I STATES 4ENT OF IERCE

IATION NBS TECHNICAL NOTE 543

Electrochemical Analysis

Section:

Summary of Activities

July 1969 to June 1970

BUREAU OF STANfittBS

UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

NBS TECHNICAL NOTE 543

ISSUED NOVEMBER 1970

Nat. Bur. Stand. (U.S.), Tech. Note 543, 92 pages (Nov. 1970)

CODEN: NBTNA

Electrochemical Analysis Section:

Summary of Activities—luly 1969 to June 1970

Richard A. Durst, Editor

Electrochemical Analysis Section

Analytical Chemistry Division

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

*< °>

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C, 20402.

(Order by SD Catalog No. C 13.46:543). Price $1.00.

FOREWORD

The Analytical Chemistry Division was established as a separate division at the National Bureau of Standards on

September 1, 1963 s and became part of the Institute for

Materials Research in the February 1, 1964, reorganization.

It consists at present of nine sections and about 100 technical personnel encompassing some 60 different analytical

competences from activation analysis and atomic absorption to

vacuum fusion and x-ray spectroscopy. These competences, and

in turn the sections which they comprise, are charged with

research at the forefront of analysis as well as awareness of

the practical sample, be it standard reference material or

service analysis. In addition it is their responsibility to

inform others of their efforts.

Formal publication in scientific periodicals is a highly

important output of our laboratories. In addition, however,

it has been our experience that informal, annual summaries of

I progress describing efforts of the past year can be very valuable In disseminating information about our programs. A word

is perhaps in order about the philosophy of these yearly

progress reports. In any research program a large amount of

information is obtained and techniques developed which never

find their way into the literature. This includes the

"negative results" which are so disappointing and unspectacular but which can often save others considerable work. Of

importance also are the numerous small items which are often

explored in a few days and which are not important enough to

warrant publication—yet can be of great interest and use to

specialists in a given area. Finally there are the experimental techniques and procedures, the designs and modifications

of equipment, etc., which often require months to perfect and

yet all too often must be covered in only a line or two of a

journal article.

in
Thus our progress reports endeavor to present this information which we have struggled to obtain and which we feel

might be of some help to others. Certain areas which it

appears will not be treated fully in regular publications are

considered in some detail here. Other results which are

being written up for publication in the journal literature

are covered in a much more abbreviated form.

At the National Bureau of Standards publications such as

these fit logically into the category of a Technical Note.

We plan to issue these summaries for all of our sections.

The following is the sixth annual report on progress of the

Electrochemical Analysis Section:

W. Wayne Meinke, Chief

Analytical Chemistry Division

IV
PREFACE

This is the sixth annual progress report of the Electrochemical Analysis Section of the Analytical Chemistry Division.

It covers the fiscal year 1970, which began on July 1, 1969 and

ended on June 30, 1970. This report summarizes the total

program of the Section, incomplete studies as well as finished

work, and stresses its relationship to the missions of the

Division and the Institute.

This Section broadly concerns itself with studies of ionic

processes in solution using electroanalytical and other related

techniques. During this year, some redirection and reemphasis

of effort were undertaken in order to bring the Section expertise to bear on important analytical problems in several areas

1 of science, medicine, and technology. As a result, much of the

earlier work of the Section, such as studies of solute-solvent

interactions in mixed solvents, has had to be reduced. The

special interests of the members of the Section lie for the

most part in solution electrochemistry including the competence

areas of potentiometry , electrometric titrations, coulometry,

and conductometric analysis.

Several changes occurred in the Section staff in the past

year which maintained an overall scientific effort of about

four man-years. The most significant staff change was the retirement of Dr. Roger G. Bates, who directed the Section since

its inception. Dr. Bates, who won International recognition

for his studies of hydrogen ion activities and pH scales in

addition to his general Interests in electrolyte solution thermodynamics and electrode reactions, has accepted the post of

professor of Chemistry at the University of Florida. Dr. Bates

will remain associated with the Section in the capacity of

Consultant

.

In order to specify the procedures adequately, it has been

necessary in certain Instances to identify commercial materials

and equipment in this report. In no case does such identification

v
imply recommendation or endorsement by the National Bureau of

Standards, nor does it imply that the material or equipment

is necessarily the best available for the purpose.

The support of the Scientific Apparatus Makers Association

(SAMA) for ionic activity studies and the U. S. Army Research

and Development Command (under Contract No. MOD-9913) for

biologic fluid studies is gratefully acknowledged.

Richard A. Durst, Acting Chief

Electrochemical Analysis Section

VI
TABLE OF CONTENTS

PAGE

1

.

INTRODUCTION 2

2. ACIDIMETRIC MEASUREMENTS 7

Tri s in Wat er 7

Buffers in Isotonic Saline 10

Tris in Isotonic Saline 13

Dissociation of Protonated Tris(hydroxymethyl)-

aminome thane in Aqueous Alcoholic Solvents.... 14

Certification of Disodium Hydrogen Phosphate

(SRM 186 He) 18

Certification of Borax (SRM 18 7b) 20

3 . ION-SELECTIVE ELECTRODES 21

Introduction 21

Single Ionic Activity Coefficients 22

Uni-Univalent Chlorides 22

Alkaline Earth Chlorides 24

Equipment 24

Procedure for Conventional Single Ionic

Activities 24

Activity Standards for Ion-Selective Electrodes. 26

4

.

POTENTIOMETRY 28

Introduction , 28

Experimental 29

Results and Discussion 31

Conclusion 34

5. COULOMETRY 36

Introduction , „ 36

Research 37

Coulometry of Zinc 37

Further Implications of Zn Generation.... 44

EDTA analysis 44

Determination of stoichiometry 44

Potassium Dichromate 46

Tris - Basimetric Standard 56

VI

1
TABLE OP CONTENTS (CONT'D)

PAGE

6. CONDUCTIMETRY 59

Introduction 59

Test Equations 59

Two-Parameter Equations 59

Three-Parameter Equations 60

Theoretical Equations 60

Experimental Section 63

Apparatus 63

Solutions and Filling of Cells 64

Pitting Equations to Data 65

Results and Discussion „ 66

Recommendations „ 72

7 . FOREIGN-CURRENCY PROGRAMS .

.

73

Properties of Electrolytes in Nonaqueous Media... 73

Physicochemical Studies in Nonaqueous Solvents... 7^

8. PERSONNEL AND ACTIVITIES 75

Personnel Listing . . . . 75

Publications and Manuscripts 75

Talks... o 77

9. REFERENCES co 79

vi 11
LIST OF FIGURES

FIGURE NO. PAGE

1. Emf cell (hydrogen vs. silver/silver chloride)

for studies of pH buffer solutions 8

2. Comparison of conventional pa^ values for

buffers in isotonic saline (solid line) and

in water (broken line) at 25 °C [6-9] <>... 12

3. Dissociation constants of tris vs. alcohol

carbon number in 0.2811 mole fraction alcoholo 15

h Dissociation constant of tris vs. solvent

density; a) methanol, b) ethanol,

c) n-propanol, d) t-butanol 16

5. Dissociation constant of tris vs. solvent

dielectric constant; a) methanol, b) ethanol,

c) n-propanol, d) t-butanol. ..„

„

16

6. Dissociation constant of tris vs. solvent

viscosity; a) methanol, b) ethanol,

c) n-propanol, d) t-butanol „ ... o .. <, 17

7. Equipment for measurement of ion-selective

electrode cell emf. „ „ 25

8. Response of the silver sulfide electrode to

silver concentration. Response slope In the

linear region of the calibration curve is

59.5mV/pAg (ambient temperature 25 ± 1 °C).... 30

9° Percent silver adsorption vs. time for five

selected materials. Initial silver concentration 2 x 10 -6M (0.216 ppm) . Average variability in measurements ± 0.5% absolute 32

10, Coulometer for the determination of the

atomic weight of zinc ».. = 42

llo Potassium dichromate samples and some of the

coulometric equipment used in standardizing

this oxidant „.<, 46

12. Two types of random errors which are

encountered in coulometry 51

13. Equivalent circuit for conductance cell,

according to reference 45 61

IX
LIST OF FIGURES (CONT'D)

FIGURE NO. PAGE

l4« Comparison of test equations. Data points

are for demal KC1, bright platinum electrodes,

cell constant 37 68

15. Percentage deviations from test equation 44.

Data points are for demal KC1. bright platinum

electrodes, cell constant 37. The solid

rectangle at the origin of the coordinates

represents the probable limiting resistance

for palladized electrodes 69

16. Percentage deviations from test equation 39.

Data points are for demal KC1, bright platinum

electrodes, cell constant 37 o 70

LIST OF TABLES

TABLE NO. PAGE

1. Table of Contents - "Ion-Selective

Electrodes" 5

2. Conventional paH and buffer values for several

tris»HCl/tris buffer ratios.... 9

3. Conventional pa^ values for buffer solutions

in isotonic saline at 25 °C 11

4. The approximate dissociation constants for

four acids in isotonic saline at 25 °C 13

5» Conventional pa^j and buffer values for

tris»HCl/tris buffer ratios in isotonic saline

solution 13

60 Dissociation constants of tris in several

alcohol-water mixtures. ... o 15

7. pH values for standard phosphate buffer

solutions o 19

8. pH values for standard borax buffer solutions. 2

9o Activity standards for sodium chloride ... „ ... . 26

10. Activity standards for potassium chloride .. » . . 27
LIST OF TABLES (CONT'D)

TABLE NO. PAGE

11. Adsorption percentages and rates for

0.216 ppm silver solution on various materials 33

12 o Silver adsorption by radioactive tracer

method of West et al. [22,23] 34

13» Analysis of Na

2

EDTA-2H

2

44

14 o Summary of data of KpCrpO„ analyses <,.. 47

15. Analysis of K Cr9 73 SRM 136b 5 (sample size - 0.5g) ... I 53

16. Analysis of smaller samples of K Cr

p 7

(SRM 136c) .....i 54

17. Analysis of K^Cr (SRM 136c) "as received"

(1-g samples) I 54

18. Results of coulometric analysis of tris - basimetric standardo 58

19. Limiting resistance R i and standard deviation

of fit for seven test equations applied to

experimental data 67

20o Fundamental parameters of conductance cell

derived from frequency dependence of resistance, o „ 71

21. Polynomial coefficients and their standard

deviations 71

XI

ELECTROCHEMICAL ANALYSIS SECTION: SUMMARY OF ACTIVITIES

JULY 1969 TO JUNE 1970

Edited by Richard A. Durst

This survey of the activities of the Electrochemical

Analysis Section, Analytical Chemistry Division, covers the

period from July 1969 to June 1970. An attempt is made to

briefly summarize a year's progress on the technical projects

of the Section, to indicate the composition and capabilities

of the unit as a whole, and to stress the Section's role in

the mission of the Institute. Summaries of the work in each

of the Section competences are given. In the area of acidity

measurements, work continued on the standardization of

tris (hydroxymethyl)aminomethane for use as a biologic pH

buffer material and standard for clinical pH measurements.

