtain the timedependence for the recombination process described above. All simulations used a time
step of 1 fs, while the length of simulations ranged from 20 ps for IBr−(CO2)5 to 2000 ps forIBr−(CO2)10, with ensemble sizes ranging from 35 trajectories for IBr−(CO2)10 to over 1700
for IBr−(CO2)5. The ensembles of trajectories gave no indication for the necessity of a fitting
form more complicated than the simple exponential form employed to fit the experimental
data. Consequently, the MD simulations were summarized by a functional form consisting ofa single-exponential fit to the fraction of total recombined trajectories over time.

The

resulting time constants increased rapidly with increasing solvation, from 5 ps for IBr−(CO2)5
to 5000 ps for IBr−(CO2)10. For IBr−(CO2)10, only 10 recombination events were observed in
2 ns for an ensemble of 35 trajectories. Due to the substantial calculation time required, these35 trajectories were not propagated beyond 2 ns. The reported 5000 ± 1000 ps recombination
time constant was obtained by augmenting the simulation data with the experimental
observation5 that all of the photoexcited IBr−(CO2)10 ions eventually return to the ground state
surface, providing an unambiguous long time asymptote for the fit. As the number of solvent
molecules is further increased, the recombination time constants dramatically shorten, with
IBr−(CO2)12 showing 70 ps recovery and IBr−(CO2)13 showing a 30 ps recovery time!
More detailed inspection of the individual trajectories in the MD simulations supports
this mechanism of trapping on the A′ excited state. The long recombination times appear toarise from the presence of a configurational transition state, where achieving a narrow range

70of solvent and solute geometry is necessary for nonadiabatic transition to the groundelectronic state of the solute. The results of molecular dynamic simulations are shown in Fig.
4.9 in comparison to the experimental results. The simulations produce recombination times
with slight variances to those measured, by a factor of 3-5, however, they are in excellent
qualitative agreement with experiment, with the exception of n=10. The magnitude of theexperimental error bars in Fig. 4.9 reflects the range of recombination times observed foreach cluster size. The details of the simulations and the nature of the solvent-induced excitedstate trap will be explored more deeply in a future publication.37
Finally, the simulations suggest that for clusters with n ≥ 10 recombination time
becomes short again (see n = 12, 13 in Fig. 4.9). To date, one data set shows this trend tofaster recombination times. This data shows that for n = 12 the recombination time is now <10 ps, in stark contrast to the previous n = 10 point of Fig. 4.9. This rebound to fastrecombination time nicely matches the calculated trend. Efforts are underway to confirm thismeasurement as well as to obtain recombination times for clusters with n >12.

71

Absorption Recovery Time (ps)Simulation
Experiment
1000

100

10

4

5

6

7

8

9

10

11

12

13

14

Number of CO2 Solvents on IBr-

Figure 4.9

Comparison of absorption recovery times for experiment (closed circle) andmolecular dynamics simulations (closed triangle). Dashed lines are provided
to guide the eye.

In addition to the qualitative agreement between theoretical and experimental
timescales, the simulations for clusters with 5 and 6 CO2 molecules also display initial delays
in product appearance similar to those observed in Fig. 4.5. Although the exact origin of
these delays is not completely clear, we assume that they reflect the time required for
dissociation, nonadiabatic relaxation to the ground state and partial vibrational relaxation, allin the absence of an excited state trap.
4.6

Conclusion
Time-resolved experimental studies of the recombination of size selected IBr−(CO2)nanionic clusters following excitation to the A' 2Π1/2 state was carried out using tandem time-

72
of-flight mass spectrometry combined with an ultra-fast laser system. The IBr− chromophore
near-IR absorption recovery was observed and the timescales of the recombination wereextracted from the experimental data. The recombination rates exhibit a very strong
dependence on the number of solvent molecules. For clusters with n = 5-7, recombination
occurs on a picosecond timescale, similar to that of I2−(CO2)n clusters. Clusters with 8 and 10
CO2 molecules exhibit strikingly longer nanosecond timescales. Such changes in therecombination rates are explained in terms of the solvent-induced potential well that is
especially deep for configurations involving solvent surrounding primarily the Br atom.
Molecular dynamics simulations confirm this picture and are in excellent qualitative
agreement with experimental data. The simulations (along with preliminary experimental
data) predict an increase of the recombination rate for larger IBr−(CO2)n (n>12) cluster ions;experiments are currently in progress to further test this conclusion.

73

References for Chapter IV
1

J. M. Papanikolas, V. Vorsa, M. E. Nadal, P. J. Campagnola, H. K. Buchenau, et al,
J. Chem. Phys. 99, 8733 (1993).

2

A. Sanov, S. Nandi, and W. C. Lineberger, J. Chem. Phys. 108, 5155 (1998).

3

A. Sanov, T. Sanford, S. Nandi, and W. C. Lineberger, J. Chem. Phys. 111, 664(1999).

4

V. Vorsa, S. Nandi, P. J. Campagnola, M. Larsson, and W. C. Lineberger, J. Chem.
Phys. 106, 1402 (1996).

5

T. Sanford, S.-Y. Han, M. A. Thompson, R. Parson, and W. C. Lineberger, J. Chem.
Phys. 122, 054307 (2005).

6

A. Sanov, T. Sanford, S. Nandi, and W. C. Lineberger, J. Chem. Phys. 111, 664(1999).

7

V. Vorsa, P. J. Campagnola, S. Nandi, M. Larsson, and W. C. Lineberger, J. Chem.
Phys. 105, 2298 (1996).

8

T. Sanford, Ph.D. Thesis, University of Colorado, 2004.

9

V. Vorsa, S. Nandi, P. J. Campagnola, M. Larsson, and W. C. Lineberger, J. Chem.
Phys. 106, 1402 (1997).

10

H. J. Werner, P. J. Knowles, R. Lindh, M. Schutz, and Others, MOLPRO, version
2002.6, a package of ab initio programs (2003).

11

M. A. Thompson, Ph.D. thesis, University of Colorado, 2007.

12

M. A. Thompson, J. Barbera, J. P. Martin, W. C. Lineberger, and R. Parson, J. Chem.
Phys. (in preparation).

13

H. Stoll, B. Metz, and M. Dolg, J. Comput. Chem. 23, 767 (2002).

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H. Stoll, private communication.

15

H.-J. Werner and P. J. Knowles, J. Chem. Phys. 89, 5803 (1988).

16

P. J. Knowles and H. J. Werner, Theor. Chim. Acta 84, 95 (1992).

17

P. J. Knowles and H. J. Werner, Chem. Phys. Lett. 145, 514 (1988).

18

H. J. Werner and P. J. Knowles, J. Chem. Phys. 82, 5053 (1985).

19

P. J. Knowles and H. J. Werner, Chem. Phys. Lett. 115, 259 (1985).

20

A. Berning, M. Schweizer, H. J. Werner, P. J. Knowles, and P. Palmieri, Mol. Phys.
98, 1823 (2000).

21

W. Press, S. Teukolsky, V. WT, and B. P. Flannery, Numerical Recipes in C: The Art
of Scientific Computing, 2nd ed. (Cambridge University Press, New York, 1992).

22

P. E. Maslen, J. Faeder, and R. Parson, Mol. Phys. 94, 693 (1998).

23

R. Parson, J. Faeder, and N. Delaney, J. Phys. Chem. A 104, 9653 (2000).

24

J. Faeder, N. Delaney, P. E. Maslen, and R. Parson, Chem. Phys. 239, 525 (1998).

25

J. Faeder, N. Delaney, P. E. Maslen, and R. Parson, Chem. Phys. Lett. 270, 196(1997).

26

N. Delaney, J. Faeder, and R. Parson, J. Chem. Phys. 111, 452 (1999).

27

N. Delaney, J. Faeder, and R. Parson, J. Chem. Phys., 651 (1999).

28

N. Delaney, J. Faeder, P. E. Maslen, and R. Parson, J. Phys. Chem. A 101, 8147
(1997).

29

A. J. Stone, The Theory of Intermolecular Forces. (Oxford, New York, 1996).

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30

C. S. Murthy, S. F. Oshea, and I. R. McDonald, Mol. Phys. 50, 531 (1983).

31

I. Yourshaw, Y. X. Zhao, and D. M. Neumark, J. Chem. Phys. 105, 351 (1996).

32

M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, et al, J.
Comput. Chem. 14, 1347 (1993).

33

M. S. Gordon and M. W. Schmidt, in Theory and Applications of Computational
Chemistry, the first forty years, edited by C. Dykstra, G. Frenking, K. S. Kim, and G.
E. Scuseria (Elsevier, Amsterdam, 2005).

34

H. C. Andersen, J. Comput. Phys. 52, 24 (1983).

35

J. C. Tully, J. Chem. Phys. 93, 1061 (1990).

36

S. Hammes-Schiffer and J. C. Tully, J. Chem. Phys. 101, 4657 (1994).

37

M. A. Thompson and R. Parson, unpublished results (2006).

38

M. E. Nadal, P. D. Kleiber, and W. C. Lineberger, J. Chem. Phys. 105, 504 (1996).

39

S. Nandi, A. Sanov, N. Delaney, J. Faeder, R. Parson, et al, J. Phys. Chem. 102, 8827
(1998).

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41

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42

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_________________
Chapter V
Chemical Education Introduction________________
5.1

Towards an understanding of student learning
The traditional lecture format, in which a professor talks and students listen, has been

the mainstay of teaching for centuries. Issues of what to teach and how to teach within thechemistry discipline date back as far as the early 1920s with a report that appeared in the firstissue of the Journal of Chemical Education.1 However, it was not until the mid-1980s that
educators started to question the format in which students were taught. One bulletin by theAmerican Association of Higher Education (AAHR) reports that the traditional lecture format
still dominates college and university classrooms and suggests “Seven Principles for Good
Practice in Undergraduate Education”2 as a start to changing the way students are taught.
Several studies after this bulletin have shown that students need to do more than just listen to
truly learn, they must read, write, discuss, or be engaged in solving problems.3-5 Despite
these many calls for education reform in the sciences,6-8 changes to the way we educate
undergraduate students continues to be the topic of many publications.9,10
In response to these ongoing calls for change, this portion of the thesis addresses
issues of student learning and education reform in undergraduate chemistry. The work
presented here focuses on two aspects within this broad topic, namely, student beliefs about
learning chemistry and the use of interactive tutorials as a supplement to traditional lectures.
While many studies focus on gains in students’ content knowledge through various teachingpractices,11 very little work has been done in studying how these practices affect the equallyimportant topic of students’ beliefs.

In addition to addressing student beliefs as part of aneffective learning environment, an educator must also address how students learn the content

77
within their course. The use of guided inquiry methods has been shown to aid students indeveloping deeper connections with difficult concepts.12,13
5.2

Measuring student beliefs about chemistry and learning chemistry
After many years of reports on the ineffectiveness of the lecture format, chemical

education researchers began to change their focus from the “content” of chemistry courses tothe “delivery” of this content to the students. This shift in focus has placed students at thecenter of learning. This “student-centered” approach has been the basis of reform efforts incourses from environmental science to physical chemistry.13-15 With these important changes
occurring, the need for easy, effective evaluations of the impact of these changes becomes
pertinent. In addition to any evaluation of the effects on students’ content knowledge ofchemistry, there is a need to monitor and evaluate the impacts on students’ beliefs aboutchemistry and learning chemistry. Distinct differences exist between novice and expert
learners concerning their beliefs about science and learning science, Table 5.1 summarizes
these differences in three main areas. An individual’s beliefs shape their own personal
experiences on a daily basis. Several studies have shown that students’ expectations can be abetter predictor of college science performance than previous math or science experience.16-18
Student beliefs can affect how they learn new information; in turn, a student’s experience canshape their beliefs.7,19,20 The measurement of student beliefs has been an area of investigationin the physics community for some years,21-25 but studies in chemistry are more limited.26
Table 5.1
Contrast of novice and expert beliefs on several dimensions of science(adapted from David Hammer27).
NoviceIsolated pieces of information
Handed down by authority.
No connection to the real world
Pattern matching to memorizedarcane recipes.

Expertcontent andstructure

Coherent framework of concepts

Describes nature.
Established by experiment
Systematic concept-based strategies.
problem solving
Widely applicable.
source78
In order to investigate students’ beliefs about chemistry and the learning of chemistry
we have modified the Colorado Learning Attitudes about Science Survey (CLASS),
originally designed for use in physics.21 The survey is designed to be used in a wide range ofundergraduate chemistry courses (from survey courses for non-science majors to graduatelevel courses); therefore, student interviews were conducted with a broad population of
students to ensure clear concise wording and meaning of all statements. The CLASS-Chemsurvey contains 50 statements to which students respond using a five-point Likert scale(strongly agree to strongly disagree). For example, “I think about how the atoms are arranged
in a molecule to help my understanding of its behavior in chemical reactions”. A complete
list of statements can be found in the appendix of chapter VI. Student responses are scored incomparison to expert chemists’ responses and grouped into nine categories. In contrast toother survey instruments, our groupings of statements into categories are not predeterminedbut emerge from student response data and reflect various aspects of student thinking. The
statements are grouped and categorized using the modified principal component analysis
method (similar to factor analysis) developed during creation of the original CLASS survey.21
5.3

Tutorials for undergraduate physical chemistry
Teaching and learning are not synonymous. An individual can teach well without

having their students learn.28 There is an old Chinese proverb which nicely summarizes thetheme of this portion of my work. “Tell me and I forget. Show me and I remember. Involveme and I understand.” Students need to do more than just listen to truly learn: they must
read, write, discuss, or be engaged in solving problems.5 The practice of “student-centered”
learning provides many formats for actively engaging students in the learning process. The
active engagement of students has been shown to improve learning and knowledge retention
in science education.29-32 I propose to use hands-on models and computer simulations inconcert with learning tutorials to engage students in an undergraduate physical chemistry

79
lecture course. The hands-on models provide an easy lecture format for students to test thephysical chemistry concepts under investigation. Previous research has shown that computer
simulations can help students develop conceptual models of physics phenomena.33 Computer
simulations facilitate knowledge construction by providing evidence to assist in theformulation and development of explanatory models.34

Otero states in her studies ofcomputer simulations that “students tend to treat this type of information more likephenomenological evidence than like “the right answer” or dictums from authority because
they actually perform the computer experiments in order to obtain it.”34
5.4

Dissertation overview: Chemical Education
The work presented in this section of the dissertation is divided into two chapters.

Chapter VI presents the modification and validation of the Colorado Learning Attitudes about
Science Survey to measure students’ beliefs about chemistry and the learning of chemistry.
Chapter VII presents the development and testing of three learning tutorials for use in anundergraduate physical chemistry lecture. Due to the diverse nature of the work presented inthis dissertation, each individual chapter will present conclusions and outline future
directions.

80

References for Chapter V
1

J. Cornog and J. C. Colbert, J. Chem. Educ. 1, 5 (1924).

2

A. Chickering and Z. Gamson, AAHE Bulletin 39, 491 (1987).

3

AAAS, Science for all Americans: A Project 2061 report on literacy goals in science,
mathematics, and technology. (AAAS, Washington, DC, 1989).

4

AAAS, The Liberal Art of Science. (AAAS, Washington, DC, 1990).

5

W. Thielens, presented at the annual meeting of the American Educational Research
Association, Washington, DC, 1987 (unpublished).

6

E. Boyer, Scholarship reconsidered: Priorities of the professorate. (The Carnegie
Foundation for the Advancement of Teaching, Stanford, CA, 1990).

7

J. D. Bransford, A. L. Brown, and R. R. Cocking, How People Learn. (National
Academy Press, Washington, D. C., 2002).

8

NRC, Transforming Undergraduate Education in Science, Mathematics,
Engineering, and Technology. (National Research Council, Committee on
Undergraduate Science Education, National Academy Press, 1999).

9

J. Handelsman, D. Ebert-May, R. Beichner, P. Bruns, et al, Science 304, 521 (2004).

10

J. N. Spencer, J. Chem. Educ. 83, 528 (2006).

11

An extensive body of teaching theories, learning tools, and reported benefits can befound on the Journal of Chemical Education website at
http://jchemed.chem.wisc.edu.

12

L. C. McDermott and P. S. Shaffer, Tutorials in Introductory Physics, First ed.
(Prentice Hall, 2003).

13

J. N. Spencer, R. S. Moog, and J. J. Farrell, Physical Chemistry: A Guided Inquiry.
(Houghton Mifflin, New York, 2004).

81
14

M. Masamura, J. Phys. Chem. A 106, 8925 (2002).

15

S. K. Lunsford and W. Slattery, J. Chem. Educ. 83, 233 (2006).

16

J. D. House, International Journal of Instructional Media 21, 1 (1994).

17

J. D. House, International Journal of Instructional Media 22, 157 (1995).

18

P. M. Saddler and R. H. Tai, Science Education 85, 111 (2001).

19

D. Hammer, American Journal of Physics 68, S52 (2000).

20

E. F. Redish, Teaching Physics with Physics Suite. (John Wiley & Sons, New York,
2003).

21

W. K. Adams, K. K. Perkins, N. S. Podolefsky, M. Dubson, et al, Phys. Rev. ST PER
2, 010101 (2006).

22

A. Elby, http://www2.physics.umd.edu/~elby/EBAPS/home.htm (Oct 2006)

23

I. A. Halloun, presented at the International Conference on Undergraduate Physics
Education, College Park, Maryland, 1996 (unpublished).

24

N. G. Lederman, F. Abd-El-Khalick, R. L. Bell, and R. S. Schwartz, Journal of
Research in Science Teaching 39, 497 (2002).

25

E. F. Redish, J. M. Saul, and R. N. Steinberg, American Journal of Physics 66, 212(1998).

26

S. L. Bretz and N. Grove, presented at the 18th Biennial Conference on Chemical
Education, Ames, Iowa, 2004 (unpublished).

27

D. Hammer, Cognition and Instruction 12, 151 (1994).

28

G. M. Bodner, J. Chem. Educ. 63, 873 (1986).

29

D. Ebert-May, C. Brewer, and S. Allred, Bioscience 47, 601 (1997).

82
30

R. R. Hake, Am. J. Phys. 66, 64 (1998).

31

D. Udovic, D. Morris, A. Dickman, J. Postlethwait, et al, Bioscience 52, 272 (2002).

32

J. C. Wright, S. B. Miller, S. A. Koscuvik, D. L. Penberthy, et al, J. Chem. Educ. 75,
986 (1998).

33

F. Goldberg and V. Otero, presented at the European Science Education Research
Association, Thessoloniki, Greece, 2001 (unpublished).

34

V. Otero, A. Johnson, and F. Goldberg, Journal of Education 181, 57 (1999).

83_________________
Chapter VI
Measuring Student Beliefs About Chemistry and Learning Chemistry________________
6.1

Introduction
As described in Chapter V, we have developed the Colorado Learning Attitudes

About Science Survey (CLASS-Chem), a survey instrument designed to measure students’beliefs about chemistry and about the learning of chemistry. In this chapter the developmentof the survey is presented along with the validation studies performed on the completed
instrument.
The remainder of this chapter is structured as follows. Section 6.2 describes thedesign of the survey instrument. Section 6.3 details the administration of the survey and thescoring of the data collected. In section 6.4 the validation studies are discussed in detail.
Applications of the newly developed and validated instrument are presented in section 6.5.
Section 6.6 presents conclusions and possible future uses of the instrument.
6.2

Instrument Design
While there are many surveys available for probing student beliefs in the physicalsciences,1-3 there is only one other instrument designed specifically for chemistry, theChemistry Expectations Survey (CHEMX).4

While both the CHEMX survey and the

CLASS-Phys survey (which is the basis for the CLASS-Chem) are originally based on the
Maryland Physics Expectation survey (MPEX),3 they diverge in their goals andmethodologies as discussed below.

84
Since the design of the original CLASS-Phys survey has been described previously,5
only brief details will be given. Statements in the CLASS-Chem survey are written to bemeaningful for a range of students and designed to address a wide variety of beliefs about:(1) learning chemistry(2) the content of chemistry knowledge(3) the structure of chemistry knowledge(4) the connection of chemistry to the real world
The design of the CLASS surveys differs from the MPEX and CHEMX in three main areas.
First, wording is carefully selected and tested with students with a range of backgrounds toprovide clear concise statements with a single interpretation; MPEX claims only to be valid
for use with calculus based courses. Next, CLASS statements do not prompt students’ beliefs
or expectations about a specific course, but about chemistry in general; many of the CHEMX
statements measure students’ views about a particular course, including laboratories. We set
out to design an instrument for use in all courses, regardless of whether they have alaboratory component.