Progress toward reference standards for the calibration of

ion-selective electrodes is reported including pM and pCl

values for both NaCl and KC1. A study using the silver sulfide ion-selective electrode for measuring trace silver ion

losses due to adsorption on selected surfaces is described.

High-precision coulometry is used to determine the atomic

weight of zinc, the purity of EDTA, and the stoichiometry of

gallium arsenide.

Key words: Acidity; conductivity; coulometric analysis;

electrochemical analysis; ionic activity; ionselective electrodes; pH measurements; potentiometry; standard reference materials.
i

:

1. INTRODUCTION

For the most part, this has been a year of change for the

Electrochemical Analysis Section, both in terms of staff and

of mission emphasis. Generally speaking, the changes in

Section activities are primarily the result of the opportunity

to apply Section expertise in electroanalytical chemistry to

help solve a variety of analytical problems in many diverse

areas, from biomedicine to solid-state materials.

Examples of this type of involvement can be best illustrated by citing two outside grants for support of Section

activities

.

In one study, a two-year program on ion-selective electrodes was started under the sponsorship of the Scientific

Apparatus Makers Association (SAMA) and the NBS Office of

Standard Reference Materials (OSRM), the purpose of this study

being to standardize techniques and to prepare high quality

reference materials, in order to facilitate the applications

of ion-selective electrodes. In brief, this Section will (1)

correlate theoretical thermodynamic data with experimental

studies of commercial electrodes and evaluate the liquid

junction errors; (2) define the ionic activities in solutions

of the reference materials; and (3) establish a self-consistent

set of activity scales for these ions . The long-range goal is

the acquisition, certification, and issuance of standard

reference materials for the calibration of ion-selective

electrodes

.

The other study, supported by a grant from the U. S. Army

Medical Research and Development Command, is concerned with the

development of methods and materials for studying the behavior

of electrolytes in biologic fluids. Specifically, this program

was established to develop methods for electrochemically

monitoring ion concentrations and gas tensions, and to develop

standard materials for calibrating the electrodes used in the
continuous monitoring of ions and dissolved gases in various

body fluids . One study being made in this program is the

standardization of a new reference material for biologic pH

measurements . The glass pH electrode has long demonstrated

its utility as a rapid and accurate index of the acid-base

balance of biologic fluids and, for the purpose of standardization, NBS had certified a special ratio of its phosphate buffer

j for the physiologically important range of pH 7 to 8. However,

i this buffer has certain undesirable characteristics for biologic studies, for example, the phosphate interacts with

certain components of body fluids such as calcium and magnesium.

For this reason, many biological scientists merely used the

NBS phosphate buffer to standardize a more compatible buffer

material. To overcome this shortcoming, work is in progress

to certify the tris/tris *HC1 system [tris = tris (hydroxymethyl)-

aminomethanej as a new physiologic pH buffer in pure water and

in isotonic saline and other synthetic biologic fluids.

In addition to this pH standard, ionic activity standards

| developed under the SAMA/OSRM grant should also find use in

applying ion-selective electrodes to biologic studies

.

-Standards for sodium, potassium, chloride, calcium, etc., will

eventually be certified in various mixed electrolyte systems

of physiologic importance. In summary, although ion-selective

electrodes are extremely promising sensors for biomedical research and clinical medicine, they are nevertheless incapable

of yielding accurate and meaningful data until they are adjusted

to standard reference activity scales in media of specified

composition.

Another area where one of our electroanalytical competences

will advance the state of the art is in the accurate determination of the stoichiometry of various semiconductor materials

such as gallium arsenide. As a participant in an international

characterization exchange coordinated by CECD (Organization for
Economic Cooperation and Development), it is expected that our

expertise in coulometric analysis will permit the determination

of the s toichiometry of gallium arsenide to an accuracy and

precision unattainable by any other analytical technique.

Similar studies will be made on high-purity KC1 where it is

expected that the chloride content can be determined coulometrically with an imprecision of only a few parts per million.

The results of these studies will enable participating countries

to assess their competence in those aspects of materials

science which are of importance for the future development of

their industries. Also, these studies will enable correlations

to be made between the composition and structure of materials

and their bulk properties.

During this year, another contribution to the advancement

of the state of the art of ion-selective electrodes was achieved

with the publication of the book, "Ion-Selective Electrodes" [1]

by the Government Printing Office. This NBS Special Publication

314 is the formal report of the proceedings of the Symposium on

Ion-Selective Electrodes held at NBS in January 1969 . This

volume contains a review of ion-selective electrodes, emphasizing the non-glass types, and provides a thorough and critical

evaluation of the subject. It consists of eleven invited review papers (Table 1) and selected discussions from the

Symposium. Both the present status and future potential of

these sensors are discussed in a wide range of scientific disciplines, from the physical sciences to biomedicine, and extensive bibliographies provide an excellent survey of the

literature for anyone using or anticipating the use of these

electrodes . Some indication of the interest in this topic can

be gained from the fact that, in the first six months that this

publication has been available, the entire first printing of

4,000 copies was sold out, and the book has gone into its

second printing for use in both the laboratory and the classroom.
Table 1. Table of Contents - "Ion-Selective Electrodes".

Theory of Membrane Electrode Potentials: An Examination of

the Parameters Determining the Selectivity of Solid and Liquid

Ion Exchangers and of Neutral Ion-Sequestering Molecules

George Eisenman

U.C.L.A.

Solid-State and Liquid Membrane Ion-Selective Electrodes

James W. Ross^ Jr.

Orion Research, Inc.

Heterogeneous Membrane Electrodes

Arthur K. Covington

University of Newcastle-upon-Tyne, England

Reference Electrodes

Arthur K. Covington

University of Newcastle-upon-Tyne, England

Thermodynamic Studies

James N. Butler

Tyco Laboratories, Inc.

Activity Standards for Ion-Selective Electrodes

Roger G. Bates and Marinus Alfenaar

National Bureau of Standards

Studies with Ion-Exchange Calcium Electrodes in Biological

Fluids: Some Applications in Biomedical Research and Clinical

Medicine

Edward W. Moore

Lemuel Shattuck Hospital
Table 1. (Cont'd)

Ion-Selective Electrodes in Biomedical Research

Raja N. Khuri

American University of Beirut, Lebanon

Analytical Studies on Ion-Selective Electrodes

Garry A. Reehnitz

State University of New York at Buffalo

Industrial Analysis and Control with Ion-Selective Electrodes

Truman S. Light

The Foxboro Company

Analytical Techniques and Applications of Ion-Selective

Electrodes

Richard A. Durst

National Bureau of Standards

Symposium Discussion

(R. A. Durst)
2. ACIDIMETRIC MEASUREMENTS

A. Tris in Water

Tris (hydroxymethyl)aminomethane is being widely used as a biological buffer. The dissociation constant of the protonated

form has been determined by emf measurements from to 50 °C

and the pK at 25 °C is 8.075 [2]. This indicates that tris

a

; buffer solutions are suitable for pH measurement and control

between pH 7 and 9

.

In order to match the pH of a tris buffer solution as closely as possible with the acidity range found in blood and

at the same time have a buffer with sufficiently large buffer

capacity, the conventional pa^ values of several buffer solutions containing various ratios of protonated and free base

were determined.

The method used followed closely the procedure for assignment of pH(S) values to NBS primary pH reference buffers. Emf

measurements of the cell (shown in Figure 1)

Pt;H

2 (g), X-Tris-HCl(m) , Tris(m), AgCl;Ag (I)

where m refers to molality and X (the ratio of tris*HCl to

tris) was varied from 1 to 4 , were made at 5, 25, 37, and 50 °C

The cell solutions were made up by dissolving the free crystalline base in standard hydrochloric acid. The acidity function

p(aHYfi-i) was derived from the measured emf of the cell with

the aid of the equation

| P (aHYci } = ^ + l0 S m

Cl" (1)

where E° is the standard emf of the cell [3] and k is (RT In

10)/F. Conventional paH values for each buffer solution were

computed by the equation

paR

= (paH

Y cl ) + log y c1- (2)

where the single ionic activity coefficient for the chloride

ion was estimated by the Bates-Guggenheim convention [4]

7
-log YC1- AI 1/2

1+1.5 I 1/2 (3)

where A is the Debye-Hiickel slope and I the total ionic

strength

.

The buffer value $ was determined by the method proposed

by Van Slyke [5] which involves the titration of the buffer

solution either with a strong base or acid.

The calculated paR values at 25 and 37 °C and the buffer

values are listed in Table 2.

The internal agreement of these paH values with the pH

scale defined by NBS primary pH standards was investigated by

intercomparing the tris buffer solutions with the standard

0.025m phosphate buffer solution having pH(S) 6.862 and 6.838

at 25 and 37 °C, respectively.

Figure 1. Emf cell (hydrogen vs. silver/silver chloride)

for studies of pH buffer solutions

.
Table 2. Conventional pa„ and buffer values for several

tris -HCl/tris buffer ratios.

Tris -HCl/tris

3.5

Molality

tris-HCl 25 °C

n

37 °C A a

3

0.02

.05

.10

8.144

8.176

8.206

7.826

7.858

7.888

-0.022

- .039

0.019

.054

.02

.05

.10

7.668

7.698

7.727

7-350

7.380

7.410

- .026

- .041

.012

.020

.02

.05

.10

7.599

7.631

7.661

7.280

7.313

7.343

- .025

- .039

.010

.02

.05

.10

7.543

7.573

7.603

7.225

7.254

7.284

- -

A = pH(X)-paH

at 25 °C (residual liquid-junction error)

The cell used was

Standard

Pt;H (g), phosphate

1

(S)

Calomel

saturated

KC1

Tris buffer, H„(g);Pt , TT , (X) l U1J

where the vertical line denotes a liquid junction. The operational pH values of tris buffer solutions were calculated by

the equation

pH(X) = pH(S) + E

X"

E

S

k

(4)

where E„ and E„ are the potential differences between the

calomel and hydrogen electrodes. The differences between the

operational pH and corresponding paH values given also in

Table 2 indicate the error caused by liquid junction potential

The results of Table 2 suggest that the tris buffer solution containing 0.02m Tris*HCl in a ratio of 3 to 1 of the

protonated base to free base could be used for pH standardiza9
tion purposes since it has a pH value very close to that of

blood, a relatively small liquid junction error, and a sufficient buffer capacity

.

B . Buffers in Isotonic Saline

In the course of searching for secondary pH standards in

media of biomedical importance, isotonic saline was the first

medium selected for study. It consists of 0.l6m sodium chloride solution in water and thus simulates blood very closely

with respect to its osmotic pressure (and ionic strength)

.

Electrochemical studies of five buffer systems were made

in isotonic saline. The buffers studied were

Molality

Tris'HCl (m) + Tris (m) 0.005 - 0.16

Bis-tris'HCl (m) + Bis-tris a (m)

Acetic acid (m) + Sodium acetate (m)

KH

2

PO i| (m) + NapHPOj, (m)

KH Citrate (m)

Emf measurements were made with Cell I containing hydrogen

and silver-silver chloride electrodes over the temperature

range from 5 to 50 °C. In each case enough sodium chloride was

added to the buffer solutions to make the total ionic strength

equal to 0.16. From the emf measurements, conventional parr

values for the buffer mixtures in isotonic saline were determined by the method outlined in the previous section (equations 1-3). Results for selected buffer solutions at 25 °C

are given in Table 3-

The comparison of conventional pa„ values in isotonic

saline with corresponding values in water at the same buffer

concentrations [6-9] in Figure 2 illustrates the neutral

salt effect caused by lowering of the activity coefficients of

the ionized buffer species by the addition of sodium chloride.

.01 - .16

.01 - .15

.005 - .035

.01 - .12

Bis-tris = 2 , 2-bis (hydroxymethyl)-2 ,2

' , 2"-nitrilotriethanol

10
Molality

0.025 0.05 0.10

8.224 8.225 8.226

6.646 6.647 6.65]

4.636 4.637 4.639

6.789 — _

Table 3- Conventional pa„ values for buffer solutions

in isotonic saline at 25 °C.

Molality

0.01 0.025 0.05 0.10 0.16

Tris 8.221 8.224 8.225 8.226 8.228

Bis-tris 6.645 6.646 6.647 6.65] 6.656

Acetate 4.637

Phosphate 6.770

Citrate 3-709 - 3.683 3-683

As predicted by the Debye-Huckel equation, the paHis raised

for the two amine buffers (tris and bis-tris) and lowered for

the two buffers made up either of a neutral weak acid (acetic)

or of an anion acid (H„P0k) and their respective salts. By

extrapolating the paH for tris and bis-tris buffers in water

[6-9] to ionic strength equal to 0.16, pa H values calculated

were 8.229 and 6.653* respectively. They agree within 0.005

units with the corresponding paH values found in isotonic

saline, 8.228 for tris and 6.656 for bis-tris.

The approximate dissociation constants for acetic acid,

dihydrogen phosphate ion, and protonated forms of tris and

bis-tris in isotonic saline were calculated from the emf

measurements with the use of the mass law and the Debye-Hiickel

limiting law. The ion size parameter was assumed to be zero

and the equations used were:

for acetic acid

' E-E° .. m

, „ mAcQH fK y. pK

a

- -ir- + log m

cl_ + log —

(5)

AcO

for dihydrogen phosphate ion

P K

2 - ^F + l0 B m

Cl"

+ lo8 id^ + 2A/T (6)

HF0

4

11
M

00

**

TRIS

«oo

K

\

PHOSPHATE

PaH"

00

«0

oo

<o

*—m—«-

BIS-TRIS

sT

m—k—*- -mACETATE

00

0.00 .03 .08 .09 .12 .15

MQLRLITY

Figure 2. Comparison of conventional paR values for buffers

in isotonic saline (solid line) and in water

(broken line) at 25 °C [6-9].

12
and for protonated tris and bis-tris

r

» E-E° . n m

E

l = —

;

+ log m„-.- + — a k

6 CI m pK = 2=^- + log mp1 _ + -SL. _ 2A/T (7)

B

The results are given in Table 4.

Table 4. The approximate dissociation constants for

four acids in isotonic saline at 25 °C.

AcOH H

2

P0];

i Tris-H"1"

T Bj s-tris -E

t m

pKy a 4.765pK

2

7.306

pK^ a

P K

a 0.01 7.939 6.364

.02 4.764 7.319 7.942 6.365

.03 4.764 7.333 7.943 6.366

.05 4.765 - 7.944 6.366

.10 4.766 - 7.945 6.370

.16 - - 7-946 6.375

C . Tris in Isotonic Saline

The method used for determining the best buffer composition of tris'HCl and tris in water was followed very closely

in isotonic saline. The results are summarized in Table 5.

Table 5. Conventional paH and buffer values for tris-HCl/

tris buffer ratios in isotonic saline solution.

Tris-HCl/tris

Molality

tris-HCl

p

25 °C

aH

37 °C A a _3_

1 0.01

.05

.10

8.220

8.225

8.226

7.904

7.908

7.909

-0.048

- .052

- .057

0.012

.058

.112

3 .02

.05

.10

7-745

7.745

7.745

7.428

7.427

7.430

- .048

- .049

- .052

.010

.026

.060

3.5

25

.02

.05

.10

°c.

7.678

7.680

7.680

7.361

7-363

7.363

- .049

- .053

- .057

.008

.028

.052

a

A = pH-paH

at

(M. Paabo)

13
D. Dissociation of Protonated Tris (hydroxymethyl)aminomethane

in Aqueous Alcoholic Solvents

In a previous report [10] , the continuing study of acidbase behavior in mixed aqueous solvents was reported. The

dissociation constant of the protonated form of tris (hydroxymethyl)aminomethane was determined in 50 weight-percent

alcohol-water solvents by means of a potentiometric titration.

This procedure, utilizing an electrochemical cell without

liquid junction, was used to extend the investigation to

alcohol-water mixtures containing the same mole fraction of

alcohol (0.2811) which yielded a better basis for comparing

the ion-solvent interactions. A mole fraction of 0.2811

corresponds to the 50 weight-percent point for the ethanolwater solvent.

The following cell was used:

Glass electrode; HC1 (0.01m) + tris in

0.281 mole fraction alcohol-water, AgCl;Ag (III)

The initial emf (E., ) was measured at equilibrium before any

tris had been added. Successive additions of a solution

0.01m in HC1 and 0.1m in tris (m = molal) in the alcohol-water

solvent under study led to emf values designated E

?

. In this

way, both E, and E„ were determined at a constant chloride

molality and a constant total ionic strength, while the buffer

ratio ( tris/tris •HC1) was changed.

The activity coefficient term in the expression for pK

is of such form as to be negligible in dilute solutions [11];

hence, a close approximation to the pK is obtained from the

equation

(E

2

-E

1

) m

fiH + P K = CRT in 10)/F + log oToImT (8)

where mRH+ and mR are respectively the molalities of protonated

tris and

measured.

tris the free tris base in the solution for which E~ was

14
A comparison of results on the weight-percent basis and

on the mole-fraction basis is shown in Table 6.

Table 6. Dissociation c< alcohol-water i

Alcohol

pK

(in 50 wt-5S

alcohol)

Methanol

Ethanol

n-Propanol

t-Butanol

7.799

7.675

7.780

7.758

pK

(in 0.2811 mole fraction

alcohol)

7.9^5

7.675

7.815

7.730

Whereas the dissociation constants of tris in 50 weightspercent alcohol-water mixtures showed no discernible linear

relation to the number of carbon atoms in the alcohol, Figure

3 illustrates that the pK exhibits an almost linear dependence

on the number of carbon atoms in the series, except ethanol.

o

o

00

METHANOL \.

en

i>

\ N-PROPANOL V 00 \ B a-rl

ETHANOL T-BUTANOL \

e

a

CO 121 1 1 1 1 3 4 NO- OF CARBONS IN ALCOHOL

Figure 3- Dissociation constants of tris vs. alcohol carbon

number in 0.2811 mole fraction alcohol.

15
Figures 4, 5, and 6 illustrate the relationship of the

pK to the solvent properties density, dielectric constant,

and viscosity, respectively.

cu

DENSITY

. 9U

Figure 4. Dissociation constant of tris vs. solvent density;

a) methanol, b) ethanol, c) n-propanol, d) t-butanol.

u.o 100/(DIELECTRIC CONSTANT)

Figure 5. Dissociation constant of tris vs. solvent dielectric

constant; a) methanol, b) ethanol, c) n-propanol, d)

t-butanol

.

16
CO a

CO

CO

b

•

N.C

*---———i—

i 1 1 i i 15.0 20.5 28.0 31.5 37.0 U2.5

VISCOSITY (MILLIPOISE)

U8.0

Figure 6. Dissociation constant of tris vs. solvent viscosity;

a) methanol , b) ethanol, c) n-propanol, d) t-butanol

In solvents which contain the same mole fraction of

alcohol, the observed trend in pK as a function of the type

of alcohol indicates that the major influence on the acid-base

behavior of the tris may be the solvent structure. Apparently

the higher degree of hydrogen bonding occurring In ethanolwater is responsible for the larger dissociation constant

(smaller pK) in that solvent.

On the basis of electrostatic effects, Figure 3 shows a reasonably linear relationship which would indicate that the

Fuoss [12] model applies for these alcohol-water mixtures.

where

log K = log K° + 0.4343b

b = aekT

(9)

(10)

e is the charge on the electron, a is the distance of closest

approach of the ions, e is the dielectric constant, k is the

Boltzmann constant, and T is the thermodynamic temperature.

(B. R. Staples)

17
E. Certification of Disodium Hydrogen Phosphate (SRM 186 lie)

The National Bureau of Standards recently acquired a new

lot of disodium hydrogen phosphate to be issued together with

potassium dihydrogen phosphate (SRM 186 Ic) as a primary

Standard Reference Material for pH measurements . Since minor

variation of pH between different lots of material may occur,

the pH(S) values of the phosphate buffer solutions were redetermined by a method used previously in this laboratory

[13].