Finally, the grouping of CLASS statements are determined andvalidated using reduced basis factor analysis, which creates empirically determined groupingsof statements based on student responses, the MPEX and CHEMX surveys categorize
statements based on predetermined, author-defined groupings.
In creating a chemistry version we first tried merely switching “physics” to“chemistry” in the CLASS survey to create the CLASS-Chem v1, but subsequent interviews(covered in chapter 6.4.1) with chemistry students revealed that three of these modifiedstatements required some minor wording changes and three other statements were not valid.
Student interviews also revealed that with the change of context some statements could notreliably distinguish between novice and expert learners. For example when responding to thestatement, “There is usually only one correct approach to solving a chemistry problem,” eventhe most novice students disagree stating that “there are many different reactions which lead85
to the same products.” Therefore, in a chemistry context this statement does not provide a
useful distinction between learners. The largest modification done when creating version two
is the addition of 11 new chemistry-specific statements. Many of the added statements
investigate views of chemical reactivity and molecular structure which we consider additional
important characteristics of expert thinking about chemistry.
Education in both physics and chemistry challenges students to develop problem
solving skills and to form cohesive networks of conceptual ideas. Difficult, and major,
components unique to chemistry curriculum involve visualization, reactivity, and molecular
structure. All of these concepts are introduced in introductory courses and are developed
throughout a wide range of chemistry classes. The visual nature of this material poses uniquechallenges in learning. Investigations of the beliefs connected to this visual component are amotivating factor in preparing a chemistry specific version of the CLASS survey.
A series of interviews with a range of students produced the additional chemistryoriented statements for the CLASS-Chem v2 survey. These statements appear in Table 6.1.
All statements, including the 42 modified statements from the physics version, haveundergone reliability and validation studies (described below) in order to produce the 50
statements currently used in the CLASS-Chem v2. All 50 statements appear in the appendix.

86

Table 6.1

Chemistry statements added to the CLASS-Chem v2.

2. To understand a chemical reaction, I think about the interactions between atoms and molecules.
11. I think about how the atoms are arranged in a molecule to help my understanding of its
behavior in chemical reactions.
12. If I have not memorized the chemical behavior needed to answer a question on an exam,
there's nothing much I can do (legally!) to figure out the behavior.
17. I can usually make sense of how two chemicals react with one another.
21. Why chemicals react the way they do does not usually make sense to me; I just memorize
what happens.
29. When I see a chemical formula, I try to picture how the atoms are arranged and connected.
33. The arrangement of the atoms in a molecule determines its behavior in chemical reactions.
37. In learning chemistry, I usually memorize reactions rather than make sense of the underlying
physical concepts.
44. Thinking about a molecule's three-dimensional structure is important for learning chemistry.
48. Spending a lot of time understanding why chemicals behave and react the way they do is awaste of time.
50. When I'm solving chemistry problems, I often don't really understand what I am doing.

6.3

Scoring and Administration
The scoring and administration is identical to that previously described for the

CLASS-Phys survey.5 Brief details will be given here. Students respond to each statement
using a five-point Likert scale (strongly agree to strongly disagree). An individual student’s‘Overall % favorable’ score is the percentage of responses for which the student agrees withthe expert’s response (including only those statements where experts have consistent views –45 of 50). Similarly, the ‘Overall % unfavorable’ score is the percentage of responses forwhich the student disagrees with the expert. A choice of neutral is neither grouped asfavorable nor unfavorable. These individual scores are averaged to determine the ‘Overall %favorable’ and ‘Overall % unfavorable’ score for all participating students. Scores andaverages are also determined for groupings of statements within categories. Each categorycontains a number of statements which portray an aspect of student thinking, thedetermination of this categorization will be addressed in chapter 6.4.3.

87
While we ask students to respond to statements on a five-point Likert scale, we
collapse this scale to a three-point scale (agree/neutral/disagree) during scoring. We havefound that utilizing a five-point scale for student responses is important for two reasons.5
First, student interpretations of agree vs strongly agree are not consistent, the same belief may
elicit a strongly agree response for one student and only an agree response for another.
Second, students state that without this distinction they would have chosen neutral more
often. We believe that we may lose some definition within the responses by groupingstrongly agree with agree (and strongly disagree with disagree), however, this collapsed scale
still provides us with comparisons to ‘expert’ responses.
The CLASS-Phys survey has been administered since fall 2003 and the CLASSChem survey since fall 2004 (v1) and summer 2005 (v2). To date, over 5000 students in over
30 courses at CU-Boulder have taken the CLASS-Chem. Currently, two other universities
are also using the survey. We administer the survey online and have been successful inmaximizing student responses by utilizing the following approach:(1) the survey isannounced in class by the instructor and the HTML link is posted on the course web site; (2)students are contacted via email and given a 5-7 day window to submit their survey, a followup email is sent a few days from the end of the window to those who have not submitted; (3)whenever possible, a small amount of credit is offered for participation as we have seen thatthe small credit increases participation significantly (e.g. matched data, defined below,
increased from 40% to 60% of enrolled students in a large (>800 student) 1st term chemistrycourse). Students may receive this credit for simply submitting their name and ID number,but very few choose this option.
The number of responses actually scored is less than the total number of submissions
for many reasons. A number of scoring controls are either built into the on-line survey orutilized during the scoring protocol. Two controls are imbedded in the on-line survey itself.
First, a timer records the amount of time each student spends at the web site. We have88
determined that students spending less than 3 minutes at the site could not be reading andunderstanding each statement before clicking on an answer.

Therefore, a student’s

submission with a time of less than 180 seconds is flagged and not counted as “good”. Thereis one statement in the survey used to gauge if the students are actually reading the statements
or simply clicking answers at random. Statement 31 is used to identify these students, “We
use this statement to discard the survey of people who are not reading the statements. Please
select agree (not strongly agree) for this statement.” During the scoring process we eliminate
any duplicate submission, we find that a handful of students take the survey twice either
because they do not remember they took it or hear about the deadline reminder and retake itjust to be sure they get course credit. We also look for repetitiveness within students’submissions as well as the number of statements answered. We do not want to include a
student’s submission if they clicked the same answer for the entire survey or only answered asmall percentage of the statements.
On average, we have about a 75-85% response rate on the survey with roughly 1015% of these responses being dropped for the above reasons; the remaining responses provide
useful pre and post data. In order to evaluate shifts in beliefs from pre to post, we compile asubset of data, “matched data” which consists of only students who have successfullycompleted both pre and post surveys. This approach ensures that the calculated changes
reflect shifts in student thinking rather than changes in populations. We have seen increasesof ~20% in participation, both pre and post as well as in “matched” data sets, when the
instructor offers some form of course credit for taking the survey.
6.4

Validation
The CLASS-Chem survey has undergone extensive validation studies. It is importantto point out the criteria we believe an instrument must meet in order to be considered valid.
First, the wording and meaning of the statements within the survey must be clear to the target

89
population. In addition, students’ responses (either ‘expert’ or ‘novice’) must be consistent
with their explanation for why they chose that response. Second, the statement answers must
be agreed upon by experts, providing face validity to the survey. Next, the grouping ofstatements into categories used to characterize the thinking of the student population must be
statistically robust – that is, responses to the individual statements are reasonably correlatedwith one another. Lastly, the instrument must demonstrate the ability to distinguish between
groups that should be distinguishable in theory – for example, between the beliefs of nonscience majors and chemistry majors. The statements in CLASS-Chem v2 are validated
through interviews with chemistry students as well as with chemistry faculty. The faculty
responses are also used to establish the expert opinion. Statement groupings are validated
using Principal Component Analysis6 on student responses.
6.4.1

Interviews
During development of the original CLASS survey, over forty students wereinterviewed.5 This series of interviews with students in various physics courses, many ofwhich were concurrently enrolled in chemistry courses as well, established the wording andcontent for the initial statements used on the survey. In addition to these interviews, ten
students in a range of courses – from chemistry for non-majors to junior level organic
chemistry – were interviewed during development of the chemistry version. Students wereselected to provide a diverse group in terms of gender, race, and major. The interview
process consisted of three parts. First, the students completed a pencil and paper version of
the survey. Once completed, students were asked about their major, course load, educational
interests, good/bad class experiences, and future goals. These statements provided
information to characterize the students and their interest as well as put them at ease byengaging in familiar conversation. The bulk of the interview consisted of the interviewer
reading the statements while the student looked at a written version. Students were asked to90
respond to each statement using the five-point Likert scale and then to reflect on any thoughts
prompted by the statement. Most students freely provided thoughts and comments on allstatements; those that did not were prompted to explain their answer choice. If questions
were asked by the student about a statement or the interview itself, they were not addresseduntil the very end of the interview session.
6.4.1.1 CLASS-Phys Statements
Student interviews resulted in minor wording changes in two statements (#’s 27 and32) and the complete removal of only 3 out of the original 42 CLASS-Phys statements (onewas not scored in the CLASS-Phys and the other two were scored but not included in any
specific CLASS-Phys category). Students expressed some confusion as to the originalcontext of statements 27 and 32. The confusion was due to the fact that the words “equation”
and “formula” are readily interchangeable in physics and have the same mathematicalmeaning; in chemistry, however, these words do not have the same meaning and hence are
not interchangeable. An “equation” in chemistry can be either the mathematical type, as inphysics, or the chemical type. A “chemical equation” is a format for writing a chemical
reaction7 and differs from a “chemical formula” which is a format for listing the number andkind of constituent elements in a compound.7 If a statement did not obviously indicate which
form of the words was being used, then the prefix “chemical” or “mathematical” wasattached. For example in the statement, “spending a lot of time understanding where
formulas come from is a waste of time,” the word “formula” was replaced with“mathematical formula.” This provided unambiguous interpretations for most of thestatements.
Based on the student interviews, the three statements below were removed from
CLASS-Chem v1.
--There is usually only one correct approach to solving a chemistry problem.

91--There could be two different correct values for the answer to a chemistry problem if I use
two different approaches.
--It is possible for chemists to carefully perform the same experiment and get two very
different results that are both correct. (Not scored on CLASS-Phys)
The first statement was removed because in a chemistry context it is readily obvious to eventhe most novice students that there are many approaches to solving a chemistry problem, forexample, students learn a number of various reaction pathways to produce the same product.
In the case of the physics version, the novice learners tended to agree with the statement and‘experts’ disagreed, providing a measure of discrimination between ‘novice’ and ‘experts’.
The second statement had similar problems with students referring to reaction pathways. The
third statement, which is scheduled for revision or replacement in the physics version due tolack of a consistent expert response, posed difficulties with the less experienced students.
Many students stated that there may be “unconsidered variables” or that there were “a lot of
twists in chemistry that break the rules.” During interviews students would also reflect on
past laboratory experiments where “everyone followed the same procedure” but the results
were very different. Based on these comments, and the fact that these specific statements
were not grouped into any of the eight categories in the physics version, we removed all threestatements. Dropping these statements also made room for more additional statements as we
did not want to exceed a total of 50 statements.
6.4.1.2 Chemistry-specific Statements
Using student interviews, we tested over twenty candidate statements to probe theadditional chemistry-specific areas of students’ beliefs, including some statements selectedfrom the CHEMX and some inspired by or revised through student interviews. Seventeen
statements proved to be valid in interviews and we kept the 11 we felt were most informative.
Many statements were revised based on vocabulary problems. It was discovered that words
such as “intuitive,” “theories,” and “structure” do not have unambiguous definitions for92
introductory students. It was found that the word “structure” must be associated with either
molecular or electronic in order to have singular meaning to many students.
6.4.2

Faculty Surveys
The 50 statements selected for the CLASS-Chem v2 survey were given to over 20

chemistry faculty at four different universities. This data was used to confirm the expert
response and also to provide additional feedback about the statements themselves. Forty-fiveof the statements had consistent expert responses. These responses (agree or disagree) are
included in the appendix. Using these responses to define the ‘expert’ view, we scored theindividual faculty surveys using the same approach as used for student responses. Figure 6.1
plots the faculty’s average ‘% Favorable’ vs ‘% Unfavorable’ scores for ‘Overall’ and eachcategory. For the 45 statements which comprise the ‘Overall’ score, the faculty surveyed
score 89.2% favorably and only 3.2% unfavorably.

93

Chemistry Faculty
Results100

Overall
Pers onal Interes t
Real World Connection

90

Favorable (%)

PS General
PS Confidence

80

PS Sophis tication
Sens e Making/Effort

70

Conceptual connections
Conceptual learning
Atom ic-Molecular Pers pective ofChem is try

60

50
0

10

20

30

40

50

Unfavorable (% )Figure 6.1% Favorable vs % Unfavorable plot of faculty responses.

Four of the five un-scored statements do not have consistent faculty responses andgauge either nature of science (#8) or learning style aspects (#s 5,10,39). We include theselearning style statements in the survey because they provide useful information about student
approaches to learning. Developing suitable nature of science statements is an ongoing areaof investigation; statement #8 will be revised or replaced in a future version. The last unscored statement is number 31; this statement, as described earlier, is used during the scoringprocess to reject surveys submitted with random guesses.
On the faculty version of the survey, participants were asked if they had any
comments or concerns about each statement. A free response box was incorporated into theon-line version to collect this information. Roughly 35% of the statements received
comments from the faculty. Some of these responses reflect the importance of the statements

94
or topics in the faculty member’s mind. A list of some of these statements along with asample response is presented below.
Statement #3. When I am solving a chemistry problem, I try to decide what would be areasonable value for the answer.
-“Knowing how to 'guesstimate' is important”-“After we "calculate" our value we ask if it seems reasonable”
Statement #20. Understanding chemistry basically means being able to recall something
you've read or been shown.
- Students “must be able to apply info”
Statement #36. Reasoning skills used to understand chemistry can be helpful to me in myeveryday life.
- “That's why I teach chemistry!!! My purpose is not just to impart chemical knowledge but
rather to teach and encourage students to think and reason for themselves. By tacklingchemistry, students are learning how to learn because chemistry is usually something they're
not too familiar with.”
Statement #42. There are times I solve a chemistry problem more than one way to help myunderstanding.
-“This is really when you understand a concept!”-“And to double check an answer! Arriving at the same result via two or more independent
methods increases the confidence level I have in the result.”
In interviewing a few of the faculty about their courses and how they interpret the resultsfrom their course, we found that many choose to focus on a few key statements which theyfind important. One such professor prides himself on providing a strong foundation in
problem solving during his course; therefore, he focuses on how the students’ responses tothe problem solving statements change over the course of the semester.
6.4.3

Categorization of Statements
A significant difference between the CLASS surveys and MPEX or CHEMX is themethod by which the statement groupings are determined. The categories in the MPEX or
CHEMX surveys are defined a priori by the developer without the use of statistical methods
to ensure their validity. During the development and validation of the physics version of
CLASS, a substantial number of students were given the MPEX survey. Upon statisticalanalysis, it was found that some groupings were made up of statements with very weak

95
correlations (<0.05). If statement groupings are to be used in characterizing facets of student
thinking, then the student responses to the statements within that grouping should bereasonably correlated (>0.15), if in fact the groupings represent student thinking. If statisticalanalysis is not used to determine correlated student responses, it is very unlikely that
predetermined categories will be made of statements which reflect student thinking.
6.4.3.1 Categorization Philosophy and Approach
The details of our categorization are presented in the previous CLASS-Phys
validation paper;5 a brief summary will be given here. Categories can be established using
two different philosophies, either “raw statistical” or “predetermined.” In the raw statistical
approach, no constraints are in place and categories emerge from the data via exploratory
factor analysis.8-10

In contrast, a predeterministic approach bases categories on expert

perspectives about how statements should be grouped.

Both of these approaches havestrengths and weaknesses.5
Exploratory factor analysis ensures that all categories are statistically valid. This
categorization procedure has been shown to provide insights into student thinking.5,11 An
example of this is the category labeled as “sense making and effort,” where student responses
show a strong correlation between statements involving how a student makes sense ofchemistry and statements concerning the amount of effort needed to solve problems. A
substantial drawback to defining categories simply using exploratory factor analysis is thatmany statement groupings are not very useful to an educator.
It is the apparent connection with particular aspects of instruction that makepredetermined categorization so widely used.

From a statistical standpoint however,predetermined categories are not a valid characterization of an aspect of student thinking if
little or no correlation exists between respondents answers. An additional drawback topredetermined categories is the fact that statements are designed to fit into a single category.

96
It was found throughout our factor analysis that statements routinely group into more than
one category and more importantly in some cases statements do not group into any
categories.
Our approach combines the strengths of both methods, providing an optimum set ofvalid categories. Figure 6.2 (courtesy of Adams et al.) summarizes the iterative process usedin choosing categories; a detailed description of the process can be found in the work of
Adams et al.5 The parameters of the factor analysis performed using the SPSS program6 are
as follows: Extraction Method: Principal Component Analysis, Rotation Method: Direct
Oblim, Missing Values: Excluded pairwise.

Raw Statistical Categories
from exploratory factor analysis

Predetermined Categories
from researcher classification

Principal component analysis
on individual potential category

Reduced
Basis
FactorAnalysis

Remove statements which do not
fit or analyze as multiple categories

Add additional statements withhigh correlation

Repeat – until a robust groupis established

Figure 6.2

Flow chart depicting reduced basis factor analysis.

Several indicators of statistical validity are evaluated in determining the strength of eachstatement grouping.

To facilitate comparison between various groupings, a robustness

calculation is used to assign a value for each group. Optimization of this value provides arobust, statistically valid grouping of statements. The robustness calculation looks at the

97
output of doing a factor analysis on each set of statements in a category. This criterion isdetermined by evaluating various indicators of statistical validity including the correlation
coefficients between statements, the percent of variance explained by the weighted
combination of statements represented by the first factor and the factor loadings for eachstatement in that first factor. (A factor analysis always produces as many factors/components
as statements in the basis.)

The robustness number for a grouping is calculated using thefollowing equation:
Robustness = (2cc + fl + 5|∆E|/N) × 3R2
where cc is the average absolute value of the correlation coefficients between statements, fl is
the average absolute value of the factor loadings for the category, ∆E represents the shape ofthe scree plot (see Fig. 6.3 for details), N is the number of statements in the category, and R2
is the Pearson product moment correlation, which represents the linearity of the scree plot
components beyond the first component. The coefficients (2, 1, and 5) are chosen to give theterms in the sum the relative weightings that we believe are the most appropriate. The shapeof the scree plot accounts for 45%, and the factor loadings and correlation coefficients areequally weighted at 27.5%. The factor of 3 sets the maximum value for the robustness at 10.
Values used to calculate robustness for the ‘Real World Connection’ category can be found in
Table 6.2; reports for all categories appear in the appendix. The total variance calculations are
based on the slopes of the scree plot in Fig. 6.3.

98

Table 6.2

Data from optimized ‘Real World’ Category

Statement Correlation Matrix
Category Values
9.68
S34
S36
S41
S43
Robustness
1.00
0.45
0.43
0.35
0.39
S34
cc
0.45
1.00
0.35
0.42
0.74
S36
fl
0.43
0.35
1.00
0.33
-1.37
S41
∆E*
0.35
0.42
0.33
1.00
4
S43
N
Factor Loadings
Total Variance*
0.99
R2*
0.76
-1.47
S34
Slope 1-2
0.76
-0.09
S36
Slope 2-4
0.71
*Based on scree plot (A) in Fig. 3
S41
0.71
S43
2

∆E = slope(1,2) – slope(2,n)

Slope(1,2)

Where n = total number of components

1.5

Slope(1,2)

1.5

1E ig e n v a lu e

E ig e n v a lu e

2

Slope(2,n)

0.5Slope(2,n)
1

0.5

1

2

3
Component Number

A
Figure 6.3

1

4

B

2

3

4

5

Component Number

Scree plots from a good category (A) and a poor category (B).

6.4.3.2 Unmodified Physics Categories
The initial implementation of the CLASS survey in chemistry courses consisted ofsimply changing the word “physics” to “chemistry” in all the statements.

Beforemodification of any categories proceeded, the robustness of the eight original categories wasmeasured and compared to those published.5 From the comparison of post semester data in
Table 6.3, we see that the statement groupings produce nearly equal robustness values foreach category regardless of the statement context (physics vs chemistry).

99

Table 6.3
Comparison of robustness values for the eight categories of the CLASS-Phys
survey with both physics and chemistry students.
Category
CLASSCLASSPhys
Chem v1
Personal Interest
8.20
7.74
Real World Connections
7.32
9.68
Problem Solving-General
6.50
6.44
Problem Solving-Confidence
7.39
6.60
Problem Solving-Sophistication
8.25
8.00
Sense Making/Effort
5.91
4.94
Conceptual Connections
5.57
4.31
Applied Conceptual Understanding
5.71
5.30
In validation of the physics version,5 the lowest acceptable robustness value was set at five.
The consistent robustness of the categories between these two populations is a strong
affirmation of the universality of the statements and our grouping procedure. With thesecategories and values as a start, we set out to investigate the series of additional statements.
6.4.3.3 CLASS-Chem Categories
The iterative process using reduced basis factor analysis depicted in Figure 6.2 wasused to optimally incorporate the 11 additional statements into the chemistry survey. The
final CLASS-Chem v2 categories and robustness factors are listed in Table 6.4. These
categories are quite similar to the original CLASS-Phys categories.

100

Table 6.4
CLASS-Chem v2 categories, statement numbers, and robustness values.
Bold indicates added statements to v2.
Categories
Statement Numbers
Personal Interest
4,13,16,28,34,36
Real World Connection
34,36,41,43
Problem Solving:
General15,18,19,21,28,30,40,47,49,50
Problem Solving: Confidence
18,19,40,47
Problem Solving:
Sophistication
6,24,25,28,40,47,50
Sense Making/Effort
13,21,26,27,38,42,46,48,49
Conceptual Connections
6,7,15,24,37,38,50
Conceptual Learning
1,6,7,12,24,25,47
Atomic-Molecular
Perspective of Chemistry
2,11,17,29,33,44

Robustness
7.74
9.68
7.16
6.60
8.48
6.17
6.01
6.71
7.13

The additional statements are spread over five original categories and one new category notin the physics version. Statements 1 and 9 were removed from the ‘Conceptual Connections’and ‘Conceptual Learning’ categories, respectively, because of poor correlation with the othercategory statements. The remaining original statements all strengthened each category to thesame degree, or more, as in the physics version.
With the addition of these statements, the category names were reviewed. It was
found that in all but one instance, the names chosen for the physics categories reflected theoverall theme of the statements grouped within them, the exception being that the ‘Applied
Conceptual Understanding’ category was renamed ‘Conceptual Learning.’ One new category
named ‘Atomic-Molecular Perspective of Chemistry’ was added and contains six of theadditional statements. Only 36 out of the 45 statements with ‘expert’ responses are factored
into one or more of the categories. This demonstrates the usefulness of the categorization
scheme used. For example, we expected that statement #35: “To learn chemistry, I only
need to memorize how to solve sample problems,” would fit into one of the problem solving

101
categories, but the analysis revealed it did not correlate with the other statements in thesecategories and hence did not describe student thinking in these areas.
6.4.4

Concurrent Validity
The CLASS survey is designed to measure students’ beliefs about chemistry and thelearning of chemistry. Therefore, an appropriate concurrent validity test would be to showthat the instrument can measure a difference in beliefs between populations which shouldhave different beliefs.