The emf of the cell

Pt;H

2 (g), Buffer (n^) , KCl(m

2 ), AgCl;Ag (IV)

was measured for buffer solutions containing three different

molalities of potassium chloride (rru = 0.005, 0.01, and 0.015

mol kg ) over the temperature range to 50 °C.

The measured emf of this cell, together with the standard

emf, was used to calculate the acidity function p(a-rrYp-| ) • The

limiting value of the latter p(aHY r-|)° at zero concentration

of added chloride was obtained by least-square extrapolation.

Conventional paH values were computed using the equation

paR

= p(aH

Y cl

)° + log y cl_ (11)

where the single ionic activity coefficient for the chloride

ion was defined by the Bates-Guggenheim convention (Eq. 3).

Three runs were made with the buffer containing 0,025m

of each of the phosphates and three runs with the buffer containing 0. 008695m potassium hydrogen phosphate and 0.03043m

disodium hydrogen phosphate. In addition, the recommendation

of practical standardization of the silver-silver chloride

electrode in 0.01m hydrochloric acid was followed [14]. Emf

measurements at 25 °C gave an E° of 0.22259V (average of 21

cells) for the silver-silver chloride electrode. This represents a difference of 0.25 mV from the Bates and Bower E°

value [3] • The same correction was applied to calculations

18
at all temperatures and the resulting pH values for the two

standard phosphate solutions are given in Table 7.

Table 7. pH values for standard phosphate buffer solutions.

t, °c

0.025m KH

2

P0

1| 0.025m Na

2

HPO i| (average of 3 runs)

008695m KH

03043m Na

2

2

P0

H HPO^

Set I Set II Average

(6.982) a (7.535)

a 7.533 7.534

5 6.949 7-502 7.500 7.501

10 6.921 7.474 7.471 7.472

15 6.898 7.451 7.447 7.449

20 6.878 7.431 7.428 7.430

25 6.863 7.416 7.415 7.415

30 6.851 7.404 7.401 7.403

35 6.842 7.395 7.394 7.394

40 6.836 7.389 7.388 7.388

45 6.832 7.385 7.385 7.385

50 6.831 7.384 7-385 7.384

55 6.831 - - - 60 (6.834) a - - -

Values in parentheses obtained by extrapolation.

However, when determined independently here in the same

.! laboratory , the E° values from emf measurements in 0.01m HC1

were in such good agreement (i.e., fell well within the

standard deviations) at 0° and 50° with the Bates and Bower

calculated values, that these calculated values were taken

as the E° in an independent determination of pH on the 1:3.5

ratio phosphate buffer solution. The comparison of pH values

by two independent determinations, each using an E° consistent

with their own experimental values, is well within any experimental error as illustrated in Table 7 (Sets I and II).

(M. Paabo and B. R. Staples)

19
F. Certification of Borax (SRM 187b)

A new lot of borax (NapBj.0

7

• 10H„0) to be issued as a

primary Standard Reference Material for pH measurements is

being certified by the established procedure [13] outlined

above. The preliminary values of pH for this material are

shown in Table 8.

Table 8. pH values for standard borax buffer solutions.

t, °C pH (0.01m borax) a

5

10

15

20

25

30

35

40

45

50

Run I Run II Average

9.460 9 .460 9.460

9.391 9.393 9.392

9.330 9-332 9.331

9.275 9.278 9.277

9.227 9.228 9.227

9.182 9.184 9.183

9.142 9.144 9.143

9.106 9.108 9.107

9.073 9.075 9.074

9.044 9.045 9.045

9.015 9.018 9.017

Average A (Run II —Run I) = 0.002 pH.

(B. R. Staples)

20
3. ION-SELECTIVE ELECTRODES

A. Introduction

A continuing program has been underway for several years

at NBS to provide a new series of Standard Reference Materials

for the calibration of ion-selective electrodes . This program

has been designed to meet the practical needs for standardization in many areas, both scientific and industrial, in which

these sensors have demonstrated an extremely wide range of

application

.

Although the response of an ion-selective electrode to a particular ion depends on the activity of that Ion in solution,

the thermodynamic activity of a single ionic species is not

uniquely defined. Recently it was proposed [15] that the convention on which activity standards for ion-selective electrodes are based be made consistent with the existing pH

convention. This convention, intended for use at ionic

strengths of 0.1 or less, was reasonable under the same limitations as the pH convention. In more concentrated solutions,

however, differences between the mean activity coefficients

of uni-univalent electrolytes become more pronounced and it

appeared that an extension of the simple form of the pH convention was not entirely justified. However, it is possible

to establish a conventional scale of activity for a single

ionic species by choosing an arbitrary scale for the activity

coefficient of that ion. Rather than selecting an entirely

arbitrary scale for single ion activity coefficients, the NBS

approach to a conventional single ion activity scale is being

based on the physical concept of hydration of ions in solution

[16]. A cooperative effort between NBS and Dr. Roger G. Bates

(University of Florida, Gainesville) and Dr. R. A. Robinson

(State University of New York at BInghamton) has resulted in

the presently advocated convention [17] based on the StokesRobinson hydration theory.

21
Stokes and Robinson [16] have derived the equation

In v. = |Z^Z I In fnu • - - In a - In [1+0 . 0l8( v-h)m] (12) + i + _ i DHv w

where f^ is the electrostatic contribution expressed as an Un

activity coefficient on the mole fraction scale, a is the

water activity, v, the number of ions produced by one molecule

of the electrolyte, h, is the hydration number and m, the

molality . In this manner, a conventional method, based on a physical

theory, of dividing mean activity coefficients into their ionic

components forms the basis of the NBS scales of ionic

activities

.

B . Single Ionic Activity Coefficients

By assuming that the chloride ion is unhydrated [16,17] > the hydration theory can be used as a means of dividing the

mean activity coefficients of unassociated chlorides into single

ionic components. This is a non- thermodynamic assumption, but,

unlike many conventions which are highly arbitrary in nature,

references provide considerable evidence to support this

assumption. Equation (12) rests on two assumptions: a) that

water bound to one or both species of ions is no longer a part

of the bulk solvent, and b) that the Debye-Huckel expression

correctly gives the true activity coefficient (mole fraction

scale) of the solvated ions:

n , -AI 1/2

In f DH ltB

» : l/2 (13)

In Eq . (13), A and B are constants of the Debye-Huckel theory,

a is an ion-size parameter, and I is the ionic strength in

molarity units (rool 1~ ) .

C . Uni-Univalent Chlorides

From the Gibbs-Duhem equation, the activity of an electrolyte MCI of molality m, is given by

22
(55.51/m) din a_r = dln(YM+

m) + din a cl

- (14)

w

If the cation Is hydrated with h molecules of water and m

? Is

its molality in moles per kilogram of unbound water.

m

m ~ l-0.0l8hm (15)

and hence

-(55.51/m') din a = -(55.51/m) din a + hdln a W WW = din (Yjjj+m') + din acl

- (16)

The activity of chloride ion is the same on the two scales:

myp-,- = m'Yp-i-. From Eqs . (14) and (16),

din (YM

+m) + hdln aw

= din (y^+m') (17)

or

In y m

+ = In Y^+ - hln aw

- In (l-0.0l8hm) (18)

It follows from the postulates of the Stokes-Robinson hydration treatment that the activity coefficient of the hydrated

species i on the mole fraction scale is correctly given in

2

terms of Eq . (13) by In f. = z. In fnH . Hence, since v=2,

In y^+ = In f

DH

- In [1-0 . 0l8(2)m' ] (19)

and it follows from Eqs. (15), (18), and (19) that

In Ym+ = In fnu - hln a - In [1-0 . 0l8( 2-h)m] (20) 'M DH w

Combination of Eq . (20) with Eq. (12) for the mean activity

coefficient of a 1:1 electrolyte and with the definition of

the osmotic coefficient <p -In a

* = 0.0l8vm (21)

gives

23
In (YM+/Y.+

) -(h/2) In a = 0.0l8hm(J) (22) M

' '+' v w or

log y M

+ = log y + + 0.00782hm<j) (23)

from which

log Y C1

- = log Y + - 0.00782hmcJ) (24)

D. Alkaline Earth Chlorides . For an unassociated salt MClp,

the same procedures lead to

In y m

++ = ^ In fDR

- hln a

w

- In [1+0 .0l8(3-h)m] (25)

from which

log Y M

++ = 2 log y + + 0.00782hm(f) + log [1+0 . 0l8( 3-h)m] (26)

Since 3 log y+ = log Y M

++ + 2 log Y C1~,

2 log y c1

- = log Y + - 0.00782hm(J) - log [1+0 . 0l8(3-h)m] (27)

E

.

Equipment

A slight modification in the measuring system has been

adopted. A digital voltmeter, DVM, accurate to 0.01 mV has

been integrated into the system and is being used to directly

measure the potential of most of the electrode systems except

those of very high impedance, such as the glass electrodes.

In the case involving high impedance, the DVM is used to

measure the output of a vibrating reed electrometer. The

measuring system, complete with temperature controlling instruments, is shown in Figure 7.

F. Procedure for Conventional Single Ionic Activities

A procedure for determining values of single ionic

activities, based on the hydration theory, is described. The

mean activity coefficients y+ are obtained from Robinson and

Stokes [18] and NBS Report 9908 [19], They are first fitted

as a function of molality by computer calculation. In the

24
Figure J. Equipment for measurement of ion-selective electrode

cell emf

.

same manner, the osmotic coefficient is obtained as a function

of molality

.

When the data are available, as in the case of NaCl and

KC1, at different temperatures, the activity and osmotic coefficients may be expressed as a function of the temperature

at particular molalities.

To obtain the molarity, M, the function M/m is expressed

as a function of molality, hence, the molarity can be shown at

various molalities

.

The hydration theory [Eq. (24)] is then used to compute

log y and log y the single ionic activity coefficients of

25
the cation and anion, respectively, then the activities are

easily obtained by

log& a. = log y. + log m. or a. = Y.m. (28)

1 to, i

to i i'ii

The resulting pM and pCl values are shown in Table 9 3 along with other pertinent results, which illustrate some of

the information that will appear on forthcoming SRM certifications for ion-selective electrode standards (NaCl) . Table

10 appears in the following Section concerning KC1 standards

for ion-selective electrodes

.

G . Activity Standards for Ion-Selective Electrodes

A number of sodium, potassium and chloride ion-selective

electrodes, obtained from various manufacturers, were compared

for Nernstian response. All electrodes checked were found to

respond "ideally" within an estimated experimental error of

about 0.6-0.8 percent of the theoretical slope at temperatures

of 10, 25, and 40 °C

.

High quality NaCl and KC1 have been obtained from

commercial sources and have been certified for homogeneity,

purity, and single ionic activities. The results for the

activity standards for Na and Cl~, based on the hydration

theory [17] , are illustrated in Table 9 5 and for K and Cl~,

in Table 10.

Table 9- Activity standards for sodium chloride

Molality Molarity Activity Activity

(m) (M) (cation)

0.000965

Y+

0.965

(anion)

0.000965

Y0.965

pNa

3-015

pCl

0.001 0.000997 3-015

.01 .00997 .00903 .903 .00902 .902 2.044 2.045

.1 .0995 .0783 .78S .0773 • 773 1.106 1.112

.2 • 1987 .148 .744 .145 .727 0.828 0.838

.3 .2975 .216 .721 .209 .697 .664 .680

.5 .4941 .350 .701 • 331 .662 .455 .480

1.0 .9789 .696 .696 .620 .620 .157 .208

1.5 1.4543 1.077 .718 .904 .602 - .044

2.0 1.9200 1.504 .752 1.187 .593 ~ TM

26
Table 10. Activity standards for potassium chloride

Molality Molarity Activity Activity

(m) (M) ( cation)

0.000965

Y + 0.965

(anion)

0.000965

Y0.965

pK

3.016

pCl

0.001 .000997 3.016

.01 .00997 .00901 .901 .00901 .901 2.045 2.045

.1 .099^ .0772 .772 .0768 .768 1.112 1.115

.2 .1983 .145 .723 .143 • 713 0.841 0.846

.3 .2967 .208 .693 .204 .680 .682 .690

.5 .4916 .330 .659 .320 .639 .482 .495

1.0 .9692 .623 .623 .586 .586 .206 .232

1.5 1 .4329 .917 .611 .836 .558 .0376 .078

2.0 1 .8827 1.219 .609 1.077 .539 — -

(B. R. Staples)

27
4. POTENTIOMETRY

Ion-Selective Electrode Study of Trace Silver Ion

Adsorption on Selected Surfaces

A . Introduction

The adsorption of low concentrations of silver ion on

container surfaces has been recognized and evaluated by radiotracer and chemical methods for some time, as demonstrated for

example in the study of the bacteriological and chemical behavior of silver [20,21]. This effect has recently been under

systematic reinvestigation using the radioactive silver tracer

method for a wide variety of materials and conditions [22,23].

These investigations were designed to give estimates of the

amounts of ions lost by adsorption to various surfaces and to

determine the most suitable storage containers and conditions

for water samples containing low levels of silver. In these

studies, silver adsorption as high as 140 percent (on Pyrex at

the 50-ppb silver level) was reported. It was shown by autoradiography that such high adsorption levels are apparently due

to inhomogeneity of silver adsorption on the surfaces, i.e.,

the calculation of the total percentage adsorption from the

measured specific adsorption assumes uniform silver adsorption

which, in fact, does not occur [23].

By making silver ion-selective electrode measurements of

the solution rather than the container surface, it should be

possible to avoid the uncertainties caused by non-uniform adsorption. That is, instead of measuring a specific surface

area which may or may not be representative of the actual degree of adsorption, the electrode senses an "average" ionized

silver level which is homogeneous and represents the difference

between the original amount of silver present and the total

amount adsorbed.

Additional advantages are realized in the potentiometric

method by the reduction of experimental complexity, both in

equipment and methodology. Measurement techniques analogous

28
to pH determinations are used without recourse to radioactive

tracers and daily isotope ( Ag) decay corrections or to

multiple sets of solutions and containers . The use of a single

set of containers and solutions further eliminates uncertainties due to differences in surface characteristics of the

vessels

.

B . Experimental

Silver stock solutions were prepared from reagent grade

silver nitrate without further purification. Emf measurements

were taken with a silver sulfide ion-selective electrode in

conjunction with a double-junction reference electrode. The

emf readout was made to the nearest 0.1 mV using a recorder

connected to the output of an expanded scale pH/mV meter.

The container materials tested in this study were: Pyrex,

Vycor, polyethylene, Teflon (FEP), and Pyrex coated with

Desicote (Beckman Instruments, Inc.).

Stock solutions were made by dissolving weighed amounts

of silver nitrate in distilled water, with no added inert

electrolytes or complexing ligands . All solutions in this

study were approximately neutral and no attempt was made to

study the effect of pH on adsorption. From the stock solution

-4 -4

(10 M) , several electrode-calibration solutions between 10

_7 and 10 M were made by serial dilution. The data obtained from

these standard solutions were used to establish the calibration

curve shown in Figure 8 which was used to relate the observed

emf readings to silver ion concentrations. From a consideration

of the calibration curve and the expected levels of adsorption

(50 to 80 percent), it was decided to use an initial silver ion

concentration of 2 x 10 M (^ 0.2 ppm) in the test containers.

This level of silver was selected in order that the measured

silver concentrations would always be read from a linear portion of the calibration curve where maximum sensitivity is

attained, I.e., down to approximately 4 x 10 M. This was in

fact achieved since the highest level of adsorption observed

29
250

240

230

220

210

200

190

180 - 170 - 160

150

140

130

-i 1 1—i—i—i i | "I 1 1 TTest Solution Concentration

(2X1

Q

6M, 0.216 ppm)

_i i

i I 10" 6 1Q-6 2 SILVER MOLARITY

-1—L.10~5

Figure 8. Response of the silver sulfide electrode to silver

concentration. Response slope in the linear region

of the calibration curve is 59 • 5mV/pAg (ambient

temperature 25 ± 1 °C)

.

was about 60 percent, corresponding to a silver concentration

of 8 x 10 M remaining in solution. It should be noted that

this silver level (0.2 ppm) is intermediate to those used in

the radiotracer studies of West, et al. [22,23] who used silver

concentrations at the 0.05 and 1.0-ppm levels.

-4

From another stock solution (2 x 10 M AgNCO, fresh calibration standards were prepared each day with which the electrode system was calibrated before, during, and after each

series of measurements on the five test solutions. These three

electrode calibration measurements were then plotted against

measurement time for an emf-drift correction. A drift-correction factor was then applied to each test solution reading

according to its actual measurement time. After correcting

for the emf drift which amounted to as much as several millivolts, the silver concentration was read from the calibration

curve

.

30
Each of the five different test beakers was washed with

dilute detergent solution, rinsed repeatedly with distilled

water, and air dried. The standard silver solution (2 x 10~ M;

0.216 ppm) was then added to each of the clean test beakers.

Emf readings were randomly taken of the five test solutions

concomitantly with the electrode-calibration measurements,

and the emf-drift corrections were applied at the conclusion

of each series. A duplicate series was run each day. Over

the 46-day span of this study, a total of 56 series was run

with the frequency of measurements decreasing toward the end

of the period. Between measurements, the test beakers were

stored under inverted beakers to prevent both evaporation and

contamination by air-borne dust.

The percent adsorption was calculated by the equation:

= Ag(0) - Ag(t)

ads. Ag(0)

where

:

Ag(0) = original silver concentration, 2 x 10~ M; and

Ag(t) = silver concentration at some time, t, after the

introduction of the solution into the test beaker.

Thus, Ag(0) - Ag(t) represents the amount of silver removed

from solution by adsorption. Because of differences in the

sizes of the beakers used and consequently the volumes of silver

solution, the surface area-to-volume ratio varied from O.85 cm

for Teflon to 0.75 cm" for other materials. This would, in

effect, tend to exaggerate the adsorption values for Teflon by

about 10 percent.

C . Results and Discussion

Adsorption percentages calculated by the above equation

are shown in Figure 9 for the time period up to 10 days . During this period of the highest adsorption rates, the Pyrex and

Desicoted Pyrex containers showed the greatest losses of silver,

reaching the 10-15 percent adsorbed levels in the first 24-hour

31
period. The other three materials adsorbed less, ranging from

about 5 percent for polyethylene down to less than 2 percent

for Teflon. Note that all of the reported adsorption percentages are mean values with a maximum variability (range) of

about 1 percent and an average variability of 0.5 percent.

25

20 -

-i—i—i—i—i—i—i—i—

i

// 1—i—i—i—i—

Pyrex /

/i I i i i l l i i J/. 20 40 60 80 100 200 220 240

TIME, hours

Figure 9. Percent silver adsorption vs. time for five selected

materials. Initial silver concentration 2 x 10 M

(0.216 ppm) . Average variability in measurements

± 0.5$ absolute.

The adsorption percentages for the periods ending 10, 30,

and 46 days are summarized in Table 11. Also given in this

table are the average adsorption rates for the time intervals

between 10, 30, and 46 days.

32
a b Table 11. Adsorption percentages and rates for 0.216 ppm

silver solution on various materials.

Average Average

10 days A$/At 30 days AjC/At 46 days

Pyrex 24.5$ 1.2 48.0$ 0.7 59-5$

Desicoted Pyrex 19-0 1.1 40.5 • 7 51.0

Polyethylene 12.0 1.0 32.5 .9 47.0

Vycor 11.0 0.9 28.0 .9 43.0

Teflon (FEP) 10.5 1.1 33.0 1.1 50.0

a b to the nearest 0.5 percent, to the nearest 0.1 percent/day

The table is arranged according to the decreasing degree

of adsorption at the end of ten days . This initial order does

not hold at the end of 30 and 46 days where both polyethylene

and Vycor replace Teflon at the low end of the adsorption

scale. Prom Figure 9, it is evident that the cause of this

relationship is the initial induction period (about 18 hours)

exhibited by Teflon but not by any of the other materials.

Although this effect was noted for Teflon by West et al., they

also observed varying degrees of induction for several of the

other materials. However, differences in the silver concentration levels make intercomparison of results difficult for these

materials

.