Figure 6.4 shows the percentage of favorable responses for the‘Overall’ statements and those in the ‘Personal Interest’ category.

It is expected thatstudents’ ‘Overall’ and ‘Personal Interest’ scores should correlate with course selection. For
example, one would not expect a student taking an introductory course for non-majors tohave a strong personal connection to the discipline, in contrast to a chemistry major taking a
junior level physical chemistry course. Not only does the survey distinguish between thesedifferent populations, but it can also differentiate student populations within the same course
as shown in Figure 6.4. Students in both general and organic chemistry who are chemistrymajors show more “expert-like” beliefs than the non-chemistry majors (made up of biology
majors, non-science majors, or other science majors) in these same courses.

102

Faculty
Physical I
Organic II (majors)
General I (majors)
Organic II (non-majors)
General I (non-majors)
Introductory

Personal Interset
Overall

Environmental
0

20

40

60

80

100

% Favorable Score

Figure 6.4
Comparison of percent favorable scores for ‘Personal Interest’ and ‘Overall’categories for a range of courses and majors including faculty.
6.4.5

Test-Retest Studies
In order to gauge the reliability of the CLASS instruments we use the test-retest

method.12,13 Reliability was measured using pre responses from two general chemistry I
courses during the fall 2005 and fall 2006 semesters. Since it is reasonable to assume there islittle variation in these large (N>800) student populations from year to year, this provides agood direct measure of survey reliability. The correlations shown in Table 6.5, of the percent
favorable, percent neutral, and percent unfavorable scores for all statements on the CLASSChem v2, show that student responses between the two years are very similar. Data from thephysics version is also presented in Table 6.5 for comparison.

103

Table 6.5
Correlation of percent favorable, neutral, and unfavorable scores from fall2005 to fall 2006 general chemistry I courses and fall 2004 to spring 2005 algebra-based
physics I.

Chemistry
Physics%Favorable
0.99
0.98

%Neutral
0.95
0.88%Unfavorable
0.99
0.98

We feel that this is a better measure than calculating a Cronbach alpha value12,13 for this typeof instrument for two reasons. First, because we have large and very consistent student
populations from one year to the next in these large courses, the retest-approach provides themost direct test of reliability. Second, the Cronbach alpha test relies on correlations between
statements, and we intentionally exclude statements with a very high degree of correlation, inorder to obtain the maximum amount of information from a given number of statements. We
did calculate the average Cronbach alpha value, using fall 2006 data from nine chemistrycourse at two different universities, for CLASS-Chem v2 to be 0.89. While this value is highand falls into the ‘good’ range,14 it is not so high that it suggests repetition within the survey
statements.

Streiner et al. state in their work on measurement scales that “if alpha is too

high, then it may suggest a high level of item redundancy; that is, a number of items asking
the same question in slightly different ways.”15
6.5

Applications
The breadth of data collected with the CLASS survey can be analyzed in a variety ofdifferent ways to extract specific results. Using physics data, our group has studied thecorrelation of students’ self-reported interest in physics to their surveyed beliefs16 as well as
differences in beliefs with gender5 and correlations between beliefs and content learning.17
Using the common statements between CLASS-Phys and CLASS-Chem we compared how
biology majors view each discipline (see 6.5.2 below).18

In addition to characterizing

104
students’ beliefs, shifts in beliefs over the course of a semester can be correlated to various
teaching methods.
6.5.1

Semester Shifts
The general trend in shifts for both physics and chemistry are in the negative

direction, meaning the students score more favorably at the start of a semester than at the end.
Table 6.6. shows pre and post scores along with calculated shifts for a general chemistry I
course. This trend is a current topic of investigation as its cause can stem from a variety ofsources. We do have data from two physics courses which do not show a decline in beliefs.
These instructors made modest efforts to address student beliefs over the course of thesemester, suggesting that such undesired impacts of instruction are relatively easy to change.
Obtaining large positive shifts in beliefs has been challenging and is an area of ongoing
research in the physics community.19
Table 6.6
one semester.

General chemistry I: Results show decline in percent favorable scores overCategory
Overall
Personal Interest
Real World Connection
Problem Solving:
GeneralProblem Solving:
Confidence
Problem Solving:
Sophistication
Sense Making/Effort
Conceptual Connections
Conceptual Learning
Atomic-Molecular
Perspective of Chemistry

PRE
53
53
58

POST
48
44
46

SHIFT
-5
-9
-12

Std.
Error*
1
2
2

59

53

-6

2

64

56

-8

2

44
66
55
42

40
56
51
40

-4
-10
-4
-2

2
1
2
2

52

51

-2

2

105
6.5.2

Comparison Between Chemistry and Physics
We have collected CLASS-Physics responses in a first-term, algebra-based Physics I

course (Phys I) and CLASS-Chemistry responses in a first-term, introductory generalchemistry course (Chem I). In prior research, we have found differences in students beliefs
correlating with choice of major;17,20 thus, in this study, we focus on just the biology majors.21
We choose first-term courses because college physics courses have been shown to alter
student beliefs.3,17 With these data, we are able to compare two large and similar populationsof students because there are a large number of biology majors and the students are required
to take both courses to fulfill their majors.
From Table 6.7, we see that both courses were large lecture courses (over 500
enrolled) with a large number of biology majors, the majority of whom are women. The
results presented here are for the 156 (Chem I) and 212 (Phys I) biology-majors
Table 6.7

Demographics of introductory courses surveyed.

Total # students

Chem I
812

Phys I - Alg
553

Total # bio majors

362

330

Total # bio majors with matched surveys

156

212

% women bio majors

70.3

72.2

% men bio majors

28.4

27.4

for which we collected matched pre- and post- surveys. The instructor for the Phys I course
is very familiar with research findings in PER and incorporated many research-based
practices into the course, including: in-class concept questions where student-student
discussions are highly encouraged and reasoning/sense-making is emphasized; interactive
feedback in lecture where students use H-ITT “clickers” to vote; conceptual questions on
homeworks and exams; and labs revised to incorporate more discovery. In implementing

106
these practices, the instructor explicitly worked to promote expert beliefs. Although the Chem
I course used concept tests and clickers, the course was comparatively traditional, with lessemphasis on peer discussion, reasoning, and conceptual learning.
Students’ responses on the pre-course surveys were compared to identify difference
between biology majors’ view of physics and chemistry prior to any college instruction in thediscipline. Statistically significant differences (p<0.01) between their responses to the
CLASS-Physics and CLASS-Chemistry surveys were measured for the ‘Overall’ score andfor three categories – ‘Real World Connection’, ‘Conceptual Connections’ and ‘Applied
Conceptual Understanding’, note: the ‘Applied Conceptual Understanding’ category was
renamed ‘Conceptual Learning’ on the second version of the CLASS-Chemistry. In figure
6.5, we see that biology majors have consistently more expert-like beliefs (denoted as points
closer to upper-left corner of plot) about physics and learning physics than about chemistryacross these categories. The most dramatic difference is observed in the ‘Real World
Connection’ category where the % favorable scores are 69.3% for physics and only 56.8% forchemistry, indicating that these biology majors see physics as substantially more connected to
the real world – as both describing and being useful to understand real world experiences.

107

Favorable (%)

100

Overall

90

Real World Connection

80

Conceptual Connections
Applied Conceptual
Understanding

70
60
50
40
30
0

10

20

30

40

50

60

Unfavorable (%)
Figure 6.5
CLASS survey scores for biology majors at the start (pre) of Phys I (solid)
and Chem I (hollow). The students were consistently more expert-like in their view ofphysics, with differences beings statistically significant (p<0.01) for both ‘Overall’ and the 3categories shown.

Figure 6.6 shows the shifts in CLASS scores over the course of the term (preto-post) for the biology majors in the Phys I and Chem I courses. Only categories forwhich the shifts are statistically different (p<0.01) are included. In Chem I, we see thebiology majors shifting to be much more novice-like in their beliefs about chemistry– a result consistent with the typical shifts observed in introductory physics
courses.3,17 In the Phys I course, however, we observe students beliefs holding steadyin most cases. We attribute this to the Phys I instructor’s emphasis on conceptual
understanding and reasoning, his infusion of real world examples, and his use ofconcept tests and peer discussion in class.

108

70

PHYS ICHEM I60

Conceptual
Connections

Sense making/Effort30

Personal
Interest

40

Real World
Connection

50

Overall% Favorable

80

Category
Figure 6.6
Pre-post shift for CLASS-Chemistry and CLASS-Physics scores where there
is a statistically significant difference in the shifts (p<0.01).
We observe significant differences in biology majors’ beliefs about physics and theirbeliefs about chemistry. In all measures, these students have more novice-like beliefs aboutchemistry, specifically seeing chemistry as more about memorizing and less about the realworld. Since these differences are present at the start of these first-term introductory courses,
these differences in beliefs were established by some combination of prior experiences. As
with many physics courses, we see that introductory chemistry courses, even those that use
concept tests and clickers, may lead to significant declines in students’ beliefs aboutchemistry and learning chemistry. Physics courses where reforms have succeeded in avoiding
this typical decline may serve as a useful model for reforming chemistry courses.
6.6

Conclusions and Future Directions
This chapter describes the modification and validation of the CLASS-Phys survey foruse in chemistry courses. The CLASS-Chem v2 consists of 50 statements, 39 slightlymodified statements from the CLASS-Phys survey plus eleven additional statements.
Validation has been performed for all statements to ensure clarity in wording and meaning for

109
a wide group of students. Statements are categorized into statistically robust groupings which
are useful to educators in evaluating various aspects of student thought.
This work establishes an instrument which can be used to study student beliefs aboutchemistry and the learning of chemistry. This instrument is a useful tool for evaluating theimpacts of teaching practices. The impacts of instruction on reducing interest in chemistry areparticularly worth noting if one is concerned with increasing the number of students majoringin chemistry.
This survey instrument can be combined with a conceptual exam in order to provide
an educator a wealth of knowledge about how their teaching practices affect students’ beliefs
and conceptual understanding. This combination would greatly enhance the decision of what
to teach and how to teach it for any course.
Extending the beliefs survey into the high-school setting would allow researchers toinvestigate broader trends in science education. Are students more ‘expert-like’ in highschool? Does the ‘novice-like’ behavior begin in high-school or at the freshman level incollege? Can we implement curriculum change at the high-school level that will impact the
number of incoming science majors?
An additional extension of the beliefs survey would be a laboratory specific version.
A great deal of time and effort is placed on developing “new and exciting” chemistry
experiments for undergraduate teaching labs. Is there a benefit to these labs? Do inquiry
based labs have an impact on students’ beliefs about chemistry? Do students believe thatthey are actually learning chemical concepts in a lab setting or simply gaining tactile labskills?
Copies of the CLASS-Phys and CLASS-Chem surveys can be found online and in
PDF format at http://CLASS.colorado.edu. Excel scoring templates are also available fromthe same address.

References for Chapter VI
1

A. Elby, http://www2.physics.umd.edu/~elby/EBAPS/home.htm (Oct 2006)

2

I. A. Halloun, presented at the International Conference on Undergraduate Physics
Education, College Park, Maryland, 1996 (unpublished).

3

E. F. Redish, J. M. Saul, and R. N. Steinberg, Am. J. Phys. 66, 212 (1998).

4

S. L. Bretz and N. Grove, http://www.chemx.org/ (Oct. 2006)

5

W. K. Adams, K. K. Perkins, N. S. Podolefsky, M. Dubson, et al, Phys. Rev. ST PER
2, 010101 (2006).

6

SPSS 12.0 for Windows (2003).

7

J. McMurry and R. C. Fay, Chemistry. (Prentice Hall, New Jersey, 1998).

8

L. Crocker and J. Algina, Introduction to Classical and Modern Test Theory. (Holt,
Rinehart, and Wilson, Fort Worth, TX, 1986).

9

S. K. Kachigan, Statistical Analysis. (Radius Press, New York, 1986).

10

J. Kim and C. W. Mueller, Factor Analysis-Statistical Methods and Practical Issues.
(Sage Publications, Beverly Hills, CA, 1978).

11

L. J. Rennie and L. H. Parker, Journal of Research in Science Teaching 24, 567(1987).

12

J. R. Fraenkel and N. E. Wallen, How To Design and Evaluate Research in
Education, 3rd ed. (McGraw-Hill, New York, 1996).

13

M. Wilson, Constructing Measures: An Item Response Modeling Approach.
(Lawrence Erlbaum Associates, Inc., Mahwah, NJ, 2005).

14

D. George and P. Mallery, SPSS for Windows Step by Step: A simple guide andreference, 11.0 update, 4th ed. (Allyn and Bacon, Boston, 2003).

111
15

D. L. Streiner and G. R. Norman, Health measurement scales: A practical guide totheir development and use. (Oxford University Press, Inc, New York, 1989).

16

K. K. Perkins, M. M. Gratny, W. K. Adams, N. D. Finkelstein, et al, PERC
Proceedings 818, 137 (2006).

17

K. K. Perkins, W. K. Adams, N. D. Finkelstein, S. J. Pollock, et al, PERC
Proceedings 2004 (2005).

18

K. K. Perkins, J. Barbera, W. K. Adams, and C. E. Wieman, PERC Proceedings(2006).

19

T. McCaskey, A. Elby, and E. F. Redish, presented at the AAPT Summer Meeting,
Syracuse, NY, 2006 (unpublished).

20

S. L. Bretz and N. Grove, presented at the 18th Biennial Conference on Chemical
Education, Ames, Iowa, 2004 (unpublished).

21

including students majoring in Molecular, Cellular, and Developmental Biology,
Ecology and Evolutionary Biology, and Integrative Physiology as well as the
now-discontinued majors of Kinesiology and Environmental, Population, andOrganismic Biology.

112_________________
Chapter VII
Tutorials for Undergraduate Physical Chemistry________________
7.1

Introduction
As described in Chapter V, we have developed learning tutorials for use in a firstsemester undergraduate physical chemistry course. These tutorials integrate a physical modelor computer simulation into the standard pencil-paper tutorial format. The models allow
students to make direct observations and predictions connected to the concepts being
addressed. The three tutorials covered in this chapter address concepts of the First Law ofThermodynamics, the Second Law of Thermodynamics, and Reaction Kinetics.
The remainder of this chapter is structured as follows. Section 7.2 describes thedesign of the study itself including observed student misconceptions and an outline ofpotential models to address these problems. In section 7.3, the developed tutorial material istested and results are presented. Section 7.4 addresses the implementation of these tutorials
into a classroom setting and compares results from this course to a control group. Lastly,
section 7.5 presents conclusions of this work and provides ideas for future directions withthese and other tutorials.
7.2

Study Design
The purpose of the current research is to develop learning tutorials to address difficult

or often misunderstood concepts within the thermodynamics and kinetics curriculum of aphysical chemistry course.

This section outlines the procedures used to identify these

problem areas and presents potential tutorial models to address these areas. The tutorial
design is based on these findings and covered in the last section (7.2.3). Copies of the tutorial
worksheets can be found in Appendix B.

113
The study of student misconceptions has been an area of investigation in chemical
education for over 4 decades.1 An investigation of the literature reveals more than a hundredstudies which address student misconceptions in chemistry.2 In this thesis I will limit thesemisconceptions to those directly pertaining to the First Law of Thermodynamics, the Second
Law of Thermodynamics, and Reaction Kinetics.
As a chemistry major I have heard the same quote from people when they ask mewhat I study, “I hate chemistry.” It is not surprising to me now that so many people have adislike for the area of science to which I have dedicated myself. Many students taking
chemistry at the high school and college level struggle to learn the material and most do not
succeed.3 Research shows that many students taking an introductory chemistry course do notcorrectly understand the fundamental chemistry concepts covered in these formal courses.4
This lack of understanding at the fundamental level provides a blockade for these students
when they attempt to learn more advanced concepts which build upon these fundamentals.
This lack of conceptual understanding has also been shown to hinder students’ problem
solving capabilities in chemistry.5 These learning tutorials are designed to aid students inconnecting to often difficult or misunderstood fundamental concepts within the physicalchemistry curriculum.
7.2.1

Student Observations and Interviews
Since the summer semester of 2005 we have been observing the first semester

undergraduate Physical Chemistry I courses (Thermodynamics and Kinetics) at the
University of Colorado in Boulder. In addition to these classroom observations we haveconducted a series of informal interviews with students enrolled in these courses. These
informal interviews came in the form of either problem solving sessions or small group
activity sessions. These observations and interviews were used to decide which concepts totarget and which tools would best address student problems.

114Classroom observations began as part of an initiative to modify the way physicalchemistry is taught at the University of Colorado. One or two observers attended every classperiod and recorded field notes about the topics covered and the depth of the coverage. Theseobservations also included students’ questions about the material being addressed. The initialuse of this information was to simply get a baseline for how the course was taught and what
information was covered in a typical semester. Sitting in on the class also provided theneeded background information about the class so that the observers could participate inproblem solving sessions. These sessions were held once a week for two hours, usuallyscheduled toward the end of the week before problem sets for the class were due, and were
not mandatory. On average only 2-3 students attended these sessions at any given meetingtime.
One direct conclusion from the classroom observations was that the instructor wascovering too much material and not spending enough time addressing any one topic toprovide the students with a depth of understanding. This “teaching to the text” mentality is acommon problem arising when instructors feel the need to cover a wide range of topics
because that is what the book presents.6-8 A portion of the transformation of the physicalchemistry course addresses this issue; however, addressing this issue is not covered in thisthesis. The results of this modification have implications on the material covered in thecourse and so a brief summary is given. In a typical physical chemistry textbook there areroughly 30 chapters.9

About one half of these chapters make up the first semester(Thermodynamics and Kinetics) material. In order to determine which topics the faculty who
regularly teach this material deem important, the syllabi from 6 schools (~ 10 courses) werereviewed and comparisons made.10 These results were presented to the physical chemistry
faculty member who was involved in transforming the course. From this information, a list
was generated of the 5 main core areas for which a physical chemistry student should have asolid fundamental understanding.

115
1. First Law of Thermodynamics
2. Second Law of Thermodynamics
3. Chemical Equilibrium
4. Simple Mixtures
5. Reaction Kinetics
Part of the transformation of the course was to limit the number of topics covered but provide
an in-depth coverage of the chosen material. Therefore, this short list was used to definetarget areas for students’ fundamental understanding.

With these five target areas in mind, a review of student questions from the class aswell as from the problem solving sessions was used in determining the individual concepts
from each area that needed the most attention. Individual concepts were deemed as needing“the most attention” if they were fundamental in nature and were needed to build further
understanding within the larger concept area (i.e., an understanding of heat and/or work on
which to build other First Law concepts). Due to the amount of time needed in fully
investigating any one of these five areas, this thesis work only covers the First Law, Second
Law, and Kinetics sections of the course.
The course under observation began the semester with the First Law ofThermodynamics. This material typically spans two chapters in the text and is covered inabout two weeks. The instructor (and the text) immediately introduces heat, work, andinternal energy, giving these topics about one class period (2 pages).

After this brief

introduction, the material turns to the various conditions under which changes can be made toa system (i.e., isothermal, adiabatic...). By the end of the first of these two chapters, thestudents are immersed in partial differential equations and the focus of the material is mainly
mathematical manipulation.

116
Student responses to in-class questions, as well as student questions themselves,
revealed that most of the class struggled with basic fundamental concepts presented in thefirst few class periods. Students did not have a clear understanding about how work and/or
heat affect the internal energy. Nor did they understand the sign conventions associated withthese forms of energy transfer (i.e., work done ON a system is positive with reference to thesystem itself). In working with students during problem solving sessions, it became clear thatin addition to “minor” problems many students did not believe that there was a difference
between “heat” and “temperature.” This “major” problem has been addressed in many
publications11-13 and has particularly devastating consequences in a thermodynamics course.
Students’ misunderstandings of the differences (or lack thereof) between heat (q) andtemperature (T) hinder their development of many fundamental concepts in thermodynamics.
For example, consider the following question from the point of view of a student who
believes that q = T.
An insulated cylinder containing an ideal gas undergoes an adiabatic (q=0) compression,
how does this compression change the temperature of the gas?
This student would likely respond that ∆T = 0 because the problem states that thecompression is adiabatic meaning q = 0, when in reality, q ≠ T and when the gas iscompressed ∆T > 0.
The two chapters following the First Law cover the Second Law of Thermodynamics.
This material is again given approximately two weeks of lecture time. Students are initiallyintroduced to the concept of entropy and use the mathematical definition of entropy inderiving the fact that entropy is a state function. This classic derivation involves the Carnot
cycle which is built of four reversible processes.