An interesting trend indicated from Table 11 is that the

greatest differences in adsorption between materials occurs at

relatively short times, i.e., within 2 or 3 days, and at longer

times the rates of adsorption become comparable. Furthermore,

as expected, the adsorption rates decrease more rapidly for

the materials that adsorbed greatest initially, but the surprising observation is that the degree of adsorption at long

times seems to become independent of the surface material.

That is, although at 46 days there is still a spread of almost

20 percent (43 to 60 percent) between the maximum (Pyrex) and

minimum (Vycor) adsorption values, the average rate of adsorption during the 30 to 46-day period is still 0.9 percent/day

33
10 days 30 days a 0.05 ppm 1.0 ppm 0.05 ppm

2-12$ 7-1535 49-140$

n. a. 7-9 65-75

0-5 7-12 40-79

2-5 16-18 58-108

4-7 2-4 8-44

for Vycor but has decreased from 1.2 percent/day to 0.7 percent/

day for the Pyrex. This trend more or less holds for all of

the materials except Teflon which at 50 percent absorbed is

still adsorbing at an average rate of about 1.1 percent/day

during the period 30 to 46 days.

In comparison to the values found by West et al. (Table

12) , our values for silver adsorption at 10 days tend to be

higher (except for Vycor) and our values at 30 days are more

consistently low (except for Teflon). The silver adsorption

on Vycor at 10 days and on Teflon at 30 days fall within the

limits found by the radiotracer method.

Table 12. Silver adsorption by radioactive tracer method

of West et al. [22,23]

Pyrex

Desicoted polypropylene

Polyethylene

Vycor

Teflon

data not available for the 1.0-ppm silver level at 30 days

data taken from reference [22].

data taken from reference [23].

D. Conclusion

From these electrode studies, Vycor appears to be the

best material of those studied in regard to the smallest longterm silver losses due to adsorption. Unfortunately, even

these losses are too serious for Vycor to be of use in the

storage of dilute silver solutions. For short-term storage,

i.e., periods of up to one day, Teflon exhibited silver losses

of less than two percent and is adequate for such periods. For

storage intervals of more than one day, none of the materials

34
tested are satisfactory and a chemical stabilizer (complexing

ligand) such as thiosulfate [22,23] would appear to be

essential

.

This study has demonstrated the feasibility of using the

silver ion-selective electrode for the direct potentiometric

determination of silver in long-term investigations of trace

silver adsorption. However, the electrometric method is less

suitable than the radiometric method for silver concentrations

below the micromolar level and is unusable for "in situ" studies

in which complexing ligands have been added. In this latter

case, measurements could be made on aliquots taken from the

test containers and determined by a standard addition procedure.

At the micromolar silver level and above, the electrometric

technique offers the advantages of less complex and costly

equipment, simplified procedure, and improved precision over

the radiometric method.

The electrometric technique could also be used for adsorption studies of other ions, e.g., Cu , Cd , Pb , and P , for which ion-selective electrodes are available which perform

_7 well down to the 10 molar level. In addition, simultaneous

multiple ion studies, i.e., for preferential adsorption, displacement, and other types of Interactions, could be performed

using ganged (multiple) ion-selective electrodes. In summary,

ion-selective electrodes should prove to be of considerable

benefit In the study of trace levels of ions on the basis of

the continuous and non-destructive nature of the measurements

and also on the sensitivity and precision that can be obtained.

(B. T. Duhart)

35
5 . COULOMETRY

A . Introduction

The long-range goal of the coulometry program is to place

chemical characterization, i.e., analytical chemistry, on an

absolute basis: to change it from a science of measurement

which requires qualifying statements descriptive in nature (such

as "based on high purity silver", or "compared to high purity

single crystal material") to a science in which the magnitude

of the measured property is "based on the values of units of

time, mass and length as maintained by the NBS". Much of the

coulometry research is geared to achieve this end. The

coulometric methods of analysis which are developed at our

facility are specifically designed to yield high reproducibility (precision) of the results. The second stage of each

research effort entails investigation to test and prove the

accuracy (or inaccuracy) of the method. When these two requirements are met (high precision and high accuracy) the

method is then adopted for use in such areas as certification

of Standard Reference Materials . The developed methods encompass the whole spectrum of chemical reactions: acidimetry,

alkalimetry, oxidation-reduction reactions, precipitation reactions and complexometry . Occasionally research in coulometry brings us very close to another area of less applied

nature, namely the area of physical constants. Thus, it becomes possible to redetermine by an independent method either

the faraday or the atomic weights of various elements . Redetermination of the atomic weight of zinc is one such undertaking.

An area of tremendous interest today is stoichiometry

,

particularly the stoichiometry of semiconductors. Presently,

a concentrated research effort is underway in this very area:

determination of the stoichiometry of gallium arsenide.

Several primary standard SRMs were characterized, evaluated and certified in the course of this year via coulometry.

36
The following section of this report will highlight some of

the significant aspects of the activities in coulometry during

the past year.

B . Research

1 . Coulometry of Zinc

Because elemental zinc is a rather active metal, little,

if any, coulometric work was done with the Zn° , Zn couple.

Its amphoteric behavior (resulting in spontaneous dissolution

either in acid or in alkaline solutions) and insolubility as the hydrous oxide in neutral solutions further detracted from

it being considered as a promising element for quantitative

electrolysis

.

Our initial effort in the electroanalytical chemistry of

zinc was made during the investigation of amalgam stripping

coulometry as a possible high-precision analytical method.

Being such an active metal, zinc appeared to be ideally suited

for testing the anodic stripping method. Our expectation at

that time was fulfilled: with samples of zinc as small as 7

mg, a precision of 0.01 percent was obtained [24], The experiment itself, however, offered only the method for determining elemental zinc and perhaps other metals in a sample

which could be converted to an amalgam, and could not be

applied to the determinations where these metals exist as

compounds

.

The recovery of zinc could not be evaluated to the desired degree of accuracy since the accepted atomic weight of

zinc (65.37) was only known at that time to 0.01 AMU or 0.015

percent, however, the results appeared to be systematically

low by about 0.01 percent. Such an error could, of course,

result from the "corrosion current" contribution to the overall dissolution of zinc. The source of this error remained

temporarily unsolved.

In the meantime, the Bureau acquired and certified

99.9999 percent pure zinc metal (SRM 682) and it became

37
challenging to test the reason for the observed behavior in

the anodic stripping experiments.

A proposal was made and, in collaboration with Professor

Robert T. Foley of The American University, investigation of

the coulometric behavior of zinc was undertaken.

The Problem : The object of this research is to determine,

by an absolute method, the electrochemical equivalent of zinc.

The obtained electrochemical equivalent will serve as the

basis for a new, independent redetermination of the atomic

weight of zinc, which at present is the subject of some controversy. Materials of different origins will be investigated

to establish natural variations in the atomic weight of terrestrial zinc.

Significance of the Research : The presently-accepted

value for the atomic weight of zinc is 65-37 [25]. The work

on the atomic weight of zinc was reevaluated last by the

International Commission on Atomic Weights in 1961 [26] . The

above value is based primarily on ZnClp/2Ag [27], ZnCl„/2AgCl

[27], ZnBr

2

/Zn [28], and ZnCl

2

/Zn [29] combining weight

ratios. Two mass spectrometric determinations of the isotopic

abundances [30,31] yield a significantly different value for

the atomic weight of zinc — 65-387. The Commission, however,

recommended retaining the chemically determined value of

65.37. Such a discrepancy in the value of the atomic weight

cannot remain unresolved, particularly since for most of the

other elements the uncertainties in the atomic weights are of

the order of 0.001 AMU, or one order of magnitude less than

they are for zinc

.

A third, independent, electrochemical method for the determination of the electrochemical equivalent and the atomic

weight of zinc is proposed which will aid in resolving the

existing discrepancy in this important physical constant.

38
The suitability of electrochemical methods for the determination of atomic weights was implied in the original

work of Faraday. In 1833 he established that the law of

definite proportions holds even when the chemical reactions

are not carried out directly but are induced by the passage

of electric current through the electrolysis cells [32]. The

amount of chemical change produced at the electrodes of a cell

is directly proportional to the quantity of charge passed.

Explicit utilization of Faraday's laws for the determination

of atomic weights was recognized very early in the development

of quantitative electrochemistry. Thus, for example, Laird

and Hulett state £33];

"Faraday's law, that a definite quantity

of electricity is associated with one gram equivalent of any ion, is, as far as we know, strictly

accurate, probably as accurate as the law of

conservation of mass. There is evidence that not

even as small a quantity of electricity as 10"^-"

coulomb passes from an electrolyte to an electrode

without a corresponding chemical change taking

place ..."

Using electrolytic deposition of cadmium in series with a

silver coulometer, Laird and Hulett were able to obtain precise Cd/Ag ratios, and assigning a value for the atomic

weight of silver they were able to calculate the atomic

weight of cadmium. A similar approach was used by Gladstone

and Hibbert earlier [3^.] for the determination of Zn/Ag and

Zn/Cu ratios, and consequently, the atomic weight of zinc.

Unfortunately, we now know that silver deposition coulometers

and copper coulometers, though precise, are not very accurate

due to the variation of the amount of occluded mother liquor

in the deposit. This aspect of silver deposition coulometers

is discussed by W, J. Hamer 135], A more direct approach to

the determination of the electrochemical equivalent is through

the use of absolute current and time measurement, employed by

D. N. Craig and co-workers 136] in the determination of the

electrochemical equivalent of silver and the faraday and by

39
us in the determination of the electrochemical equivalents of

benzoic acid and oxalic acid [37].

The difference between chemical values for the atomic

weight of zinc (65-37) and the value obtained mass spectrometrically (65.39) is of the order of 0.03 percent. The

anticipated value of the atomic weight obtained by the electrochemical method will have an uncertainty of 0.002 percent

(this uncertainty will result primarily from the uncertainty

of the f araday : 96487-0 ± 1.6 abs. C/g-equiv) . Nonetheless,

even this uncertainty is 1.5 orders of magnitude smaller than

the existing discrepancy in the atomic weight of zinc. The

significance of such an improvement in a physical constant as

important as the atomic weight is self-evident.

The Method : The investigation undertaken here entailed

the following specific studies which were necessary for

accurate evaluation of the electrochemical equivalent and the

atomic weight of zinc:

(1) study of the exchange currents and the rate of

corrosion of zinc and zinc amalgams in various electrolytes

used in the proposed coulometers (Tafel's relationship);

(2) study of the current efficiency as a function of

current density for anodic dissolution of zinc;

(3) study of the current efficiency as a function of

current density for cathodic deposition of zinc into amalgam;

(4) design, construction and quantitative performance

evaluation of anodic zinc coulometer;

(5) design, construction and quantitative performance

evaluation of cathodic zinc coulometer;

(6) study of the effects of various parameters on the

electrochemical equivalent of reference zinc sample (parameters

include current density, current density distribution, impurities in electrolyte, electrolysis time, mass of zinc involved in the reaction and surface area of electrodes);

40
(7) determination of electrochemical equivalent and

atomic weight of zinc using materials of three levels of

purity : (a) NBS Standard Reference Material 682 Zinc - 99.9999 percent,

(b) NBS Standard Reference Material 683 Zinc - 99-999 percent,

(c) commercial zinc - 99.9 percent;

(8) survey of zinc of various origins for possible

natural variations in the isotopic composition.

Results : The first stage of research permitted the

selection of the optimum electrolyte and electrodes to be

used in further studies as well as evaluation of the magnitude

of spontaneous corrosion of zinc and zinc amalgam and the

corrections for this effect . The need for an inert atmosphere

was also resolved here, and the second and third stages of the

investigation established optimum current densities to be

used in the final coulometric experiments which, if exceeded,

would result in oxidation of water to oxygen in the case of

the zinc anode, oxidation of mercury in the case of zincamalgam anode and reduction of hydrogen ion in the case of

zinc or zinc-amalgam cathode.

The fourth and fifth stages involved the design of the

apparatus, which permitted accurate measurement of the mass

difference for zinc cathodes and anodes involved in the

electrochemical reactions. The resistance of coulometers

must be sufficiently low to permit the passage of currents

up to one ampere (using a 60-V power supply, the resistance

must be 60 ohms or less). The coulometric configuration

finally used in the experiments is shown in Figure 10.

This configuration of the gravimetric coulometer combines

many desirable features. Anodes are suspended freely from a permanently attached support wire, thus no mass transfer takes

place as a result of the clamping of the lead wire. Experi41
Figure 10. Coulometer for the determination of the atomic

weight of zinc

.

ments involving the measurement of mass changes of the support

wire when large quantities of charge (10 coulombs) were passed

show no systematic change in its mass. This being the case,

there can be no net mass transfer between the support lead and

the suspension wire of the zinc anode.

A nitrogen atmosphere can be easily maintained over the

solution, thus reducing the rate of spontaneous dissolution

of zinc

.

The provision of a flat ground-glass joint in the middle

of the cell permits the insertion of porous-glass frits or

Millipore filters across the cell to determine whether or not

there is any physical sedimentation of zinc particles due to

deterioration of the anode in the course of dissolution.

42
Finally, a cup cathode filled with mercury at the bottom

of the cell can be used for the gravimetric determination of

the zinc deposit

.

The sixth stage of the research involved investigation of

all possible experimental parameters (other than purity of

zinc) on the electrochemical equivalent of one lot of zinc,

selected to serve as the reference material.

Although the published results of mass spectrometric investigations indicate no significant variations in the isotopic

composition of zinc, nevertheless to insure that the value

obtained in this research is truly representative of the

terrestrial zinc, an experimental survey of primary zincbearing minerals from worldwide sources would be highly desirable. It is hoped to conduct this comparative study on virgin

minerals which have not been subjected to metallurgical processing, since the latter could produce isotope separation

(isotope separation can occur in such processes as distillation which is commonly used in purification of zinc).

The results of this research are presently being prepared

for publication in the appropriate journals. In brief, however, no systematic differences were detected in the electrochemical equivalent of zinc samples originating from various

sources. The anodic coulometer with zinc amalgam anode is

capable of operating at a high level of precision (standard

deviation of a single measurement is 0.002 percent). Oxygen

in zinc metal has a significant effect on the electrochemical

equivalent, and must be removed (vacuum fusion). The anodic

coulometer is unaffected by metallic impurities, as one would

expect since only a few metals are more active than zinc.

Oxygen in the electrolyte enhances the corrosion of zinc

amalgam. In the absence of oxygen the corrosion current density

-7 -2

is only 5 x 10 A cm . The results of this research permit

calculation of the atomic weight of zinc with a 95 percent

confidence limit of 0.001 percent.

43
2 . Further Implications of Zn++ Generation

a. EDTA analysis . In addition to fundamental interest in the atomic weight of zinc, the electrogenerated zinc

ion can be very conveniently used as a reagent for complexometric coulometry. The equilibrium constant for complexation

of Zn with EDTA is about 3 x 10 , making it highly suitable

for coulometric titration of EDTA.

A new coulometric method was developed for EDTA analysis

which makes use of amperometric end-point detection under

conditions where the Indicator signal is proportional to the

++ uncomplexed Zn concentration. Samples of the disodium salt

of EDTA, weighing two grams, were titrated by this method.

The preliminary results indicate a highly reproducible titration as shown in Table 13-

The material has not been assayed by another independent

method to test the accuracy of these results, but the manufacturer's assay is 99.9 percent.

Table 13- An alysis of Na.,EDTA •2H

2

0.

Sample No. Assay, percent A , percent

1 99.937

8 - 0.0015

2 99.933

8 + .0025

3 99.937

2 - .0009

Average 99.936^

Standard deviation of a single determination

a = 0.0022 percent

b. Determination of stoichiometry . The newly developed EDTA titration method is applied to the analysis of

metals for the purpose of determination of compound stoichiometry. Thus, in the cooperative characterization exchange pro44
gram under the auspices of the Organization for Economic

Cooperation and Development (OECD), one of the materials which

is studied from the standpoint of its stoichiometry is gallium

arsenide (i.e., Ga:As ratio). The determination of gallium is

in fact carried out in our laboratory by the EDTA back-titration

method.

Coulometric analysis of gallium arsenide stoichiometry

is interesting for several reasons. Stoichiometry of semiconductors is in general of interest to the electronics industry because of the dependence of their electrical properties

on small deviations in stoichiometry. At present there are

no satisfactory methods for this purpose at the required degrees of accuracy and precision. To establish the stoichiometry (or the departure from it) for a 1:1 compound such as

GaAs by coulometry, it is not necessary to know the atomic

weights of the elements in question. The only prerequisite

is to develop 100.000 percent efficient coulometric reactions

upon which the measurements of electrochemical equivalents

will be based. Once the quantity of electric charge (number

of electrons) which is required to carry arsenic in a given

sample through a definite chemical change (e.g., As[III] -> As[V] + 2e) and gallium in the same sample through a chemical

change unique for this element has been determined, stoichiometry can be easily established. It represents merely the

ratio of charges consumed In the two independent reactions

.

Such a determination does not even require accurate mass

,

current or time measurement as long as these values are the

same for the two independent determinations.

If, on the other hand, current, time and mass measurements

are made accurately the additional information could be invaluable. First, since arsenic occurs in nature as a monoisotopic

element, its atomic weight is known to the nearest 0.0001 AMU

(or about 0.0002 percent). The atomic weight of gallium, on

the other hand, is known only to the nearest 0.01 AMU, There45
fore, knowing the stoichioraetry of GaAs and knowing the sample

mass accurately the atomic weight of Ga can be computed from

the Ga/GaAs ratio. Furthermore, the atomic weight of Ga can

be computed independently from Faraday's law.

Projection into the future promises successful application

of this method to such compounds as zinc sulfide, zinc telluride, indium compounds, determination of the ferric ion,

analysis of cupric compounds, mercuric compounds and the like.

3 . Potassium Dichromate

Potassium dichromate, one of the most commonly used oxidimetric standards has been issued by NBS for a number of

years. Exhaustion of the last lot (SRM 136b) and the continuing

demand for this standard necessitated its renewal. As with the

previous lot, the Office of Standard Reference Materials relies

on the coulometric method for absolute standardization of this

oxidant

.

Twenty subsamples of KpCr ? 7

, representing a single lot of

the material, were analyzed. Thus, each five weight percent of

Figure 11. Potassium dichromate samples and some of the

coulometric equipment used in standardizing this

oxidant

.

46
this lot of the material was tested. Approximately five grams

of material were taken from each bottle, dried for six hours

at 130 °C in an air atmosphere drying oven, and stored in a

P

p

Oj- desiccator. One-gram samples (one from each bottle) were

weighed out by substitution using standard stainless steel

weights (true mass = 0.999901g). The weight of the sample was

corrected to true mass by applying appropriate corrections for

the buoyancy of air.

Weighed samples were transferred into 125-ml Erlenmeyer

flasks and titrated coulometrically in a random sequence over

the period of a few weeks by a method developed in this laboratory [38]. The results of analysis are summarized in Table 14

Table 14. Summary of data of K

? Crp07 analyses

Titration Bottle

sequence number Assay, % Residuals

1 3 99.9849 0.0027

2 19 99.9821 - .0001

3 8 99-9840 .0018

4 10 99-9847 .0025

5 1 99.9797 - .0025

6 11 99.9845 .0023

7 2 99.9790 - .0032

8 17 99.9801 - .0021

9 5 99.9825 .000^

10 20 99.9864 .0042

11 14 99.9874 .0052

12 15 99.9792 - .0030

13 12 99.9786 - .0036

14 6 99.9794 - .0028

15 9 99.9794 - .0028

16 18 99.9825 .0003

17 4 99.9804 - .0018

18 1.6 99.9863 .0041

19 7 99.9796 - .0026

20 13 99.9833 .0011

Mean 99.9822

c = 0.0028

SD of the mean = 0.0006^

47
Discussion of the Results : The mean value of the assay

of this material is 99-9822 percent. The standard deviation

of this mean, based on 19 degrees of freedom, is 0.00064 percent. One can assume that the mean assay of the lot represents

the mean of all populations of the twenty arbitrary subdivisions of the lot. The traditional approach to standard reference materials is to ask the following questions. Is this lot

of material homogeneous? If so, how accurately is the value

of the assay known? What uncertainty should be assigned to

the mean which represents the property content of this material?

Unfortunately, some of the questions cannot be answered unequivocally. In the following paragraphs, I will attempt to

present my views on the subject.