Once this material is covered, thecourse/text begins to build on this introductory material eventually leading to derivation of
the Gibbs energy equation (G = H – TS). The entire second chapter on the Second Law

117material covers the Maxwell relations and various derivations which can be used to describe
thermodynamic systems.
Due to their lack of fundamental understanding of the First Law concepts presented
above, many students struggle to understand the Carnot cycle and state function derivation.
Not only do students struggle with the equations and definitions associated with the Carnot
cycle, but students could not connect to a physical picture of what this “cycle” represented.
This material is generally presented solely in terms of a pressure versus volume plot where
the four stages are graphed.
The fundamental concept of Gibbs energy is introduced to chemistry students infreshman level general chemistry courses; this concept is built upon in physical chemistry andused to derive many different relationships.

Very little attention is paid to students’“understanding” of Gibbs energy and what it means for a process/reaction to be spontaneous.
When students are asked to evaluate if a process/reaction is spontaneous or not, many
students only focus on one part of the picture; similar results were found by Granville in1985.14 For example, students state that an endothermic processes (∆H > 0, where theprocess takes in thermal energy) can not occur spontaneously because energy is being added,or that reactions where the entropy decreases (∆S < 0) can not be spontaneous because thistoo requires energy. However, these students are failing to consider all the variables and how
they are combined in the Gibbs energy (∆G = ∆H – T∆S) when determining spontaneity.
Towards the end of the semester, the course material turns towards kinetics. Aboutfour weeks (and four chapters) are typically dedicated to this topic, including a section on the
kinetic molecular theory of gases.

This material is independent of all of the previous

thermodynamic material presented; in fact, many courses reverse the order of topics andbegin the semester covering the kinetic molecular theory and kinetics.

In the kinetic

molecular theory students learn about molecular speeds, collision rates, and diffusion. This
material is tied up in one chapter before beginning the kinetics sections. In learning kinetics,

118
students are reintroduced to rate equations, rate constants, and other fundamental concepts
first presented in general chemistry.

After this reintroduction, students begin various

derivations of rate laws and methods of determining rates and rate constants. The last two
chapters (of the three kinetics chapters) solely address the kinetics of “complex” reactions
and molecular reaction dynamics, respectively. Many courses either do not cover these
sections or plan to cover them but run out of time in the semester.
The temperature dependence of reaction rates is addressed in general chemistry when
students are introduced to the Arrhenius equation (k = Ae-Ea/RT). Students learn that a reaction
rate which obeys the Arrhenius equation increases with increasing temperature. At thegeneral chemistry level, very little effort is placed on explaining WHY this is true. However,in covering the kinetic molecular theory of gases in physical chemistry, students learn aboutvelocity and energy distributions and how these scale with temperature.

Despite theadditional chapter of material, and week of class time, when asked to explain WHY a given
reaction rate increases with temperature many students present flawed responses. The mostcandid of these responses is simply “because that is what we were taught in generalchemistry,” others respond mathematically by explaining the Arrhenius equation itself andwhy k increases as T increases. Two typical responses involve the potential energy profiles(see Fig. 7.1) common in all general and physical chemistry text books. Students state thateither the reactant potential energy raises or the transition state potential energy lowers as
temperature is increased. To clarify what was meant by this many students were asked tosketch how the profile changed, a typical sketch is seen in Fig. 7.2.

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Potential Energy

Transition State

Ea

Reactant
Product

Reaction Progress
Figure 7.1
Typical reaction energy profile showing potential energies for the reactant,product, and transition state.

120

Figure 7.2
temperature.

Student sketch of how potential energy of transition state varies with

As one can imagine, there are many other misconceptions and difficulties associatedwith a first semester physical chemistry course. However, as stated in the introduction above,
only a select few will be addressed here. In the light of the problems presented above, thenext section will pinpoint the various student misunderstandings and present models which
can be used to address these issues.
7.2.2

Physical Models
All of the examples presented in the previous section involve concepts first presented

to students during introductory general chemistry. Therefore, when presented during thephysical chemistry course, all students have had some previous exposure to the material. It is121
likely that students either did not fully understand these concepts when they were first
confronted with them or they learned them in such a way that after several semesters they nolonger have a working knowledge set. In either case, our goal is to develop a model to help
the students understand the concepts at hand and gain some connection which they can accessat later times. To do this, we set out to provide active learning strategies which have beenshown to improve learning and knowledge6,8,15,16 while at the same time providing the studentwith some “real world” connection to the material. This “real world” connection will be
addressed further for each individual model in the next section.
7.2.3

Tutorial Design
Tutorial use is on the rise in both Chemistry and Physics. The two most popular

published tutorial series in these disciplines are the Process Oriented Guided Inquiry
Learning (POGIL)17 series and the Tutorials in Introductory Physics.18 Both of these series
were reviewed and fundamental structures of each were utilized in our work. The threetutorials presented here differ from both of these published series in that our tutorials aredesigned around a physical model or computer simulation.
7.2.3.1 First Law of Thermodynamics
Throughout the classroom observations and student interactions presented in section
7.2.1 above, it was clear that many students either possess a very weak understanding or nounderstanding at all of the fundamental concepts of the First Law of Thermodynamics. There
are many stock demonstrations and everyday experiences that can be used as a model to help
students connect with these fundamentals. One common classroom demonstration is the Fire
Syringe. This demo consists of a glass cylinder and piston sealed with o-rings. A piece of
flash paper or tissue paper is placed inside the cylinder and the piston is quickly depressed.
Students observe that the piece of paper ignites due to the increased temperature of the gas

122trapped inside the cylinder. This model provides a great visual connection of an adiabatic
compression for students as they can readily observe the fire ball. However, the cost of these
instruments is around $30 each and no student will have access to these models outside of theclassroom setting.
The same adiabatic compression can be performed using a simple bicycle tire pumpwith the outlet hose blocked off. In this case students can feel the barrel of the pump get hot
as the plunger is depressed. This does not have the visual effect of the fire syringe but
students still get a hands-on evaluation of what happens during the change. One main
advantage of using the bicycle pump model is that most students have access to a pumpoutside of the classroom environment. In addition to models for adiabatic compressions, any
compressed air can may be used as a model for adiabatic expansions. In this model students
can feel the can getting cold as the gas is expanded out of the container. At some point inevery student’s life they have used some sort of compressed gas can, many students reportthat they have indeed noticed that the temperature decreased. We feel that this model
provides the best “real-world” connection of an adiabatic process for many reasons. First,
almost every student has already made this observation but most have never thought about itin terms of a thermodynamic process. Second, most students have some sort of compressedgas readily available to them outside of the classroom environment; therefore, once thisphenomenon is put into thermodynamic terms many students will recall this each time theyexperience the phenomenon in their daily life. Lastly, we want to provide in class models
that all students can experience and use. This model provides the most cost effective way toprovide many duplicates for individual groups to use.
7.2.3.2 Second Law of Thermodynamics
The physical chemistry course sequence has long had the reputation as being thehardest chemistry course one will take as an undergraduate. This reputation stems both from123
the abstractness of the concepts presented during this series and the rigorous mathematicalcontent of the material. Traditionally taught physical chemistry courses tend to focus on themathematical aspect of the material and students’ “understanding of the material” is based
primarily on their calculations. This mode of instruction and evaluation does not provide theinstructor or student any insight about the content knowledge of a specific topic. One
example of this is the Second Law of Thermodynamics and its connection with Gibbs
energy.14,19,20
A widely used model in both general and physical chemistry courses to teachstudents about Gibbs energy and its dependence on Enthalpy and Entropy is the rubber band
demonstration. A typical example can be found at this address:
http://www.usm.maine.edu/~rhodes/Goodies/RubBandThermo.html
In this demonstration each student is given a rubber band and they are prompted through aseries of “experiments” in order to determine the change in Gibbs energy, Enthalpy, andEntropy during stretching and relaxation. This model provides a nice every day example togain insight to these thermodynamic properties. An added advantage to using this “realworld” model, instead of a typical chemical reaction, is that in determining the Entropychange students must consider the change in Gibbs energy and the change in Enthalpy. In the
typical chemical equation example students can simply evaluate any change in the number ofmoles or phase in making a determination about Entropy changes.
An additional model similar to the rubber band demonstration is to use protein
folding as an example. However, this model does not provide a “hands-on” system to study
but may help biochemistry students gain a strong connection to the material. In using thisexample students must be focused on the Enthalpic and Entropic changes and not thehydrophobic/hydrophilic effect.

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7.2.3.3 Reaction Kinetics
Traditionally students are introduced to reaction kinetics during the second half of thegeneral chemistry series. Very early in this kinetics material students are presented with theidea of the reaction coordinate and shown reaction potential plots similar to that of Fig. 7.1
above. Students are also introduced to the concept of the temperature dependence of areaction rate and are frequently asked to perform calculations using the Arrhenius equation (k= Ae-Ea/RT). However, throughout our student interactions it became clear that students do nothave a robust fundamental picture for how the temperature change actually affects thereaction on a molecular level. As pointed out above, students try to use the only knowledge
to which they have access when struggling to explain the temperature dependence. This leads
to false explanations of how the increased temperature alters the potential energy of thesystem.
Despite the additional coverage of the Kinetic Molecular Theory of Gases in physicalchemistry, students still struggle in applying molecular collisions to reaction rates. This
material is traditionally presented with multiple equations and plots followed by some 2Dgraphics in a text. This format does not provide students with a visual picture of what is
actually happening at the molecular level during a reaction. To aid in this molecular level
understanding we intend to use a reversible reaction simulation developed by the physics
education technology (PhET) group at the University of Colorado.
The reversible reaction simulation (http://phet.colorado.edu/web-pages/index.html) allows
students to monitor the collisions which take place between reactant molecules and gain avisual picture of how these collisions provide the energy needed to react, see Fig. 7.3. The
simulation provides a variety of additional information to the students as well. As students
raise the temperature of the reaction, they can directly see this impact on the distribution of
kinetic energy and speed in two independent plots. In addition to providing a visual picture

125
for the students to connect molecular motion to reaction rate, the simulation also provides aformat for collecting temperature dependent data. A built in stop watch and count of reactant
and product molecules allows students to record number of molecules and time data. These
data can be used find the rate constant (k) of the reaction.

Rate constants at various

temperatures can be measured and used to generate the Arrhenius parameters (A and Ea)
generally given on problem sets and homework.

A

B

Figure 7.3
Screen image of reversible reaction simulation showing a potential energy
plot with several reactant molecules. Kinetic energy and speed distributions are also plotted
for the molecules shown.

Other kinetics simulations exist for student use; however none clearly display theactual molecular motions leading to reaction. Several examples are presented below.
http://www.chem.uci.edu/undergrad/applets/sim/simulation.htm

126
http://cheminfo.ou.edu/~mra/Kinetics/HBr.htm
http://jchemed.chem.wisc.edu/JCEDLib/WebWare/collection/reviewed/WW007/index.html
http://www.jce.divched.org/Journal/Issues/2002/May/abs638.html
http://www.chm.davidson.edu/ChemistryApplets/kinetics/ReactionRates.html

In many of these simulations, molecular collisions are shown and students can vary thetemperature in order to observe its effect. However, this increase is not visually tied to areaction rate. Other programs allow students to make changes in the initial concentrations ortemperature of the reaction and follow the change in reaction rate; however, this is done withgraphical means only.
7.3

Testing
Based on the issues uncovered during classroom observations and student interviews

tutorial worksheets were developed. As stated above, these worksheets are centered around aphysical model or computer simulation. Each individual tutorial is designed to assist students
in building up an understanding of several concepts which ultimately tie into a larger concept.
The prepared tutorials were tested on a volunteer basis with students enrolled in the physicalchemistry course. Students met in small groups (3-4 total) and each session was audio
recorded. The tutorial sessions were scheduled after the course instructor covered all thematerial pertaining to the individual topic. Each session was placed before the class exam
covering the material; this placement provided incentive for student participation as they
were told that it would be a good review of the material they had covered.
The testing phase of the tutorial development began during the Summer 2005
semester and has continued through the Fall semester 2006.

During each semester

modifications were made based on student feedback and our observations. This section
reviews the testing phase and addresses the individual components of the tutorial separately.

127
Each portion of the tutorial will be outlined in detail and examples of observations andstudent discussions will be provided.
7.3.1

Scoring Rubric
All of the pre, post, and exam questions used in the testing and implementation

phases are scored using one of two rubrics. The pre and post quizzes contain two different
types of questions. There are initial questions which are used to gauge student understandingof the basic concepts underlying the main concept being addressed. Each quiz contains one
detailed question which asks students to explain the thermodynamic or kinetic reasoning
behind some process or observation. The initial questions on the pre/post quizzes are scoredwith the rubric presented in Table 7.1 below. This rubric provides a three-point scale (fromzero to two) to determine the correctness of the student response. The detailed pre/post quiz
questions as well as all of the exam questions (covered in 7.3.5) are scored using the rubric
presented in Table 7.2 below.
Table 7.1

Grading rubric used for introductory quiz questions.
RubricScore
01
2

Criterion
Student has no idea or student response is totally incorrect.
Student responds correctly to question but provides
incorrect reasoning.
Student responds correctly to question and provides
correct reasoning.

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Table 7.2

Grading rubric used for detailed quiz questions.
RubricScore

Criterion

0

Student has no idea or student response is totally
incorrect or irrelevant as compared to the expert responseon the central concept(s).

1Student response includes some aspects of the expert
response on the central concept(s) but major aspects ofthe expert response on the central concept(s) are missing
or incorrect.

2

Student response matches expert response on the central
concept(s) but with one important aspect of the central
concept(s) missing or incorrect.

3

Student response essentially matches expert response on
the central concept(s) but some of the details concerning
the central concept(s) are missing or incorrect.

4

Student response matches the expert response on thecentral concept(s).

This rubric scores each response on a five-point scale from zero to four. A high numericalvalue indicates that a student’s response closely matches an expert response on the central
concept(s) addressed in the question. A low numerical value indicates a poor match with anexpert response.
7.3.2

Pre Tutorial Quizzes
In order to gauge the incoming knowledge base of the students as well as any

learning gains associated with performing the individual tutorials we administer a pre-tutorial
quiz. Students are given about 10 minutes to complete the quiz individually before beginninggroup work on the tutorial.

In the early testing phases the pre quiz was used as an

introduction to the material being covered as the tutorials were not tied directly to the course
itself. These quizzes mainly addressed the introductory material and definitions that students
would need to perform the tutorial itself and were not used in measuring learning gains
associated with the tutorial. Beginning with the Fall 2005 semester, the tutorials were tied to129the course material. Tutorials were scheduled after the specific material was covered in
lecture but before the exam covering the material. This allowed us to gauge the students’incoming knowledge after completing the lectures, reading, and problem sets.
7.3.2.1 First Law of Thermodynamics
The pre-quiz for the First Law of Thermodynamics tutorial assesses students’incoming knowledge about work, heat, and their connection to internal energy. A copy of thequiz appears in Appendix B1. The first question appears in two parts; the first part isdesigned simply to gauge the students understanding of the sign or wording conventions
associated with work. Students are asked whether work is done ON or BY as gas that isbeing compressed. The second part of question one addresses the thermal energy exchange
during the same compression. Here students are asked if there is a transfer of thermal energy
during the compression, the question states that the cylinder in non-insulated. The data fromthis first question (covered below) is used to ensure that students understand these individualcomponents so that when we review responses to more detailed questions we can analyze theoverall concept itself. In the second question, students are given a scenario of an insulated
cylinder containing an ideal gas. Students are asked how the internal energy and temperatureof the gas are affected by a compression of the gas.
The results of the pre-quiz are presented in Table 7.3. Here we see that over 85% of
the students correctly respond that work is done ON the gas in question 1a. In question 1b
student scores are split at ~40% between students who correctly respond that thermal energy
is transferred out of the system and students who do not respond correctly for a variety ofreasons. This first question tells us that most of the students can correctly identify when work
is done ON or BY a gas during a process but less than one-half understand the thermal energy
transfer associated with this compression. In question 2 we see that nearly 50% of the student
responses are scored as a one on our rubric (Table 7.2). This indicates that students are

130
missing many of the important aspects of the First Law concepts associated with this ideal
gas compression after typical course instruction, reading, and problem sets.
Table 7.3
First Law of Thermodynamics pre-quiz results. Data reflects percentage ofstudents with each individual rubric score. Questions 1a and 1b are scored using Table 7.1,
question 2 is scored using Table 7.2.
Rubric Score

Question
N = 28

0

1

2

1a

10

4

86

1b

39

18

43

2

0

46

32

3

4

18

4

Additional important findings during the scoring of question 2 are the misconceptions
held by the respondents. Greater than 30% of the responses show some indication that thestudent does not distinguish between heat (q) and temperature (T), this misconception has
been observed in many previous research studies.11-13,21 The majority of these responses
contain statements equivalent to the following quote: “this is an adiabatic compression,
therefore q = 0 and the temperature remains constant”. In addition to the misconception thatheat and temperature are equivalent, greater than 40% of the responses reflect student
reliance on the Ideal Gas Law equation (PV = nRT) in addressing the temperature change
upon compression. A similar reliance on the Ideal Gas law has been observed in previous
studies.19,22 The conclusion of many of these responses is that “the pressure and temperature
are directly related and when pressure increases so does the temperature of the gas”. Many
students add in that temperature and volume are also directly related (indicating thattemperature should decrease as volume decreases) but that “volume changes less thanpressure so the temperature still increases”.

Some combination of these two main

misconceptions make up the reasoning behind the majority of the low rubric scores presented
for question 2 in Table 7.3.

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7.3.2.2 Second Law of Thermodynamics
The pre-quiz for the Second Law of Thermodynamics tutorial assesses students’incoming knowledge about heat, entropy, and the temperature dependence of the Gibbs
energy. A copy of the quiz appears in Appendix B3. The quiz uses an example of an ice
pack consisting of two chemicals which when mixed together get cold. In the first question
students are told that the pack feels cold to the touch, they are then asked if this means that
thermal energy (heat) is going INTO the reaction mixture or OUT OF the reaction mixture.
We ask this question knowing that many students struggle with the concept of heat. The
second question asks the student to determine the Entropy change as the reaction proceeds.
In this question students are instructed to use the sign of the Gibbs energy (the reaction is
spontaneous) and Enthalpy (endothermic reaction) along with the Gibbs equation in solving
for the Entropy change. This question provides information about how students connect theindividual thermodynamic properties together. The last question asks students about thetemperature dependence of the reaction based on the information they have about thethermodynamic properties.

This question provides information about a students

understanding of the balance between Enthalpy and Entropy when considering a reactions
spontaneity.
The results of the pre-quiz are presented in Table 7.4. We see in the results from thefirst question that ~25% of the students still incorrectly address the thermal energy transfer.
The significance of this result is heightened when we consider that this quiz was given nearly
halfway through the course and yet one-quarter of the students still struggle with the conceptof heat. In question 2 we see that more than 50% of the students scores (rubric score = 1)
reflect major conceptual aspects missing in their understanding of entropy change.

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Table 7.4
Second Law of Thermodynamics pre-quiz results. Data reflects percentage
of students with each individual rubric score. Question 1 is scored using Table 7.1, questions
2 and 3 are scored using Table 7.2.
Rubric Score
Question
0

1

2

3

4

1 (N=31)

23

3

74

2 (N=31)

0

52

16

13

19

3(N=14)

0

43

36

7

14

Question 3 was added to the quiz after the Spring 06 semester in order to gain more detailed
information about the temperature dependence; it is for this reason that the total number of
responses is less than the previous two questions. In this question we see that more than 75%of the students (rubric score ≤ 2) have a weak understanding of the effect of temperature on
the spontaneity of the reaction.
In scoring the pre-quizzes we also observe two main misconceptions held by thestudents. First, many students (>15%) relate the reactions overall spontaneity solely to theincrease in Entropy (∆S > 0) and not the Gibbs energy. This is true only when considering∆Suniverse, not ∆Ssystem.14

This belief can lead students to a misunderstanding of thetemperature dependence of the Gibbs energy (hence, the reaction spontaneity) because they
do not view spontaneity as a balance between Enthalpy and Entropy. In addition to thespontaneity misunderstanding, more than 15% of the students state that “because the ice packis cold it must be giving up heat (thermal energy)”. This misunderstanding of the thermalenergy transfer leads to an incorrect determination of the Enthalpy change for the process.

133
Many of the low scores on questions 2 and 3 are mainly due to some combination of the twoissues presented here.
7.3.2.3 Reaction Kinetics
The pre-quiz for the Reaction Kinetics tutorial assesses students’ incoming
knowledge about what conditions effect reaction rate and how the reaction rate is dependent
on temperature. A copy of the quiz appears in Appendix B5. This quiz is designed to gauge
the students understanding of reaction rate at the molecular level. The first question asks
students what conditions are required in order for a reactant molecule to become a productmolecule. This question provides information about what each student finds important for areaction to occur. In the second question, students are asked specifically if the energy barrierheight, on the figure provided, changes as a function of temperature. This question came
directly out of our observations that students use this line of reasoning when explaining thechange in reaction rates. In the last question, students are asked to explain why a specificreaction rate increases with increasing temperature.
The results of this pre-quiz are presented in Table 7.5. Here we see that according toquestion 1, 75% of the students (rubric score = 2) have a good understanding of what isrequired for a reactant molecule to become a product molecule. Most responses reflect thatstudents understand that the reactant molecules must surmount the reaction barrier (activationenergy, Ea) at the transition state in order to produce products. However, in question 2
student responses are split at 46% between those that believe the energy barrier itself lowers
as temperature increases (rubric score = 0) and those that state that the barrier is independentof temperature (rubric score = 2). Question 3 shows that nearly 90% of the responses (rubric
score ≤ 2) reflect a poor understanding of why a given reaction rate increases with increasing
temperature. Many of these students do make some connection to an increase in energy but
fail to connect this energy increase to the reaction rate correctly.

134

Table 7.5
Reaction Kinetics pre-quiz results. Data reflects percentage of students witheach individual rubric score. Questions 1 and 2 are scored using Table 7.1, question 3 isscored using Table 7.2.
Question

Rubric Score

N = 24

0

1

2

1

25

0

75

2

46

8

46

3

0

42

46

3

4

12

0

The main misconception addressed in this quiz is the belief that a reaction barrier(activation energy) or transition state is temperature dependent. While 46% of the student
responses reflect this belief, it is not surprising after talking with students. While chemistry
students are introduced to the reaction energy profile (Fig 7.1) in general chemistry and use
this type of diagram often, it is clear that few students actually understand what the diagram
represents. Many students state that, “as temperature is increased the energy of the reactants
is increased”. They then go on to explain that this “increased energy raises the left side of thegraph (reactant potential energy) essentially lowering the activation energy”. Despite past
instruction in both general and physical chemistry few student correctly connect thetemperature increase to an increase in the kinetic energy of the molecules.
7.3.3

Tutorial Worksheets and Models
Each individual tutorial worksheet and associated model is designed to help a student

gain a stronger connection with the concepts at hand. To do this, the individual components
which make-up the concept as a whole are addressed separately. This structure allows
students to uncover the principles associated with each component before tying them together135
in understanding the larger concept. In contrast to the pre and post quizzes, students work ingroups of 3-4 on the tutorials. Groups are encouraged to discuss all opinions concerning theindividual questions and concepts before writing their answers. Each tutorial is designed totake about 40 minutes so that they will fit within one 50 minute class period.
7.3.3.1 First Law of Thermodynamics
The First Law tutorial is designed to assist students in learning the fundamentals ofwork and heat and how these two components are related to the internal energy of a system.
The tutorial begins with a prediction section designed to help engage the students. The
tutorial worksheet then goes on to individually address both work and heat for an expanding
gas before asking students to connect these together in explaining changes in internal energy.
The entire tutorial worksheet can be found in appendix B2.
To begin, students are shown a figure of a can covered with a balloon. Students are
told that the can contains a gas at high pressure and that the gas will be expanded into theballoon. Students are asked to predict, and explain, what will happen to the temperature of
the gas inside the can during the expansion. Once students come to an answer, each group is
given a can and balloon to test their prediction. Through observation of the individual
groups, most students easily predict that the gas, and the can, will get cold. Some students
qualify their answer with the simple fact that they have felt this before. Despite their correct
predictions, many groups struggle to correctly explain WHY the gas gets cold. Nearly every
group begins their explanation using the ideal gas law. Individual students will point out how
a decrease in pressure will lead to a decrease in temperature. Other students will counter
these explanations with the fact that the volume of the system (can AND balloon) also
increases. It is at this point when groups begin to realize that the ideal gas law may not fully
explain this situation. A few groups make the leap to using the First Law with no outsideadvisement; most groups require some assistance to start down that path.

136
After testing their predictions, groups start their investigation of work. The tutorial
worksheet shows two cylinders sealed with pistons which contain the same ideal gas. Eachpiston has a block sitting on top. One cylinder is insulated and the other is not. The block isremoved from both pistons and the groups are asked if work is done ON the gas or BY thegas after removal of the block. Observations show that it does not take much time (<1minute) for all groups to conclude that with the reduced external pressure the piston moves up
as the gas expands. All students correlate this expansion with the gas DOING work. Verylittle discussion takes place in any group and no group members express a belief that work
was done ON the gas.
After coming to a consensus on the work question, students are asked about thetransfer of thermal energy in the two systems after the blocks are removed. If there is atransfer of thermal energy, students are asked to draw an arrow on the diagram indicating thedirection of the transfer. It is at this point that we see students really starting to discuss theirown beliefs and trying to defend those beliefs. The two cylinders are labeled as isothermal
and adiabatic, many students begin their explanation by defining what these terms mean.
Students immediately point out that there is no thermal energy transfer for the insulated
cylinder, the one labeled as adiabatic. In most groups a few minutes of discussion surroundthe isothermal case. It is usually pointed out by one group member that there must be atransfer of thermal energy and the discussion centers around the direction of this transfer.
Groups eventually decide that if the gas is DOING work (reducing the energy of the gas) then
the transfer of thermal energy must be counter to this and thermal energy ENTERS the gas.
At this point, very few groups or individuals have connected any of these changes with thetemperature of the gas.
The last two questions ask the groups to explain how the heat and work involved inthese expansions affect the internal energy of each gas. Question 3 first asks about theinternal energy of gas A, the isothermal expansion. All groups tend to start out by one of two

137
methods. The first method is when one of the group members simply states that in an
isothermal process the change in internal energy should be zero, at this point usually no
explanation is provided other than they know this is true. The second method has groupmembers looking back at questions 1 and 2 and writing down their previous results for theheat and work associated with gas A. In either case, all groups tend to discuss how if the gas
is DOING work after the block is removed than this will tend to lower the internal energy.
They then go on to state that the temperature will also lower. This line of discussion leads
groups to state that in order for the temperature, and internal energy, to remain constant (it is
an isothermal process) then the thermal energy entering the gas must be equal to the energy
lost due to work.
The last question on the tutorial (question 4) asks about the internal energy of gas B,
the insulated (adiabatic) system. Most groups quickly reach consensus on this question. All
groups begin by pointing out the fact that in this system the energy lost due to the work done
BY the gas can not be “replaced” by thermal energy entering because the cylinder isinsulated. This leads to the conclusion that the internal energy must be reduced because thegas is doing work and that this “loss of internal energy”, means the temperature of the gas is
less.
During the discussions surrounding the last question most groups connect the internalenergy and temperature reduction of the adiabatic system back to the air can that they
originally made a prediction on. This connection ultimately leads to some brief discussionthat a process can be adiabatic even if the container (cylinder or can in this case) is not
insulated. It seems that before this discussion, most students simply relied on being told thata given process occurred adiabatically or isothermally and never really considered what thatmeant. In section 7.3.4 (post-quiz), we will see how the discoveries made during this tutorial
affect the individual student scores.

138
7.3.3.2 Second Law of Thermodynamics
The Second Law tutorial is designed to assist students in learning the fundamentals of
Gibbs energy, Enthalpy, Entropy, and how these components are related to the spontaneity ofa process. The tutorial begins with a prediction section designed to help engage the students.
The tutorial worksheet is designed around using a simple rubber band to determine these
thermodynamic properties. The entire tutorial worksheet can be found in appendix B4.
To begin, students are shown a figure of a rubber band being stretched by a weight.
Students are asked to predict what happens to the height of the weight as the rubber band isheated. Instinctively all groups and individual students respond that the weight will lower
because “as you heat the rubber band it will stretch”. When asked how they “explain” this,three general responses are given. Many students state that the rubber molecules can “movearound more when heated and therefore the band can stretch”, or that “when you heat theband the rubber gets soft and the weight stretches it more”. A large fraction of students
simply state that, “I don’t know why the band should lengthen I just feel that it should”.
Once the groups come to some conclusion they are allowed to test their prediction using amodel set-up exactly like the diagram, students use a heat gun to warm the rubber band. All
students are impressed and confused when they observe that the rubber band contracts andthe weight is lifted as heat is applied. Immediately students begin to ask WHY this happens.
At this point students are told that once they work through the tutorial they should be able toanswer that question of WHY for themselves.
For the tutorial, each student is given their own rubber band and students work ingroups of 3-4. The tutorial begins by asking the students if a stretched rubber band relaxes
spontaneously when released.
relaxation is spontaneous.

All students come to the same conclusion that yes, theNext students are asked, based on their response about the

spontaneity, if the Gibbs energy of the rubber band increases or decreases in going from the139
stretched to the relaxed position. This first question begins brief discussions about the sign of∆G for a spontaneous process. Most students quickly remember that ∆G is less than zero fora spontaneous process, so “the Gibbs energy decreases as the band is relaxed”.
In the next step of the tutorial students determine the Enthalpy change during thestretching/relaxing of the rubber band. Students are instructed to place the rubber band flat
against their lip and to note any change in the temperature as they stretch and relax the band.
As each student performs this procedure, discussions begin about if the band is hot or cold
when stretching and relaxing. After a few minutes all groups conclude that the band iswarmer when it is being stretched and cooler when it is being relaxed. The second question
on the worksheet asks if thermal energy is entering or leaving the rubber band as it isrelaxing. Students begin to state that, “when I relax the band I feel that it is cooler on my lip,this means that thermal energy is leaving my lip and entering the rubber”. One or two
students struggle to understand how feeling the band is cooler means that thermal energy(heat) is entering. This confusion was also present during the air can tutorial but to a larger
extent. In all cases, the correct explanation was discussed with another group member before
continuing on.
Question 3 now asks about the sign of the thermal energy transfer for the relaxation.
With little discussion, groups conclude that “if thermal energy is entering the rubber bandthen the sign of q (thermal energy exchange, heat) for the band is positive”. They are thenasked in the same question whether the enthalpy of the rubber band increases (∆H > 0) or
decreases (∆H < 0) for the process. This portion of the question sparks discussion in allgroups as they try to connect the transfer of thermal energy to the change in Enthalpy.
Students search their brains to remember equations which relate the two variables; others try
to reason out connections by thinking about endothermic and exothermic reactions.
Ultimately all groups conclude that if qband > 0 than ∆H > 0. Before continuing on, theworksheet prompts students to tabulate their data about the changes in both Gibbs energy and140
Enthalpy for both stretching and relaxing. Most students realize that for the stretchingprocess they simply need to flip the sign for the Gibbs energy and Enthalpy determined forrelaxation.
At this step the student are asked about the change in Entropy for the rubber band forboth stretching and relaxing.

Unlike other chemical examples, students do not have achemical equation to refer, which allows them to view a change of state or calculate thenumber of moles. Here they must use the Gibbs equation (∆G =∆H – T∆S) to determine how
the Entropy changes. The students are now forced to look at the equation for Gibbs energy
and relate the signs of the variables they know to what the sign for entropy should be.
Student discussions begin with either the stretching or relaxing case. The results of one suchdiscussion are summed up by an individual’s statement that “for relaxation the Gibbs energy
is negative (spontaneous) and the Enthalpy is positive (Endothermic) so the only way to get anegative Gibbs energy is if the Entropy is positive”. A few groups also concluded that inaddition to ∆S being positive, T∆S must be larger than ∆H. Other groups needed to be asked
if the sign of ∆S was the only requirement, only one group needed more than this simple hint.
The last portion of the worksheet asks students if they can create conditions underwhich a rubber band will spontaneously lengthen (ie: without being pulled on). In doing thisstudents are told to consider the values of ∆H and ∆S to be temperature independent. With
this task at hand, groups begin to discuss how they can change the sign of ∆G for stretchingfrom positive to negative, which would indicate a spontaneous process. With the Gibbs
equation in front of them as well as the signs for all of the variables, most groups quickly
decide that at room temperature (for stretching) the T∆S term was larger than the ∆H term
making ∆G positive. Therefore, if they lower the temperature (T) to the point where ∆H islarger than T∆S the sign on ∆G will be negative. With this conclusion students begin to
discuss how this relates to the opposite effect seen when the rubber band was heated andcontracted raising the weight.

141
7.3.3.3 Reaction Kinetics
The Reaction Kinetics tutorial is designed to assist students in learning thefundamentals of reaction rates and their temperature dependence.

The tutorial uses a

computer simulation depicting a potential energy plot and a variable number of reactant
molecules.

Students are informed that this reaction model simulates a cis-transisomerization. The tutorial worksheet provides basic simulation instructions (shown in boldon worksheet) as well as guided observations and questions. The entire tutorial worksheet canbe found in appendix B6.
To begin, students are instructed to insert a given number of A molecules (reactants)
into the simulation and observe how an A molecule becomes a B molecule (product).
Working in groups of 3-4 students begin to note that the A molecules undergo many
collisions and a few occasionally jump up to the height of the reaction barrier but do not crossto become a product. After about 2 minutes of observation, students begin to observe that a
few A molecules reach the reaction barrier and are traveling in the correct direction to
become B molecules. These observations spark discussion that it is not simply that the A
molecules have enough energy (ie: they are higher than the barrier) but they must move in theproper direction (ie: the cis-trans isomerization requires twisting about the central bond axis).
In the next step the effect of raising the temperature is investigated. The simulation
easily allows students to raise the temperature and observe the effects. All students state that“the molecules begin moving faster and colliding more often; this makes them jump over thebarrier faster”. Students are asked specifically if raising the temperature had any effect on theheight of the reaction barrier itself. Some students raised the temperature again just to be sureof their answer but ultimately all students’ state that the barrier height does not change.
In the next step students use the built-in stop watch to record how long it takes for the
first B molecule to be formed when 50 A molecules are inserted at 350 K. This provides a142
number for comparison in a later step. With molecules inserted at 350 K students are
instructed to sketch and discuss the plot of the Number of Particles versus Kinetic Energy
shown on the screen of the simulation. Most groups spend on average about 5 minutes
discussing what the plot means and eventually come to the conclusion the most of themolecules have a small range of energies and only a few vary from that range, shown as asmall tail to the right on the plot.
Following this procedure at 350 K the students are asked to predict if the first B
molecule will be formed faster at 750 K (compared to 350 K). Groups then run the simulation
at 750 K and make their observations. The tutorial now asks how the time to form B
compares between the 350 and 750 K cases as well as how the collision rate of molecule Achanges. Groups quickly conclude that B molecules form faster at 750 K and the collision
rate of the A molecules is higher at 750 K. Question 10 helps to focus the students at thispoint. The tutorial points out that, for the forward reaction, the equation for the rate offormation of molecule B is d[B]/dt = kf[A]. Students are then asked how the rate coefficient(kf) varies from 350 K to 750 K, and to explain this difference in terms of the molecularmotions. During the discussion of these questions students begin to start connecting all thepieces together. Students state that “both times we added the same number of A molecules so[A] is the same but at 750 K B formed faster, so this must mean that kf is bigger at 750 K”.
Others point out that “the molecules start going crazy and colliding a lot at 750 K so they getover the barrier faster”.

After several minutes some groups start to connect collision

frequency to the rate coefficient, others need a little assistance and are asked about therelationship between collision frequency and kf.
At this point the students are asked to sketch the Number of Particles versus Kinetic
Energy plot from the simulation at 750 K and compare this to their predicted plot. Herestudents begin to discuss why the plot gets wider and the peaks at the lower energies decreasein height. Students’ comments reflect that they are beginning to connect the increase in143
temperature to a “larger range of kinetic energies”. Lastly the tutorial asks how the plots at
350 and 750 K compare and what this indicates about the TOTAL energy at eachtemperature. Most students have already discussed the similarities and difference in the plots
during the previous question and tend to focus on the total energy difference. A few students
ask, “what do you mean by total energy, you mean kinetic plus potential energy?” Onceclarified, all groups conclude that the total energy is greater at 750 K than at 350 K and thatthe potential energy at both temperatures is identical.
It is during these final discussions that many groups begin to see the connections
between the kinetic energy, molecular collisions, and increased rate. The understanding ofthese connections as well as the belief that the reaction barrier height changes withtemperature will be investigated on the post-quizzes in the next section.
7.3.4

Post Tutorial Quiz
In order to quantify any changes in student understanding of the topics covered in thetutorials we administer a post-tutorial quiz. The questions on these quizzes are identical tothose administered on the pre-quiz. This allows direct comparison of student scores andfilters out any bias due to question wording or context. Students were given the quiz
immediately after finishing the tutorial worksheets, quizzes were not part of the group work.
Each group of students was given as much time as necessary to complete the post-quiz,
however, no student took more than 5 minutes to complete their quiz.
7.3.4.1 First Law of Thermodynamics

The pre-tutorial quiz in section 7.3.2.1 reflected the level of understanding of several
fundamental topics connected with the First Law of Thermodynamics. Here we will outline
the effect on students’ understanding, using the same topics and questions, after use of the144tutorial designed to cover these topics. A copy of the post-tutorial quiz can be found inappendix B1.
For the first part of question 1 on the pre-quiz (see Table 7.6), 86% of the responses
reflect students’ understanding that as a gas is compressed it has work done ON IT. This
number drops to 82% (a change of one student) on the post quiz. In looking at how theindividual students move from pre to post we see that 2 of the three students who initiallyscored zero remain at zero, the third moved from zero up to two. The one student who scoredone on the pre-quiz moved down to zero on the post. Two of the students scoring two on the
pre-quiz drop down to zero on the post. A review of field notes from the various tutorial
sessions reveals that the three students showing declines down to zero on the post-quiz were
all in the same work group. This group was one of the first to participate in the tutorial andthere was a significant language barrier component associated with all three members. On
subsequent tutorial sessions these students did not all work together. In lieu of these few
declines, the post-scores reflect that most of the students understand that a compression does
work ON a gas.
Table 7.6
First Law of Thermodynamics post-quiz results and pre-post gains. Data
reflects percentage of students with each individual rubric score. Questions 1a and 1b arescored using Table 7.1, question 2 is scored using Table 7.2. Average gain is calculated forquestion 2 only.
Question
N = 28
1a
1b
2

Pre
Post
Pre
Post
Pre
Post

0
10
18
39
10
0
0

1
4
0
18
4
46
7

2
86
82
43
86
32
10

Rubric Score
3
4

18
29

4
54

Avg. Gain40%**Note: Each individual student gain is calculated as post score minus pre score; average gainreflects the entire sample group.

145
The second half of question 1 shows a large increase in students’ understanding ofthermal energy transfer during the compression example. The percentage of students whocorrectly answer question 1b has doubled after performing the tutorial. Here we observe no
declining scores and note that two of the three students scoring zero on the post are from thegroup mentioned above. This dramatic increase suggests that the tutorial design and group
discussions do indeed help students in understanding the concept of thermal energy transfer.
Finally, on the second question we calculated an average gain of two points (40%) on
our scoring rubric (see Table 7.2). These average gains reflect the gains achieved by all
students sampled, where individual student gains are calculated as their post score minus their
pre score. Table 7.6 shows that on the pre-quiz, 78% (rubric score ≤2) of the responses
reflect some significant misunderstanding of the First Law concepts. This number drops toonly 17% on the post quiz. No declining scores were calculated and 6 of the 28 responses
reflected no change (4 of these students scored either 3 or 4 on the pre-quiz) after using thetutorial. The size and direction of these rubric scores nicely displays the effect of the tutorialconstruction in helping students gain an understanding of the fundamentals of the First Law
of Thermodynamics.
In addition to the rubric score gains, we see significant changes in student
misconceptions after using the tutorial. During the pre-quiz, 42% of the responses showedthat students were relying on the ideal gas equation when considering the temperature change
upon compression. This number drops to zero after the tutorial session. The percentage ofstudents who equate heat (q) and temperature (T) drops from 32% to 10%, this reflects thedifficulty in students grasping the concept of thermal energy.

146
7.3.4.2 Second Law of Thermodynamics

The pre-tutorial quiz in section 7.3.2.2 reflected the level of understanding of several
fundamental topics connected with the Second Law of Thermodynamics. Here we will
outline the effect on students’ understanding, using the same topics and questions, after use of
the tutorial designed to cover these topics. A copy of the post-tutorial quiz can be found inappendix B3.
In the first question we see that on the pre-quiz (see table 7.7) nearly 75% of the
respondents correctly address the transfer of thermal energy which takes place during thechemical reaction, this percentage increases to 94% after the tutorial. A bigger jump is seen
if we compare the scores from the similar First Law question (pre/post question 1b) where
only 42% responded correctly before the tutorial and 86% afterwards. While there is a
decline of roughly 10% between the post-score on the first activity quiz and the pre-score on
the second activity quiz, the population contained 5 students (12%) who did not participate in
the first activity.

147

Table 7.7
Second Law of Thermodynamics post-quiz results and pre-post gains. Data
reflects percentage of students with each individual rubric score. Questions 1 is scored using
Table 7.1, questions 2 and 3 are scored using Table 7.2. Average gain is calculated forquestions 2 and 3 only.
Rubric Score
Question
0

1

2

1

Pre

23

3

74

N = 31

Post

3

3

94

2

Pre

0

52

16

3

4

13

19

Avg. Gain30%*
N = 31

Post

0

6

10

16

68

3

Pre

0

43

36

7

14
20%*

N = 14

Post

0

7

29

14

50

*Note: Each individual student gain is calculated as post score minus pre score; average gainreflects the entire sample group.
Question 2 asks students about the change in entropy for the given reaction, tocorrectly address this question; students must connect the change in both the Gibbs energy
and Enthalpy using the Gibbs equation. Table 7.7 indicates that only 32% of respondents
correctly address the entropy change (rubric score ≥3) on the pre-quiz. After finishing thetutorial 84% of the responses reflect expert-like connections in addressing the Entropychange. This equates to an overall average gain of 1.5 (30%) on our scoring rubric. In
looking at individual student shifts, only one student showed a decline (from 2 down to 1)
and nine students show no shift (including the 6 who scored a 4 on the pre-quiz). These
overall results show that the tutorial has helped a large fraction of the students connect thefundamental thermodynamic properties of Gibbs Energy, Enthalpy, and Entropy together fora given reaction.

148
Question 3 was added to the pre and post quizzes after the summer 2006 semester inorder to specifically address the temperature dependence of the given reaction and its effecton spontaneity. Table 7.7 shows that only 21% of the students (rubric score ≥3) correctly
identify and address that the reaction is not spontaneous at all temperatures. This number
rises to 64% after completion of the tutorial with an average gain of 1 (20%) on the scoring
rubric. Students with the largest gains on question 3 also showed gains of 2 or more onquestion 2 indicating that they initially struggled with both connecting the thermodynamic
properties together and the concept of the temperature dependence of the Gibbs energy(spontaneity).
In addition to the gains reflected in table 7.7 for questions 2 and 3, student responses
showed declines in the misconceptions present in those responses. On the pre-quiz responses,
5 students (16%) state that the entropy increases for the reaction because “entropy must
increase for a spontaneous process”. After the tutorial only one student (3%) response shows
this belief. The pre-quiz also shows that 16% of the students associate the cold feeling of theice pack as indicating thermal energy leaving the reaction mixture. This number drops tozero after the tutorial.
7.3.4.3 Reaction Kinetics

The pre-tutorial quiz in section 7.3.2.3 reflected the level of understanding of several
fundamental topics connected with Reaction Kinetics. Here we will outline the effect on
students’ understanding, using the same topics and questions, after use of the tutorial
designed to cover these topics. A copy of the post-tutorial quiz can be found in appendix B5.
The kinetics simulation utilized in this tutorial provides a molecular level picture forthe students about what is needed for a product molecule to become a reactant molecule. The
effect of the tutorial can be seen in the post scores represented in Table 7.8. Here we see anincrease from 75% to 88% (rubric score of 2) in the correct responses to question 1 about the149conditions needed to form a product molecule. Only one student’s response did not show
some sign of correctness after performing the tutorial. Field notes indicate that this student
only answered questions during the tutorial session when directly asked by the tutorial leader
and that the other three students in the group excelled at the material.
Table 7.8
Reaction Kinetics post-quiz results and pre-post gains. Data reflects
percentage of students with each individual rubric score. Questions 1 and 2 are scored using
Table 7.1, question 3 is scored using Table 7.2. Average gain is calculated for question 3
only.
Rubric Score
0
1
2
3
4
Avg. Gain
Pre
25
0
75
1
Post
4
8
88
Pre
46
8
46
2
Post
0
0
100
Pre
0
42
46
12
0
3
36%*
Post
0
0
21
21
58
*Note: Each individual student gain is calculated as post score minus pre score; average gainreflects the entire sample group.
Question
N = 24In interviewing students it became clear that many students believe that heating areaction actually affects the potential energy profile of the reaction as indicated in Fig. 7.2 ofsection 7.2 above. Question 2 of the pre-quiz indicates that 46% of the student responses
reflect this belief (rubric score of 0). However, after using the simulation and performing thetutorial this number drops to zero. This dramatic change speaks highly about the visual
nature of the tutorial design and its specific attention to this misconception.
The last question on the pre/post quiz asks students to address the temperaturedependence of a reaction. Initially only 3 students (12%) have a response which somewhat
matches an expert response but lacks an important detail (rubric score of 3), no responses
completely address the question. After completing the tutorial nearly 80% of the responses
yield a rubric score of 3 or more and 58% match an expert response with a rubric score of 4.
This means that after completing the tutorial, a majority of the students can correctly address

150
the temperature dependence of a reaction using the same conceptual connections as an expert.
This results in an overall gain of 1.8 (36%) on the rubric presented in Table 7.2.
The main misconception associated with this material is the temperature dependenceof the reaction potential energy. This is nicely addressed in the results of question 2 where
100% of the students report that the reaction barrier itself is not temperature dependent.
7.3.5

Exam Questions
Based on the results presented in the previous sections there is no doubt that the

tutorials have a large positive impact on student responses. However, this data may be biasedby the fact that the post-testing was performed immediately after performing the tutorial.
This test method does not reflect any impact on students longer term comprehension andunderstanding of the material contained within tutorial. In order to gauge the effectiveness ofthe tutorial after some period of time we set out to analyze students responses on examquestions placed on the in-class exams during the Spring 2006 semester. This testing format
also allows a comparison between those students’ scores who participated in the tutorials to
those who did not, on average about 50% of the class did not participate in the tutorials.
However, for reasons that do not need to be covered in this thesis, the exam questions
submitted to the course instructor were not implemented on the exams. There was at least
one semi-conceptual question on each exam which will be reviewed here. In the course
implementation and evaluation section (7.4 below), common exam questions are analyzed forboth a test and control group. This analysis will allow some determination of longer term
effects of the tutorial use as well as providing a direct comparison with a control group that
did not participate in the tutorials.
The first in-class exam covers material through the First Law of Thermodynamics.
The exam contains only one conceptual question which can be loosely tied to students’fundamental understanding of the First Law concepts, this question is presented below.

151
Define heat and work. Why is it incorrect to speak of heat or work associated with a system?
While this question will provide data about students’ definition of heat and work, it will nottell us anything about their connection to changes in internal energy for a given process. For
this first exam 14 of the 28 students in the class participated in the First Law (Air Can)tutorial. This exam question was scored using the rubric in Table 7.1 with a maximum scoreof 2. The average score for the 14 students who participated in the tutorial was 1.6, theaverage score for the 14 non-participants was 1.4. These numbers indicate no statisticaldifference between the two groups of students and provide us no gauge of the students’conceptual knowledge of the First Law of Thermodynamics.
The second class exam covered material through the Second Law ofThermodynamics. On this exam the only conceptual question involving Gibbs energy comesas the second part of a calculation. The first part of the question tells students to consider agiven reaction and to calculate the change in Gibbs energy given a table of ∆H°f and S° data
for the molecules which participate in the reaction. After students perform the calculation
they are asked in part B:
Will this reaction be spontaneous at all temperatures? Explain.
It is this portion of the question that we are interested in. However, a students’ response will
be greatly affected by their calculation from part A of the question. Therefore, we only
compare student responses whose calculation in part A is correct. When scoring thesequestions we find that the average scores for both sets of students (9 with tutorial
participation and 8 with out) are identical at a value of 1.3.
The fourth exam (the third exam contained material not covered in any of thetutorials) during the semester covered the topics of the Kinetic Molecular Theory of gasses
and Reaction Kinetics. On this exam, one conceptual question appears (which is very similar
to the actual submitted question) which will allow us to gauge students understanding of thetemperature dependence of a reaction rate.

152
Explain why for thermally activated reactions, an increase in temperature results in an
increase in the rate of the reaction. Provide a molecular level explanation for what is goingon.
There were 10 students who participated in the kinetics tutorial and 13 students who did not.
This question was scored using the five-level rubric in Table 7.2. The average score for thegroup who performed the tutorial was 3.5, for the other group the average was 2.6. These
numbers reflect a statistically significant difference (P value = 0.005) in the responses of thetwo groups. Responses from students who performed the tutorial addressed most of the
major components correctly, while those in the group not participating in the tutorial lacked
one or more vital components.
This data from this last exam question shows us that we can indeed measure adifference in scores on a conceptual question which pertains to the concept(s) at hand.
During the next section we will analyze a series of these exam questions as we compare one
section of a physical chemistry course which took part in all three tutorials to a section which
did not use any tutorials.
7.4

Course Implementation and Evaluation
The learning tutorials presented in this chapter have been designed to target difficult

or often misunderstood concepts which are fundamental in a physical chemistry course.
These tutorials are meant to enhance the lecture material for the course, not replace it.
Therefore, the tutorials should be integrated into the curriculum at an appropriate time toprovide the most benefits for the students. This integration can take place in two fashions.
First, the tutorials can be used very early on in the introduction of these topics in order toprovide a launch pad for the rest of the material. Or second, they can be place just after thenormal coverage of the topics and serve as an enhancement and review of the lecture materialon the topic.

153
The final versions of the tutorials, presented in Appendix B, were integrated into the
Physical Chemistry course at CU-Boulder during the Spring 2007 semester. Each tutorial
was performed in class and the tutorials were inserted after the instructor covered the lecturematerial on the given topics. Students were given participation points for performing thetutorial and associated quizzes.
7.4.1

Pre/Post Analysis
The pre-quiz was taken during the first 10 minutes of the class period in which thetutorial was performed. The post-quiz was taken during the first 10 minutes of the classperiod immediately following the tutorial class period. Data from both quizzes will bepresented and discussed here; copies of the individual quizzes can be found in Appendix B.
The First Law of Thermodynamics tutorial took place during the fourth week of thesemester, roughly 2 weeks prior to the first exam in the course. Table 7.9 shows the pre andpost quiz scores as well as the average gain for question 2. Here we see that all 26 students
correctly answer question 1a about whether work is done ON or BY as gas being compressed,
the tutorial had no affect on this question. On question 1b, about the thermal energy transfer,
we see an increase in the percentage of correct responses (rubric score = 2) from 69% before
the tutorial to 85% after. Even after performing the tutorial we still see 15% (rubric score ≤1) of the students struggling with the correct conceptual understanding of thermal energy
transfer for a given process. Question 2 asks students about the temperature and internalenergy change upon an adiabatic compression. Here we see over 30% of students scoring 3(responses essentially match an expert response) or above on the pre-quiz. After performing
the tutorial 81% of the responses are scored as 3 or above. The average gain for this group of
students is

154
Table 7.9
First Law of Thermodynamics pre/post-quiz results and pre-post gains. Data
reflects percentage of students with each individual rubric score. Questions 1a and 1b arescored using Table 7.1, question 2 is scored using Table 7.2. Average gain is calculated forquestion 2 only.
Question
N = 26

Rubric Score

0
1
2
3
4
Avg. Gain
Pre
0
0
100
1a
Post
0
0
100
Pre
19
12
69
1b
Post
3
12
85
Pre
35
23
11
23
8
2
36%*
Post
0
4
15
35
46
*Note: Each individual student gain is calculated as post score minus pre score; average gainreflects the entire sample group.
1.8 (36%) , slightly lower than the previous gain of 2.0 (40%) seen in Table 7.6. Nearly 40%of the pre-tutorial responses reflect reliance on the Ideal Gas equation when trying to explainchanges in gas temperature; this number drops to 4% (one student) after the tutorial.
Initially, 2 students’ responses (8%) equate heat (q) and temperature (T) and therefore
conclude that temperature is constant for an adiabatic process. This misconception is notreflected in any of the post-tutorial responses.
The Second Law of Thermodynamics tutorial took place on the 9th week of thesemester, exactly one week before the second exam. Table 7.10 shows the pre and post quizscores as well as the average gains for questions 2 and 3. In question one on these quizzes we
see that initially only 70% of the students correctly identify the direction of thermal energy
transfer for the given reaction. This number rises to 100% after the tutorial. During thetutorial session this topic brought about much discussion amongst groups. At one point theentire class fell silent except for two students arguing their individual points about thermalenergy transfer. A similar question was asked in the previous tutorials quizzes (Question 1b
above), there we also saw a ~70% correct response rate initially with 85% post. This
indicates that any gains made, concerning the transfer of thermal energy, during the first

155
tutorial do not appear in this material 5 weeks later. This observation, combined with thequantity and depth of the conversations witnessed during the previous tutorial session on thismaterial, indicates that students continue to struggle with this idea and may need several
detailed exposures in order to connect to this concept. Question 2 asks students about thechange inTable 7.10
Second Law of Thermodynamics pre/post-quiz results and pre-post gains.
Data reflects percentage of students with each individual rubric score. Questions 1 is scoredusing Table 7.1, questions 2 and 3 are scored using Table 7.2. Average gain is calculated forquestions 2 and 3 only.
Rubric Score
0
1
2
3
4
Avg. Gain
Pre
26
4
70
1
Post
0
0
100
Pre
44
26
4
9
17
2
30%*
Post
17
9
9
9
56
Pre
22
44
17
4
13
3
28%*
Post
17
9
9
9
56
*Note: Each individual student gain is calculated as post score minus pre score; average gainreflects the entire sample group.
Question
N= 23

Entropy during the given reaction. On the pre-quiz only 26% of the student responses matchthat of an expert (rubric score ≥ 3). This percentage increases to 65% after performing thetutorial. The overall average gain is 1.5 (30%) on the rubric grading scale, this gain is
identical to that measure previously in Table 7.7. In the last question students are asked
about the temperature dependence of the reaction. In Table 7.10 we see that on the pre-quiz
only 17% of the responses addressed the temperature dependence in a manner similar to an
expert (rubric score ≥ 3). After completing the tutorial this percentage raises to 65%. The
average overall gain is 28% with over one-fourth of the students showing individual gains of
60% or more.
In addition to the measured changes on the pre-post quiz questions, there are also
some changes in the student misconceptions presented within their answers. On the pre-quiz

156
responses, 9% of the student state that the entropy increases for the reaction because “entropy
must increase for a spontaneous process”. After the tutorial none of the responses show thisbelief. The pre-quiz also shows that 30% of the students associate the cold feeling of the ice
pack as indicating thermal energy leaving the reaction mixture. This number drops to zeroafter the tutorial.
The reaction kinetics tutorial took place on the 13th week of the semester, exactly
one week before the third exam. Table 7.11 shows the pre and post quiz scores as well as theaverage gain for question 3. In question 1 we see that a large percentage (83%) of thestudents have some idea about what a reactant molecule needs in order to become a productmolecule. After the tutorial all the students’ responses reflect an understanding of what isrequired. In question 2, greater than 50% of the responses state that the transition statebarrier for the reaction is temperature dependent and lowers as the reaction temperature is
raised. In addition to these responses, approximately 10% of the students state that the barrierheight does not change; however, the reasoning behind their answer is lacking or flawed.
Table 7.11
Reaction kinetic pre/post-quiz results and pre-post gains. Data reflects
percentage of students with each individual rubric score. Questions 1 is scored using Table
7.1, questions 2 and 3 are scored using Table 7.2. Average gain is calculated for question 3
only.
Rubric Score
0
1
2
3
4
Avg. Gain
Pre
0
17
83
1
Post
0
0
100
Pre
54
8
38
2
Post
0
0
100
Pre
4
50
42
4
0
3
32%*
Post
0
8
8
54
30
*Note: Each individual student gain is calculated as post score minus pre score; average gainreflects the entire sample group.
Question
N= 24

After performing the tutorial, none of the students report that the barrier changes as a functionof temperature. We also see this learning gain reflected in students’ answers to question 3.

157
Before the tutorial, greater than 50% of the responses had little correlation to the important
aspects needed in addressing the question. In addition, 42% of the responses had somedetailed information but lacked one or more key points. After the tutorial, over 80% of thestudent responses match, or nearly match, the response of an expert. The average gain forquestion 3 is calculated to be 32%, with 41% of the students showing individual gains of 40%
or more.
The main misconception addressed in the kinetics tutorial is students’ belief about thetemperature dependence of the reaction barrier. The results of question 2 nicely show that the
tutorial effectively addresses this misconception. The visual nature of the simulation allows
students to see what factors do change with temperature and how these factor influence thereaction rate. Without this information, students try to reason out answers with the parts ofthe problem that they understand, i.e., the change in the “energy” barrier and heat “energy” isadded.
7.4.2

Comparison with Control GroupUp to this point in our testing we have only had minor comparisons (in section 7.3.5)of student responses between groups of students who have performed the tutorials and thosethat have not. This direct comparison on common questions will provide a more meaningful
gauge of the affect of the learning tutorials on students understanding of these fundamental
concepts. To do this, we have analyzed common exam questions between two different
physical chemistry courses.
The test group, which utilized the learning tutorials, was taught by a faculty member
at the University of Colorado in Boulder. The control group was taught by a faculty member
at the University of Colorado in Denver. Both faculty members regularly teach theundergraduate physical chemistry sequence. The test group contains 32 students and thecontrol group contains 22 students.

All students in the courses are majoring in either

158
chemistry, biochemistry, or engineering. The incoming chemistry knowledge of both groupsof students was measured using a physical chemistry concept test. These scores will be used
to provide some degree of normalization between the two courses. We acknowledge thatsampling two different courses with two different instructors is not an ideal comparison whenmeasuring learning aspects. However, because these tutorials focus on the fundamentals of a
few important concepts, we feel that these two populations will provide some significant
contrasts.
7.4.2.1 Pre-Semester Concept Exam
In order to measure students’ incoming physical chemistry concept knowledge all
students were given a physical chemistry concept exam on the first day of class. This exam
was developed at the University of Colorado by a post-doctoral associate in the Physics
Education Research group, a copy can be found in Appendix B7. The exam contains 34
questions covering concepts from the Thermodynamics and Kinetics material of an
introductory physical chemistry course. The questions are either true/false or multiple choiceanswers, no calculations or mathematical derivations are involved.
On average, the test group scores ~7% higher on the concept exam than the control
group. However, as shown in Table 7.12, this difference is not statistically significant.
Therefore, because the incoming knowledge of the two groups is essentially identical thescores on the common exam questions will be evaluated in their raw form (ie: unnormalized). An additional comparison between the two groups will also be made. This
comparison comes in the form of a second (calculation based) common exam question andwill be addressed in the next section.

159

Table 7.12
Comparison of average scores on pre-semester concept exam for control andtest groups. Question statements can be found in Appendix B7.
Control Group

Test Group

Average Score (%)

49.2

56.3

Standard Deviation

19.3

21.4

Standard Error

3.31

3.67

Z

1.44

*P-value

0.15*P-value for two-tailed z-test, value is not statistically significant at the p<0.01 level.
7.4.2.2 Common Exam Scores
In order to evaluate the learning gains associated with the tutorial use common examquestions will be evaluated comparing the test and control groups. Each of the three exams
contains two common questions, one conceptual and one calculation. Each exams concept
question covers student understanding of the fundamental concepts of the specific material(ie: First Law, Second Law, and Kinetics). The calculation question is used to compare theperformance of the two groups on material which was not part of the learning tutorials. Bothsets of questions are graded by the individual instructors using their own grade key. The
conceptual questions are further evaluated using the scoring rubric presented in Table 7.2.
The first exam in both courses covers material from the First Law ofThermodynamics. The common exam questions can be found in appendix B8. Figure 7.4
shows the average scores for both the common conceptual question and the calculation. For
the control group, the average score on these questions was 62% and 58%, respectively. For
the test group, we see a slightly higher, but not statistically different, score on the calculationquestion of 60%. However, on the conceptual question the test group scores significantly
higher at 90%. These test scores are the grades assigned by each instructor using their own

160
grade key. Figure 7.4 also shows the scores on the conceptual question graded with the
rubric (Table 7.2) used to evaluate the pre and post quizzes. These rubric scores are slightly
lower than those assigned by the instructor but still show a statistically significant difference
between the two groups. In scoring the conceptual questions with the rubric we also notedifferences between the content of the responses. In the control group, 32% of the responses
reflect students’ reliance on the Ideal Gas equation in addressing the change in the internalenergy and the temperature of the air in the pump. This number drops to 6% for the test
group. As noted in previous sections, students incorrectly equate thermal energy transfer (q)and temperature (T). On this exam, 6% of the responses from the control groups contain thisA v e rag e S c o re (% )misconception while none of the responses from the test group contain this misconception.

100

Control

90

Test

80
70
60
50
40
30
20
10
0
Conceptual

Calculation

RubricFirst Law Exam Problems
Figure 7.4
Comparison of average scores for control and test groups on common
questions. Rubric score reflects average score on conceptual question using scoring rubric
presented in Table 7.2. The difference in the Conceptual scores and Rubric scores are
statistically significant at the p<0.01 level.
The second exam in both courses covers material from the Second Law ofThermodynamics. The common exam questions can be found in appendix B9. Figure 7.5

161
shows the average scores for both the common conceptual question and the calculation. For
the control group, the average score on these questions was 37% and 79%, respectively.
When we look at the scores for the test group we see that on the calculation problem the test
group scores lower with an average of 67%. This 12% difference has a calculated p-value of
0.02 and indicates a statistically higher score (at the 95% level, p<0.05) for the control group.
However, this difference is not significant at the 99% level (p<0.01) which is used as thecriterion in the other comparisons made here. In evaluating the instructors scoring of theconceptual question we see that the test groups’ average of 83% is statistically higher with ap-value < 0.00. When the conceptual question is scored with the grading rubric, the test
groups’ average is 80% and the control groups’ average is 34%, again showing a significant
difference

at

the

99%

level.

100

Control
Test

A v e ra g e S c o re (% )

90
80
70
60
50
40
30
20
10
0
Conceptual

Calculation

RubricSecond Law Exam Problems

Figure 7.5
Comparison of average scores for control and test groups on common
questions. Rubric score reflects average score on conceptual question using scoring rubric
presented in Table 7.2. The difference in the Conceptual scores and Rubric scores are
statistically significant at the p<0.01 level.

162
The conceptual question responses also show differences in the misconception that
only the change in Entropy determines the spontaneity of the reaction. In the control group,
36% of the responses reflect statements stating that the reaction is spontaneous because
Entropy increases, no indication is present as to the changes in either Enthalpy or Gibbs
energy. In the test group, 13% of the responses fall into this category. In addition to thisbelief, we also note students’ responses about the transfer of thermal energy during thereaction. It was previously noted that many students associate the “reaction getting cold”
with thermal energy leaving the system and entering the surrounding. It is encouraging tonote that only 5% of the responses from the control group and 0% from the test group reflect
this belief for the conceptual question on the exam.
The results of this comparison study do show significant differences between the
responses of the test and control groups. On both measures (instructor scored and rubric
scored) the test group, which performed the tutorials, responses reflected and expert’s
response more than those of the control group. The test group responses also showed fewer
indications of flawed logic or misconceptions when compared to the control. In addition, thepresence of these misconceptions in the test groups’ exam responses is nearly identical towhat was measured directly after the tutorial use. This finding indicates that in the time
between tutorial and exam the information obtained by the students remains robust anduseful.
The third exam covers material from the Kinetics portion of the courses.

The

common exam questions can be found in appendix B10. Figure 7.6 shows the average scoresfor both the common conceptual question and the calculation. For the control group, theaverage score on these questions was 68% and 88%, respectively. When we look at thescores for the test group we see that on the calculation problem the test group scores lower
with an average of 58%. This 30% difference has a calculated p-value <0.000 and indicates astatistically higher score for the control group. In evaluating the instructors scoring of the163
conceptual question we see that the test groups’ average of 85% is higher with a p-value of0.02. When the conceptual question is scored with the grading rubric, the test groups’
average is 76% and the control groups’ average is 56%, this difference in scores has a p-valueof 0.03.
100

Control
Test

Average Score (%)

90
80
70
60
50
40
30
20
10
0
Conceptual

Calculation

RubricKinetics Exam Problems

Figure 7.6
Comparison of average scores for control and test groups on common
questions. Rubric score reflects average score on conceptual question using scoring rubric
presented in Table 7.2. The difference in the Conceptual scores and Rubric scores are
statistically significant at the p<0.05 level.

The conceptual question responses do not show much difference in the
misconception of the potential energy barrier variation with temperature. None of the 32
students in the test group mentioned any variation in the energy barrier with temperature; infact, more than half of their responses contain indications of the students’ knowledge about
the potential energy being only a function of the molecules makeup and orientation. In thecontrol group, only one out of the 15 responses addresses the misconception that the energy
barrier itself varies as a function of temperature.

164
The results of this comparison study do show differences between the responses of
the test and control groups. On both measures (instructor scored and rubric scored) the test
group, which performed the tutorials, responses reflected more expert-like responses thanthose of the control group. The test groups written responses were more complete and went
into more explanation than the control group’s responses. In addition, the test group’s
responses contained more cause and effect connections which were lacking for the control
students. When comparing the performance of the two groups on the calculation problem,the control group vastly outperformed the test group. In reviewing the specific material
addressed by each instructor, it became clear that the control group received more instruction
on reaction mechanisms and the steady-state approximation (the topic of the calculation
problem). The control group also covered the Kinetic Molecular Theory of Gases in greater
detail than the test group.

This finding emphasizes the effectiveness of the computer

simulation and tutorial in addressing this material. Despite the test groups’ limited exposure
to the material, their average score on the conceptual problem was ~10% higher than thecontrol group. While this difference only has a p-value of 0.02 it does reflect the test groups
higher conceptual understanding of the temperature dependence of reaction rates.
7.5

Conclusions and Future Directions
The results of this study indicate that there are several fundamental concepts within

Thermodynamics and Kinetics which students commonly struggle to understand. Even after
instruction in a Physical Chemistry lecture course (as well as numerous problem sets andinitial instruction in a General Chemistry course) many students do not understand thebuilding blocks of Thermodynamics. Some of these students additionally harbormisconceptions which can block their further conceptual gains.
We have developed interactive learning tutorials which are designed to target these
difficult areas within Thermodynamics and Reaction Kinetics. Our tutorials are developed

165
around a physical model or computer simulation. The physical models allow students toexperience some of the thermodynamics phenomena previously only presented as pictures orword problems. The computer simulation used in the reaction kinetics tutorial provides
students with an active visual medium for understanding how temperature affects reaction
rate. These tools provide the students with both a “real-world” connection to and strong
physical picture of the concepts themselves. The structure of the tutorial itself is designed tostep students through the important building blocks which underlay the concept at hand. This
guided inquiry allows students to connect with all the individual pieces needed in order tofully address the concepts covered.
During the initial testing phase (section 7.3), it was shown that the tutorials weresuccessful in addressing student misconceptions as well as producing gains in conceptual
understanding. After the First Law tutorial (Table 7.6) we saw large increases in students’
understanding of thermal energy transfer and measured average gains of 40% (2 points on
rubric scale) in students’ responses about heat, work, and internal energy. The Second Law
tutorial produced gains of 30% (1.5 points on rubric scale) for student responses about
Entropy change and 20% (1 point on rubric scale) for the temperature dependence of Gibbs
energy (see Table 7.7). After the Reaction Kinetics tutorial we measure large decreases in thenumber of students who report that the potential energy profile for a given reaction istemperature dependent (see Table 7.8). We also see a gain of 40% in the average response
about the temperature dependence of a reaction rate. These findings indicate that the tutorials
themselves can aid students in understanding some of the fundamental concepts addressed ina standard physical chemistry course.
When the developed tutorials were placed in a classroom setting we measuresignificant learning gains from the tutorial use when compared to a control course not using
the tutorial materials. The students in both groups performed equally well on identical
calculation problems given as part of their in class exams. However, the test group scores on

166
the conceptual problems were significantly higher than those of the control group. While we
did not control for differences such as teaching style, text book, or homework problems
within the two courses, a familiarity with both instructors teaching style and course materialindicates that there should be no significant differences between the courses.
In addition to this study, an important future investigation would be a comparison
between the gains achieved using these “model based” tutorials and other standard “pencil
and paper” tutorials. The models presented here allow students to make direct observations
and predictions connected to the concepts being addressed, where the pencil and paper format
does not. It is unclear whether this type of study will show a difference in gains measured
immediately after the tutorial use but it may show differences in long term retention. The
models give the students a “real-world” example of the material being addressed; thisconnection may improve retention by allowing students to relate difficult concepts tocommon examples.
These three tutorials are a small fraction of the possible interactive learning tutorials
which can be developed to address difficulties with chemistry topics. The wealth of physicalmodels and computer simulations available today can provide material for both General
Chemistry and Physical Chemistry tutorials. The tutorials covered in this work were onlyused in small class settings (N < 40) where small group work was easily employed. These
ideas can be extended to large courses by extending the tutorial sessions into the course or lab
recitation sessions. This small setting will provide an ideal size to perform small grouptutorials without impinging on the lecture class itself. This “tutorial session” format is being
used in many different programs across the country and is currently part of the redevelopmentof the Physics curriculum at CU-Boulder.

167

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________________
Appendix A
CLASS-Chem Supplementary Tables________________A.1

CLASS-Chem v2 Statements

A.2

Robustness data for ‘Personal Interest’ category

A.3

Robustness data for ‘Real World Connections’ category

A.4

Robustness data for ‘Problem Solving: General’ category

A.5

Robustness data for ‘Problem Solving: Confidence’ category

A.6

Robustness data for ‘Problem Solving: Sophistication’ category

A.7

Robustness data for ‘Sense Making/Effort’ category

A.8

Robustness data for ‘Conceptual Connections’ category

A.9

Robustness data for ‘Conceptual Learning’ category

A.10

Robustness data for ‘Atomic-Molecular Perspective of Chemistry’ category

183

A.1

CLASS-Chem v2 Statements

All 50 statements which appear in the second version of the CLASS-Chem instrument. The letter
before each statement number indicates ‘expert’ response,
where D = disagree, A = agree, and NS = not scored.

1. A significant problem in learning chemistry is being able to memorize all theinformation I need to know.
2. To understand a chemical reaction, I think about the interactions between atoms andAmolecules.
3. When I am solving a chemistry problem, I try to decide what would be a reasonableAvalue for the answer.
A 4. I think about the chemistry I experience in everyday life.
NS 5. It is useful for me to do lots and lots of problems when learning chemistry.
6. After I study a topic in chemistry and feel that I understand it, I have difficulty solving
D
problems on the same topic.
D 7. Knowledge in chemistry consists of many disconnected topics.
8. As chemists learn more, most chemistry ideas we use today are likely to be provenNSwrong.
9. When I solve a chemistry problem, I locate an equation that uses the variables given inD
the problem and plug in the values.
NS 10. I find that reading the text in detail is a good way for me to learn chemistry.
11. I think about how the atoms are arranged in a molecule to help my understanding ofA
its behavior in chemical reactions.
12. If I have not memorized the chemical behavior needed to answer a question on anDexam, there's nothing much I can do (legally!) to figure out the behavior.
A 13. I am not satisfied until I understand why something works the way it does.
D 14. I cannot learn chemistry if the teacher does not explain things well in class.
15. I do not expect equations to help my understanding of the ideas in chemistry; they areDjust for doing calculations.
A 16. I study chemistry to learn knowledge that will be useful in my life outside of school.
A 17. I can usually make sense of how two chemicals react with one another.
18. If I get stuck on a chemistry problem on my first try, I usually try to figure out aAdifferent way that works.
A 19. Nearly everyone is capable of understanding chemistry if they work at it.
20. Understanding chemistry basically means being able to recall something you've readDor been shown.
21. Why chemicals react the way they do does not usually make sense to me; I justDmemorize what happens.
A 22. To understand chemistry I discuss it with friends and other students.
23. I do not spend more than five minutes stuck on a chemistry problem before giving up
Dor seeking help from someone else.
24. If I don't remember a particular equation needed to solve a problem on an exam,D
there's nothing much I can do (legally!) to come up with it.
25. If I want to apply a method used for solving one chemistry problem to anotherD
problem, the problems must involve very similar situations.
26. In doing a chemistry problem, if my calculation gives a result very different fromD
what I'd expect, I'd trust the calculation rather than going back through the problem.
D184
27. In chemistry, it is important for me to make sense out of mathematical formulas
before I can use them correctly.
A 28. I enjoy solving chemistry problems.
29. When I see a chemical formula, I try to picture how the atoms are arranged andAconnected.
30. In chemistry, mathematical formulas express meaningful relationships amongAmeasurable quantities.
31. We use this statement to discard the survey of people who are not reading theNSquestions. Please select agree (not strongly agree) for this question.
32. It is important for the government to approve new scientific ideas before they can beDwidely accepted.
33. The arrangement of the atoms in a molecule determines its behavior in chemicalA
reactions.
A 34. Learning chemistry changes my ideas about how the world works.
D 35. To learn chemistry, I only need to memorize how to solve sample problems.
36. Reasoning skills used to understand chemistry can be helpful to me in my everyday
Alife.
37. In learning chemistry, I usually memorize reactions rather than make sense of theDunderlying physical concepts.
38. Spending a lot of time understanding where mathematical formulas come from is aD
waste of time.
39. I find carefully analyzing only a few problems in detail is a good way for me to learn
NSchemistry.
A 40. I can usually figure out a way to solve chemistry problems.
D 41. The subject of chemistry has little relation to what I experience in the real world.
42. There are times I solve a chemistry problem more than one way to help myAunderstanding.
43. To understand chemistry, I sometimes think about my personal experiences and relateAthem to the topic being analyzed.
44. Thinking about a molecule's three-dimensional structure is important for learningAchemistry.
A 45. It is possible to explain chemistry ideas without mathematical formulas.
46. When I solve a chemistry problem, I explicitly think about which chemistry ideas
Aapply to the problem.
D 47. If I get stuck on a chemistry problem, there is no chance I'll figure it out on my own.
48. Spending a lot of time understanding why chemicals behave and react the way theyD
do is a waste of time.
49. When studying chemistry, I relate the important information to what I already knowArather than just memorizing it the way it is presented.
50. When I'm solving chemistry problems, I often don't really understand what I am
Ddoing.
A

185

A.2

Robustness data for ‘Personal Interest’ category

Personal Interest
average CC average fl
0.334
0.665

delta E
-1.775

R^2
0.917

N
6

S13
0.212

S16
0.484
0.281

S28
0.277
0.205
0.281

ROBUSTNESS
7.736

Correlation Matrix
S4
S4
S13
S16
S28
S34
S36

0.212
0.484
0.277
0.516
0.381

S34
S4
S16
S36
S28
S13

0.754
0.743
0.724
0.706
0.545
0.517

slope 1-2
-1.876slope 2-n-0.100

Factor Loadings

Total Variance

0.281
0.205
0.316
0.245

0.281
0.372
0.422

0.287
0.282

S34
0.516
0.316
0.372
0.287
0.447

S36
0.381
0.245
0.422
0.282
0.447

186

A.3

Robustness data for ‘Real World Connections’ category

Real World Connections
average CC average fl
0.389
0.736
Correlation Matrix
S34
S34
S36
0.447
S41
0.427
0.349
S43
Factor Loadings
0.763
S34
0.762
S36
0.711
S41
0.707
S43
Total Varianceslope 1-2
slope 2-n-1.466-0.093delta E
-1.373

R^2
0.999

N
4

S36
0.447

S41
0.427
0.352

S43
0.349
0.422
0.335

0.352
0.422

0.335

ROBUSTNESS
9.680

187

A.4

Robustness data for ‘Problem Solving: General’ category

Problem Solving: General
average CC average fl
0.285
0.594
Correlation Matrix
S15
S15
S18
0.120
S19
0.072
S21
0.260
S28
0.127
S30
0.280
S40
0.197
S47
0.208
S49
0.283
S50
0.297
Factor Loadings
S50
0.770
S47
0.719
S49
0.718
S40
0.691
S21
0.641
S28
0.597
S19
0.492
S30
0.477
S18
0.399
S15
0.438
Total Varianceslope 1-2
slope 2-n-2.647-0.082delta E
-2.565

R^2
0.977

N
10

S18
0.120

S19
0.072
0.193

S21
0.260
0.128
0.205

0.193
0.128
0.082
0.156
0.305
0.281
0.225
0.188

0.205
0.318
0.183
0.284
0.252
0.336
0.246

0.289
0.240
0.346
0.373
0.434
0.461

ROBUSTNESS
7.175
S28
0.127
0.082
0.318
0.289
0.248
0.316
0.364
0.298
0.474

S30
0.280
0.156
0.183
0.240
0.248
0.225
0.210
0.294
0.244

S40
0.197
0.305
0.284
0.346
0.316
0.225
0.482
0.403
0.465

S47
0.208
0.281
0.252
0.373
0.364
0.210
0.482
0.427
0.532

S49
0.283
0.225
0.336
0.434
0.298
0.294
0.403
0.427
0.482

S50
0.297
0.188
0.246
0.461
0.474
0.244
0.465
0.532
0.482

188

A.5

Robustness data for ‘Problem Solving: Confidence’ category

Problem Solving: Confidence
average CC average fl
0.300
0.687
Correlation Matrix
S18
S18
S19
0.193
S40
0.305
0.281
S47
Factor Loadings
0.785
S40
0.762
S47
0.617
S18
0.583
S19
Total Varianceslope 1-2
slope 2-n-1.107-0.148delta E
-0.959

R^2
0.885

N
4

S19
0.193

S40
0.305
0.284

S47
0.281
0.252
0.482

0.284
0.252

0.482

ROBUSTNESS
6.599

189

A.6

Robustness data for ‘Problem Solving: Sophistication’ category

Problem Solving: Sophistication
average CC average fl
0.348
0.662
Correlation Matrix
S6
S6
S24
0.298
S25
0.259
S28
0.275
S40
0.462
S47
0.364
S50
0.377
Factor Loadings
S50
0.761
S47
0.754
S40
0.738
S24
0.653
S6
0.650
S28
0.611
S25
0.470
Total Varianceslope 1-2
slope 2-n-2.222-0.099delta E-2.123

R^2
0.983

N
7

S24
0.298

S25
0.259
0.315

S28
0.275
0.275
0.164

0.315
0.275
0.423
0.412
0.344

0.164
0.190
0.258
0.254

0.316
0.364
0.474

ROBUSTNESS
8.479
S40
0.462
0.423
0.190
0.316
0.482
0.465

S47
0.364
0.412
0.258
0.364
0.482
0.532

S50
0.377
0.344
0.254
0.474
0.465
0.532

190

A.7

Robustness data for ‘Sense Making/Effort’ category

Sense Making/Effort
average CC average fl
0.235
0.564
Correlation Matrix
S13
S13
S21
0.335
S26
0.267
S27
0.313
S38
0.152
S42
0.133
S46
0.207
S48
0.318
S49
0.260
Factor Loadings
S21
0.686
S48
0.674
S49
0.651
S13
0.596
S26
0.592
S46
0.514
S27
0.503
S38
0.468
S42
0.389
Total Varianceslope 1-2
slope 2-n-2.004-0.063delta E
-1.941

R^2
0.973

N
9

S21
0.335

S26
0.267
0.352

S27
0.313
0.223
0.152

0.352
0.223
0.269
0.163
0.232
0.327
0.434

0.152
0.194
0.130
0.187
0.349
0.309

0.176
0.171
0.161
0.274
0.200

ROBUSTNESS
6.167
S38
0.152
0.269
0.194
0.176
0.123
0.163
0.268
0.182

S42
0.133
0.163
0.130
0.171
0.123
0.152
0.167
0.237

S46
0.207
0.232
0.187
0.161
0.163
0.152
0.309
0.275

S48
0.318
0.327
0.349
0.274
0.268
0.167
0.309
0.310

S49
0.260
0.434
0.309
0.200
0.182
0.237
0.275
0.310

191
A.8

Robustness data for ‘Conceptual Connections’ category

Conceptual Connections
average CC average fl
0.260
0.603
Correlation Matrix
S6
S6
S7
0.222
S15
0.221
S24
0.298
S37
0.225
S38
0.153
S50
0.377
Factor Loadings
S50
0.737
S24
0.650
S37
0.627
S6
0.591
S15
0.579
S7
0.566
S38
0.473
Total Varianceslope 1-2
slope 2-n-1.549-0.094delta E
-1.455

R^2
0.926

N
7

S7
0.222

S15
0.221
0.161

S24
0.298
0.228
0.301

0.161
0.228
0.294
0.173
0.353

0.301
0.200
0.334
0.297

0.295
0.238
0.344

ROBUSTNESS
6.007
S37
0.225
0.294
0.200
0.295
0.144
0.435

S38
0.153
0.173
0.334
0.238
0.144
0.167

S50
0.377
0.353
0.297
0.344
0.435
0.167

192
A.9

Robustness data for ‘Conceptual Learning’ category

Conceptual Learning
average CC average fl
0.283
0.618
Correlation Matrix
S1
S1
S6
0.234
S7
0.181
S12
0.298
S24
0.219
S25
0.185
S47
0.182
Factor Loadings
S24
0.726
S12
0.723
S47
0.707
S6
0.595
S25
0.556
S7
0.537
S1
0.485
Total Varianceslope 1-2
slope 2-n-1.849-0.092delta E
-1.758

R^2
0.918

N
7

S6
0.234

S7
0.181
0.222

S12
0.298
0.253
0.251

0.222
0.253
0.298
0.259
0.364

0.251
0.228
0.189
0.368

0.536
0.290
0.390

ROBUSTNESS
6.714
S24
0.219
0.298
0.228
0.536
0.315
0.412

S25
0.185
0.259
0.189
0.290
0.315
0.258

S47
0.182
0.364
0.368
0.390
0.412
0.258

193
A.10

Robustness data for ‘Atomic-Molecular Perspective of Chemistry’ category

Atomic-Molecular Perspective of Chemistry
average CC average fl
0.299
0.641
Correlation Matrix
S2
S2
S11
0.448
S17
0.376
S29
0.415
0.265
S33
0.346
S44
Factor Loadings
0.757
S2
0.754
S11
0.750
S29
0.602
S17
S44
0.578
S33
0.403
Total Varianceslope 1-2
slope 2-n-1.593-0.132delta E
-1.461

R^2
0.967

N
6

S11
0.448

S17
0.376
0.341

S29
0.415
0.530
0.352

0.341
0.530
0.163
0.293

0.352
0.146
0.130

0.125
0.339

ROBUSTNESS
7.128
S33
0.265
0.163
0.146
0.125
0.217

S44
0.346
0.293
0.130
0.339
0.217

194

Appendix B
Physical Chemistry Tutorial Sheets and Concept Test
B.1

First Law Pre/Post Quiz

B.2

First Law Tutorial Worksheet (Air Can)

B.3

Second Law Pre/Post Quiz

B.4

Second Law Tutorial Worksheet (Rubber Band)

B.5

Kinetics Pre/Post Quiz

B.6

Kinetics Tutorial Worksheet (PhET Sim)

B.7

Chem 4511 Concept Test

B.8

First Law Exam Questions

B.9

Second Law Exam Questions

B.10

Reaction Kinetics Exam Questions

195
B.1

First Law Pre/Post Quiz

Name:First Law Pre/Post Questions

1. The figure below shows an ideal gas contained in a non-insulated cylinder. A piston
is tightly fit so that no gas escapes; friction is negligible between the piston and thecylinder walls.

Ideal gas

A block is dropped onto the piston compressing the gas.
a. Is work done ON the gas or BY the gas in this example? Explain your reasoning.
b. After the block is dropped, is there a transfer of thermal energy as heat? If so, in
what direction is the transfer? If not, why not?
2. The figure below shows an ideal gas contained in a cylinder. A piston is tightly fit sothat no gas escapes; friction is negligible between the piston and the cylinder walls. The
cylinder walls are insulated.
Insulation

Direction of piston
Ideal gas

The piston is pushed into the cylinder. Explain how this impacts the internal energy
and temperature of the gas. Please be as thorough as possible in your answer.

196

B.2

First Law Tutorial Worksheet (Air Can)

Name:First Law Worksheetballoonvalve

Air canw/gas

Can filled with high pressure gas and sealed with a balloon.
Use the figure above to make a prediction.
What happens to the temperature of the gas inside the can as you allow the gas toexpand into the balloon?

Why does this temperature change occur? Explain the reasoning for your answer in a
few sentences.
Note: Consider the system to be the balloon, the can, and the gas, everything outside of
the can and balloon is considered the surroundings. There is NO loss of gas molecules
during this expansion.

Now test your prediction with one of the air cans at the front of the room.

197

We will now investigate two thermodynamic systems.
Mass removed from pistons

Ideal GasA

Ideal gas A is isothermally expanded.

insulated

Ideal Gas
B

Ideal gas B is adiabatically expanded.

In the figure above, two cylinders are filled with the same ideal gas. A piston is fit sothat no gas escapes; friction is negligible between the piston and the cylinder walls. The
block is removed from each piston, the piston moves upward.
(1) In each case, does the gas do work or is work done on the gas? Explain yourreasoning in a few sentences.

(2) Is there a larger transfer of thermal energy as heat between Gas A and thesurrounding or between Gas B and the surroundings? Explain your reasoning in a
few sentences. Draw an arrow on each figure indicating the direction of thermalenergy flow.

(3) For the expansion of Gas A, how do the work and heat involved in this process
affect the internal energy of the gas? Explain your reasoning in a few sentences.

(4) For the expansion of Gas B, how do the work and heat involved in this process
affect the internal energy of the gas? Explain your reasoning in a few sentences.

198

B.3
Name:

Second Law Pre/Post Quiz
Second Law Pre/Post Activity Questions

The instant cold packs that you purchase for First Aid kits contain two solid chemicals
initially separated from each other; the reaction upon mixing is shown below.

Ba(OH)2·8H2O (s) + 2 NH4Cl (s) → BaCl2 (aq) + 2 NH3 (aq) + 10
H2O (l)1. The chemical reaction shown above takes place at room temperature when thechemicals are mixed together. As products form, you touch the pack and notice that thepack feels cold. Is thermal energy (heat) going in or out of the reaction mixture as thereaction progresses? Explain your answer in a few words.

2. Use the Gibbs equation (∆G=∆H-T∆S) along with the changes in Gibbs energy (∆G)
and enthalpy (∆H) to determine the change in entropy (∆S = S(f)-S(i)) as the reaction
proceeds? Explain the reasoning you used to get your answer.

3. Is this reaction spontaneous at all temperatures? Please explain why or why not.

199

B.4

Second Law Tutorial Worksheet (Rubber Band)

Name:

Second Law Prediction

standrubber band
weightruler

The figure above shows a rubber band stretched by a heavy weight; the ruler indicates theheight of the weight.
Predict what will happen to the length of the rubber band if the temperature of the rubberband is increased. In your answer express the reasoning behind your prediction.

Once you and your group have come to a conclusion, test your prediction using theapparatus set-up at the front of the room.

200

stretching

relaxing
Rubber Band(relaxed)

Rubber Band
(stretched)

1. The figure above shows the stretching and relaxing of a rubber band.
a, Does the stretched rubber band spontaneously relax? Explain your answer in a few
words.
b, Based on your answer for spontaneity, does the Gibbs energy (G) increase or decreaseas the band goes from the stretched to the relaxed position?
We can determine the enthalpy change (∆H) for the rubber band by the following
procedure:-Place the relaxed rubber band in contact with your lip and note temperature-Quickly stretch the band while still in contact with your lip-Quickly allow the band to relax while still in contact with your lip-REPEAT several times and note the temperature change for stretching/relaxing
2. Upon relaxing does thermal energy enter or leave the rubber band?
3. What is the sign of thermal energy transfer (q) for the rubber band? Does enthalpy
increase (∆H>0) or decrease (∆H<0) upon relaxing? Please explain your answer in a few
sentences.
Use the table below to record the sign (+ or −) of the change in Gibbs energy andEnthalpy from the previous questions.
∆G∆H
stretching
relaxing
4. Use the data from the table above along with the equation for Gibbs Energy (∆G =∆H-T∆S), to reason out what the change in entropy (∆S) is for stretching and relaxing.
Explain your reasoning below.
5. Consider the values of ∆H and ∆S you observed at room temperature to be
independent of T. Could you create conditions under which the rubber band will
spontaneously get longer? Please explain your answer in a few sentences.

201

B.5

Kinetics Pre/Post Quiz

Name:

Pre/Post Questions

The figure below shows the minimum potential energy profile for the conversion of cis2-pentene to trans-2-pentene.

Potential Energy

Transition State

Ea

CIS

TRANS

Reaction Progress

1. What conditions are required for a reactant molecule (cis-2-pentene) to become aproduct molecule (trans-2-pentene)?

2. Does the height of the energy barrier, the value shown on the figure as Ea, change
as the temperature increases? In other words, does the difference in energy between
the potential energy of CIS and the transition state change with temperature? Please
explain your answer in a few sentences.

3. Experimentally, it has been determined that the rate of conversion from cis to transincreases as the temperature increases. Why does the rate of the reaction increase withincreasing temperature? Please explain your answer in a few sentences and refer to theenergy diagram if possible.

202

B.6

Kinetics Tutorial Worksheet (PhET Sim)

Name:

Worksheet A

Model vs Physical Reality:
This simulation is a model of a chemical reaction. It indicates that reactants and products
have different potential energies by physically separating them. However, in many
experiments the reactant and product molecules are not physically separated but instead
collide and interact with one another. The simulation represents the reactant and productspecies as simple spheres. In reality most molecules are not spheres.
This simulation shows a reversible reaction of one molecule (A) turning into anothermolecule (B) along a reaction pathway. This is analogous to what happens in a cis-transisomerization:
kf
kr

Molecule A

Molecule B

1. Using the simulation, describe your observations of how an A molecule becomes a B
molecule. Be sure to note molecular motions and collisions.
To observe molecules with the simulation:
Type “20” in box next to “Molecules in Chamber” for molecule A
Hit “Enter” key on keyboard
You can click [Pause] at any time to stop all motion
Note your observations below.
Now we will observe how temperature changes impact molecular motion.
Use mouse to slide bar on “HEAT CONTROL” to “ADD”
Note your observations below.
2. What happens to molecular motion as you raise the temperature?
3. Did increasing the temperature affect the height of the energy barrier? In other words,
did the shape of the potential energy curve change? Explain in a few sentences.

203

4. Here you’ll determine how long it takes for the first B molecule to form from A.
Procedure:
Click [RESET], to erase parameters
Click [PAUSE], to stop motion while you make changes
Click “energy histograms”, this will open a window with two plots
Change “temperature of new particles” to 350 K
Click [START] on stop watch in lower left corner
Type [50] in box next to A, hit ENTER key on keyboard, this will add A molecules
Click [PLAY] to start motion
Click [PAUSE] as soon as the first B molecule is formed
Time to form the first B molecule?______________________
5. Sketch the plot of Number of Particles versus Kinetic Energy. What does this plot
indicate about the kinetic energy of the molecules? Note on your sketch which molecules
you think have more energy than the barrier.
6. How long would it take to form the first B molecule if the temperature were 750 K?
Please explain your reasoning in a sentence or two.
7. Before checking with the simulation, sketch what you think the plot of Number ofMolecules verses Kinetic Energy will look like for the reaction at 750 K.
Now let’s record how long it takes to form the first B molecule at 750 K.
Click [RESET]
Change “temperature of new particles” to 750 K
Click [START] on stop watch
Type [50] in box next to A, hit ENTER key on keyboard
Click [PLAY]
Click [PAUSE] as soon as the first B molecule is formed.
8. At 750 K how long does it take to form the first B molecule? How does this compare
to the time needed at 350 K?
9. How does the collision rate (Z) of molecule A change as temperature is increased
from 350 K to 750 K? Explain your answer in a few sentences.

204

The rate of formation of molecule B, d[B]/dt, for the forward reaction (A→B) is written
as: d[B]/dt = kf[A].
10. How does the rate coefficient (kf) at 350 K compare to the rate coefficient (kf) at 750
K? Based on molecular motions, why are the two values for k different?
11. Sketch the plot of Number of Particles versus Kinetic Energy at 750 K. Compare
this plot to your predicted plot in question 7.
12. How do the Number of Molecules verses Kinetic Energy plots at 350 K and 750 K
differ? What does this indicate about the TOTAL energy of the molecules at the different
temperatures?

205

B.7

Chem 4511 Concept Test

1. In lab, a student is considering two options for increasing the internal energy of a gas.
Assume the gas behaves ideally. He or she can compress the gas into a smaller volume,or let it expand against atmospheric pressure so that it takes up a larger volume. Of these
two options:a.
Either compressing the gas or letting the gas expand will increase the internalenergy of the gasb.
Neither compressing the gas nor letting the gas expand will increase the internalenergy of the gas.
c.
Only compressing the gas will increase the internal energy of the gasd.
Only letting the gas expand will increase the internal energy of the gas
2. Which graph best represents the relationship between Pressure and Volume for an
ideal gas? Volume increases to the right along the x-axis. Pressure increases as you
move up along the y-axis. Assume the temperature and number of moles of gas remain
constant.
a.

c.
Pressure

Pressure

VolumeVolumed.

b.

Pressure

Pressure

VolumeVolume206

3. A chemical reaction has a negative value for ∆rS and negative value for ∆rH. The
entropy of the products is less than the entropy of the reactants and the enthalpy of the
products is less than the enthalpy of the reactants. Assume that pressure is constant, andthat ∆rS and ∆rH do not change with temperature. This reaction:
a.
b.
c.
d.
e.

will be spontaneous at all temperatures
cannot be spontaneous at any temperature
can be spontaneous at high temperatures but not low temperatures
can be spontaneous at low temperatures but not high temperatures
None of the above

4. A student is given two samples of He gas. There is one mole of He gas in eachsample. The pressures and temperatures of the two samples are not the same. The
student reversibly heats the first sample until it has a pressure of 2 atm and a temperatureof 300 K. The student irreversibly cools and compresses the second sample until it has apressure of 2 atm and a temperature of 300 K. In the end, which sample has greaterinternal energy?
a. The sample that was heatedb. The sample that was cooled.
c. It cannot be determined here, because we don’t know the initial conditions.
d. They have the same energy.
5. A cylinder of He gas is used to fill balloons. The valve on the He gas cylinder isopened, allowing some He gas to escape into a balloon attached to the valve. Assume the
He behaves like an ideal gas. Immediately afterwards, which of the following is true for
the He that remains in the cylinder?
a. The temperature of He in the cylinder does not change.
b. The temperature of He in the cylinder is higher than before the valve was opened.
c. The temperature of He in the cylinder is lower than before the valve was opened.
d. The direction of temperature change cannot be determined.

207

6. Is the following chemical reaction likely to be an elementary reaction?
4 NH3 + 5 O2 Æ 4 NO + 6 H2O
a.
Yes
b.
No
c.
It is not possible to determine if a reaction is elementary by looking at thechemical equation.
7-10. In studying the elementary chemical reaction, O3 + CO Æ O2 + CO2, theconcentration of CO is in excess of the concentration of O3. The initial concentration of
CO is 100 times the initial concentration of O3, [CO]0 = 100 [O3]0. Assume there are nocompeting chemical reactions, but there is a non-reactive “bath” gas of He or N2.
Assume the system does not go to equilibrium. Determine if the following are true or
false. Choose True(a) or False(b).
7. True(a) or False(b)of CO2 production.
8. True(a) or False (b)CO2 produced.
9. True(a) or False(b)ofDoubling the concentration of O3 will double the initial rate
Increasing the concentration of O3 will increase the amount of
Increasing the concentration of CO will increase the amountCO2 produced.
10. True(a) or False(b) Doubling the concentration of CO will double the initial rateof CO2 production.

208

11-16.

cis-1,2-dichloroethylene can convert to trans-1,2-dichloroethylene. Here, wewill abbreviate these cis and trans. The cis reacts to form trans with a rate coefficient kf,
and trans reacts to form cis with the rate coefficient kr. Here, kf ≠ kr
kf
kr

Cl
Cl

cis

Cl

Cl

trans

Initially,only cis is present. Determine if the following are true or false. Choose True(a)or False(b).
11. T(a) or F(b) At equilibrium, [cis] = [trans]
12. T(a) or F(b) At all times,[trans] = A constant value (the equilibrium constant)[cis]

13. T(a) or F(b) At all times, d[cis] / dt = - kf [cis]14. T(a) or F(b)At early times, when the reaction begins, kf [cis] > kr [trans]

15. T(a) or F(b)At equilibrium, kf [cis] = kr [trans]

16. T(a) or F(b)After the system has reached equilibrium, kf [cis] < kr [trans]

209

17. The elementary chemical reaction, NO3 + NO Æ 2 NO2, has a rate coefficient k.
Initially only NO and NO3 are present. Assume there are no competing reactions, andthat no other reactions happen at the same time. At any time during this reaction the rateof change of NO3 can be written as:

d [ NO3 ]= −k [ NO ]
a.
dt
b.

d [ NO3 ]= −k [ NO3 ]dtc.

d [ NO3 ]= k [ NO ][ NO3 ]dtd.

d [ NO3 ]= −k [ NO ][ NO3 ]dte.

d [ NO3 ]= −kdt

18. A student has two identical samples of N2 gas. He or she heats one under constantvolume conditions, until the temperature doubles. The other one is heated under constantpressure conditions until the temperature doubles. After heating, which is true:a.
The same amount of thermal energy or heat was added to both systems.
b.
More thermal energy or heat was added to the system at constant volume.
c.
More thermal energy or heat was added to the system at constant pressure.
d.
Not enough information was given to determine which system required more
thermal energy or heat.

19. An NO molecule collides with an O3 molecule. The NO molecule removes an O
atom from O3 to create NO2 and O2. Assume there are no competing reactions.
a.The rate for this reaction can be written as k[NO][O3], where k represents the rate
coefficient for the reaction.
2
b.The rate for this reaction can be written as k[NO][O3] , where k represents the rate
coefficient for the reaction.
c.The reaction is first order overall, and second order with respect to NO.
d.It is not possible to write the rate for this reaction, or determine its order unless given
information that the reaction is elementary.

210

20– 22. The First Law of Thermodynamics may be stated as: Energy can be converted
from one form to another, but cannot be created or destroyed. For the following 3
mathematical statements, choose True (a) if the expression is a restatement of the firstlaw. Choose False (b) if the expression does not restate the first law.
20. T(a) or F(b) w = - ∫ P dV, work is the integral of the pressure multiplied by thechange in volume
21. T(a) or F(b) q = ∫ Cv dT, heat is the integral of the Heat capacity multiplied by
the change in temperature.
22. T(a) or F(b) ∆U = q + w, A change in internal energy for a system can be theresult of changes in heat and work.

23. You are given two cylinders of O2 gas. The pressure and volume of the twocylinders may be different. In the first cylinder, the collision frequency of the O2
molecules is 100 collisions per second. In the second cylinder the collision frequency of
the O2 molecules is 500 collisions per second. Which statement is true?
a. The gas molecules colliding at a higher frequency are colliding more often because
they are at a higher temperature.
b. The gas molecules colliding at a higher frequency are at a higher temperature because
the collisions release energy as heat.
c. The gas molecules colliding at a higher frequency are at a lower temperature because
the collisions release energy as heat.
d. Not enough information is given to determine which of the two gas samples is at ahigher temperature.
24. A sample of He gas is compressed adiabatically. The sample of He gas is thesystem. Assume ideal gas behavior for the He. In this case,
a.
b.
c.
d.
e.

The system absorbs heat.
The surroundings absorb heat.
The temperature of the system goes down.
Work is done on the surroundings.
The surroundings do work.

211

25. An ideal gas occupies a container at pressure P1, temperature T1, and volume V1.
The same amount and type of gas exists in a second container with pressure P2, volume
V2, and temperature T2. If the second container is twice the size of the first, (V2 = 2 x
V1), and the temperature in the second container is half the temperature of the first, (T2 =½ T1), which best describes the pressure in the second container?
a.

The pressure is the same in both containers P1 = P2b.

The pressure in the second container is half the pressure in the first, P2 = ( 1 ) P1

c.

The pressure in the second container is 1

2

the pressure in the first, P2 = ( 1 )

4

4

P1
d.

The pressure in the second container is 1e.

None of the above8

the pressure in the first, P2 = ( 1 ) P1

8

26. You add a large amount of table salt (NaCl) to a glass of water and thoroughly stir thesolution. Some NaCl precipitates out as a solid on the bottom of the glass. You add
more NaCl to the solution. The result of adding more NaCl is:a. There will be more Na+ and Cl- ions in the solution
b. There will be more solid NaCl on the bottom of the glassc. Both a and b
27-28. Choose True(a) or False(b). Under certain experimental conditions the chemical
reaction:NO (g) + O3 (g) Æ NO2 (g) + O2 (g)proceeds spontaneously. Under those same experimental conditions, it must be true thatfor this reaction:
27. T(a) or F(b) Gibbs energy goes down, ∆rGo < 0

28. T(a) or F(b) Entropy increases, ∆rSo > 0

212

29. In an endothermic chemical reaction, the reactants must absorb energy in order toform products. Can an endothermic reaction occur spontaneously at room temperature?
a.
Yes
b.
No
30. Imagine you are compressing the air in a bicycle pump by quickly pushing down on
the pump handle. Assume there is no friction in the pump. The valve on the pump is
closed so that air cannot escape.
Pump Handle

Closed ValveIn each statement, ‘air’ refers to air inside the pump that is being compressed.
Which statement is true?
a. The temperature of the air goes up because thermal energy or heat goes into the air
during compression.
b. The temperature of the air doesn’t change because thermal energy or heat does not go
into the air during compression.
c. The temperature of the air goes up because of work done on the air in compression,
not because of thermal energy or heat going into the air.
d. The temperature of the air goes up because of work done on the gas in compression,and because thermal energy goes into the air.
31. You are given a cylinder containing a mixture of Oxygen gas and Helium gas. The
mixture is in equilibrium. Which atoms or molecules are moving with greater speed?
a.
b.
c.
d.
e.

The O2 molecules
The He atoms
Neither, they are the same.
The one that has a higher partial pressure.
The one that has a lower partial pressure.

213

32. Which statement is true for a chemical reaction at equilibrium?
a.
The Gibbs energy is zero.
b.
As time passes, there is no change in the Gibbs energy. In other words, thechange in Gibbs energy with time is zero.
c.
Both the Gibbs energy and the change in Gibbs energy with time are zero.

33. Choose T(a) or F(b). Pure liquid water and air are in a sealed container. Somewater has evaporated, so there is water in the gas phase above the liquid. If salt is added
to the liquid water, equilibrium will shift so that there are fewer water molecules in thegas phase.

SealedContainer

{

.
.

.

.
.

. .

.

Water molecules in the gas phase,
above the surface of the liquid

Liquid Water

34. Work is done on a system. Based on the conventions we have used in this class,a.
For the system, dw > 0 , (the change in work for the system is positive)b.
For the system, dw < 0, (the change in work for the system is negative)c.
The change in work for the system is zero if the process is done reversiblyd.
The change in work for the system is zero if the process is done adiabatically

214

B.8

First Law Exam Questions

10 point concept question
The figure below shows a bicycle tire pump with the valve closed so that no air canescape. Imagine that you quickly push the handle down, compressing the air inside. You
can assume that there is no friction in the pump and that the air behaves like an ideal gas.
handlepistonclosedvalve

During this adiabatic compression, what happens to the temperature of the air inside thepump? Explain, in a few sentences, the reasoning behind your answer. In youranswer be sure to address heat, work, and internal energy.

10 point calculation question
A 2-liter bulb contains n moles of nitrogen gas at 0.5 atm pressure and temperature T.
On addition of 0.01 mole of oxygen, it is necessary to cool the bulb to a temperature of
10°C in order to maintain the same pressure. Calculate the number of moles n and thetemperature T of nitrogen present originally. Assume that the gases behave as
perfect gases.

215

B.9

Second Law Exam Questions

10 point concept question
The “instant ice packs” you can buy commercially contain two liquid chemicals. Whenthese two chemicals are mixed together, a spontaneous reaction takes place and the ice
pack feels cold to your hand.
a. (5 pts.) What is the sign of ∆S (entropy) for the reaction? Please explain yourreasoning in a few words.

b. (5 pts.) Is this reaction spontaneous at all temperatures? If so, WHY? If not, WHY
NOT? Please explain your reasoning in a few words, be sure to address both enthalpy
and entropy in your answer.

15 point calculation question
One mole of an ideal, monatomic gas initially at 1 atm and 273 K expands isothermallyand irreversibly to 44.8 litre, under conditions such that w = 420 J.
Calculate q, ∆U, ∆H, and ∆S for the process.

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B.10

Reaction Kinetics Exam Questions

10 point concept question
Experimentally, it has been determined that the rate of decomposition of nitrogendioxide, shown below, increases with increasing temperature. Why does the rate ofdecomposition increase with increasing temperature? Explain your answer in termsof the molecular motion of nitrogen dioxide.
2 NO2(g) → 2 NO(g) + O2(g)15 point calculation question
Consider the reaction: H + O3 → OH + O2
Calculate the Arrhenius A factor at 300 K. Assume that the collision diameter dH = 100
pm and dO3 = 300 pm. Compare this result with the experimental value of 1.7 x 1010 dm3
mol-1 s-1 for this reaction.