The precision of the analytical method was previously

evaluated [38], and the estimate of the standard deviation of

a single determination was 0.0029 percent. Since the evaluation of the method was conducted on a single bottle of material,

this standard deviation reflects a combination of only two

possible distributions: (1) random errors of measurement (a ),

and (2) within the bottle heterogeneity of material (a, )

.

It is therefore reasonable to express the overall standard

deviation as a rms value of the two contribution factors, i.e.:

a tot

= /am

+ a h

= °- 002 ^. (30)

Unfortunately, these two components cannot be evaluated separately without apriori knowledge of either the precision of

the method or the heterogeneity of material used to test the

method (without varying experimental conditions) , Consequently,

in evaluating the homogeneity of a given lot of material one

can only estimate the difference in between-bottle variability

from within-bottle variability. The random fluctuations of

composition (within-bottle variability) cannot be separated

from the random errors of the method.

48
The data obtained in this investigation (Table 14) show

that between-bottle variability is negligible in comparison

with combined within-bottle variability and variability due

to the random error component of the method.

o+_ . = 0.0029$ tot

a, . , ,, 1 = 0.0028$ between-bottles

One can therefore treat all of the titration results as samples

representing a single population. This random error contribution to the overall uncertainty of the assay at the 9?-percent

confidence level is

-^—— = 0.0014$ (3D

/n

Let us consider other pertinent data which can shed light on

the sample vs. method contribution to the overall error.

In the coulometric measurement process, two types of

random errors are involved: (1) errors independent of, and

(2) errors dependent on the magnitude of the measured property.

These two types of errors can be illustrated by the following

example. The charge which is passed through the coulometric

cell is equal to

Q = / Idt. (32)

Coulometric titrations are conducted at constant current; however, the word "constant" should really be "virtually constant",

since there is always some random fluctuation of current. This

current can be subdivided into two parts: time-independent,

1° ; and time-dependent, I(t), i.e.,

I = 1° + I(t) (33)

or

Q = I°t + |

t I(t)dt. (34)

4 9
As indicated above in the constant-current mode of operation,

it is assumed that

/

t I(t)dt = (35)

Clearly, this condition is fulfilled if I(t) is a random or

periodic function of time and if t -> °° . Thus, the larger the

magnitude of the measured property, requiring longer periods

of time, the more nearly is this condition fulfilled. This,

then, is magnitude-dependent error.

Moreover, 1° is compared to the voltage of the saturated

Weston cell as an I°R drop through a standard resistor. In any

given experiment, the comparison between this I°R drop and the

emf of the Weston cell can be in error by some magnitude AI°

which is determined by the sensitivity of the comparison system.

This error will be time-independent and consequently independent

of the magnitude of the property measured. Over a large number

of experiments, n, however,

n

^iTM Z AI? = (36)

The errors of type (1) include such things as day-to-day variation of the standard frequency, diurnal variation of the standard resistor, standard cells, air density (in corrections of

mass to vacuum), sample transfer losses, etc. Errors of type

(2) may include end-point uncertainty, sensitivity of the

balance, switching error, etc.

Thus if one plots these two types of errors against sample

size, the qualitative graph shown in Figure 12 should be

obtained

.

The variability of the results due to within-bottle heterogeneity of material will also behave as a type (2) error,

since in a given population of crystals the a priori probability

of any one crystal having a certain amount of the given property

is constant.

50
TYPE 2 ERROR

TYPE 1 ERROR

MAGNITUDE OF MEASURED PROPERTY (e.g., sample size)

Figure 12. Two types of random errors which are encountered

in coulometry

The possibility of the existence of within-bottle variability of material is not unrealistic since the material contains 0.018 percent of inert impurity (assay of 99o982 percent,

very low impurity content based on emission spectrum and

spark-source mass spectrometric analyses, and slow weight loss

on prolonged drying at elevated temperatures indicates possible

occlusion of mother liquor in the crystals) „ Its distribution

within the sample need not be uniform since a relatively small

number of crystals is taken in any one sample for analysis

(e.g., 1-gram sample contains, on the average, 6500 crystals).

If one is working in region B of the error curve it is

not possible to separate the method errors from the heterogeneity of material unless 100.00-percent pure material is

used to test the method. In the case of "absolutely" pure

material, there is no impurity to be distributed and therefore

all random errors are due to the method. On the other hand,

51
even with impure material (99-982 percent), when one is working

in region A, the error of type (1) can be attributed only to

the method.

Let us, therefore, examine the available data of Tables

14, 15, and 16. These titration results were obtained with

1-gj 0.5-g, and 0.1 —0.2-g samples, respectively. The precision of these three sets of data (expressed as the standard

deviation of a single determination) is 0.0028 percent, 0.0029

percent, and 0.0030 percent, respectively. Thus, a factor of

five change in sample size (6500 crystals in 1-g sample to

1300 in 200-mg sample) changes the precision from 0.0028 to

0.0030 percent, or seven relative percent.

Referring to Figure 12, we must therefore be operating

in region A. As indicated above, heterogeneity of material

would, of necessity, manifest itself as region B. For this

reason, one can conclude that the random error of the analytical

results reported here can be ascribed to a large extent to

the method uncertainty and not heterogeneity of the material.

Such reasoning, then, permits us to separate the random error

of the method from within-bottle variability of material.

The analyses of three samples of material on an "as

received" basis (not subjected to drying) are shown in Table

17. It is quite clear that the material belongs to the same

population as the dried samples

.

On the other hand, we have no control over the environment

(e.g., humidity) to which the samples will be exposed by the

user and for that reason, specification of the drying procedure

is warranted as a precautionary measure,,

In the overall assessment of data, one can combine the

results of Tables 14, 15, and 16 since no significant difference

exists between these sets of data. Thus, excluding one outlier

from Table 16, the mean assay of the material is

99.982 ± o 0011#,

where the uncertainty figure represents the 95-percent confi52
Table 15 . Analysis of K

2

Cr

2 0„, 136b 3 (sample size - 0.5g)

Sample

Number Set I Set II

Assay

Set III Set IV Set V

1 99.980

Q 99.975^ 99 -974

2 9^.983,- 99.978

5

2 99.978

g

99.973

6

99.973 4 99.973

7

99.977

?

3 99.975

x 99.973

g

99. 973

5

99.977

?

4 99.975

?

99.978

?

99.974

?

99.977 x

5 99.978

9

99-978

3

99.977 8

99.976

2

6

Average

99-98l

2

99.978

3

99.976

Q 99.97^ 99.978

6

99.977

3

SD for each

set

0.002^ 0.002^ O.OOlg 0.006 0.000

g

Set VI Set VII Set VIII Set IX Set X

1 99.976

9

99.984

6

99.978

9

99.978

3

99.976

Q

2 99.976 6

99.982

Q 99.977-l 99.978

?

99 . 976

g

3 99.977

5

99.968

5

99. 976

4 99.976

9

4 99-978 4 99.975 2

99.978

5

5 99.978

?

99.979 6

6

Average 99.977

6 99.977 6

99-978-

L 99.978

Q

99-976

5

SD for each 0.000

g

0.006

Q

0.001^ 0.001

Q

0.000

7

set

Overall average: 99 . 977 2

, a - 0.002

aTaken from Reference [38]

53
Table 16. Analysis of smaller samples of K

2

Cr

2 ?

(SRM 13

Bottle

Number Samp le size » g Assay, % Residuals

2

2

2

0.2

.1

.2

99-9873

99.9832

99-9798

0.0031

- .0010

- .0044

5

5

5

0.2

.2

.2

99.9823

99.9882

99-9824

-0.0019

.0040

- .0018

12

12

12

0.2

.1

.2

Avg

99.9686 a 99.9840

99.9865

-0.0002

.0023

99.9842

a = 0.0030

aThis result appears to be an outlier. It is excluded

from consideration of this set of data.

Table 17. Analysis of K^v^.j (SRM 136c) "as received"

(1-g samples )

.

Bottle Numb er Assay, % Residuals

2 99.9802 -0.0032

5 99.9852 + .0018

12 99.9849 + .0015

Mean 99-9834

a = 0.0028

dence interval for the mean based on 30 degrees of freedom.

The accuracy of the result is also dependent on the

systematic errors of the determination. The estimate of

possible systematic error in these analyses due to uncertainties in molecular weight, faraday, emf standard, resistance

standard, and mass standard, is o 0033 percent.

54
The overall 95-percent confidence Interval is

Random + CT syst

= ' ° W (37)

In certifying a standard, an overly conservative (just as an overly optimistic) assignment of uncertainty limits does

disservice to those who use the standard because it, in fact,

conceals some of the available information about the standard.

Uncertainties must be assigned realistically.

In the case at hand, the estimate of the 95-percent confidence interval for the mean (making allowances for possible

systematic errors) was shown to be O.OO 1^. It would thus appear

that o 005 percent is a realistic estimate of the magnitude of

the uncertainty of the mean-measured property (the oxidimetric

assay of LCr ) . The above treatment of data and the conclusions drawn on

the basis of that treatment are valid, however, they represent

a view from a definite, clearly defined standpoint — the

estimate of the uncertainty of the mean property. The uncertainty figure of 0.005 percent refers to the mean property

of the whole lot of the material (assuming on the basis of the

indications of the limited number of measurements that the

heterogeneity of the material is negligible) , including the

allowances for known possible systematic errors, and the reduced random error of measurement by the well established

ta//n treatment due to the natural tendency of random errors

(r. ) to distribute normally about zero, so that in the limit

n

lim V1 n , «,

(n-~>) f=1

r

i = ° ^38)

An alternate treatment of SRM analytical data which arose

in the course of discussions on poly crystalline materials in

general can also be applied to KpCrpCU [39] • This treatment

is directed towards probabilistic evaluation not of the mean

property of the material itself (i.e., not heterogeneity,

55
separation of the random errors of the method, etc.), but

rather the treatment of material-method-man system performance

at the time of the analysis. On the basis of this treatment,

a two-sided tolerance limit, Ks , can be assigned to the mean

value of the measured property, X.

Treating the data of Table 14 in this manner where y = 0.95 (the probability is 95 percent that at least a proportion

P of the distribution in included within ± Ks limits) and the

proportion of the population is also 95 percent (i.e., P = 0.95)

for sample size n=20, K = 2.752 and s = 0.0028 percent, one

can say that the assay of the material (based on the F = 96486.7 C

TT c /-q equiv

-

; electrical, frequency, and mass

standards as maintained by NBS ) is

99.9822 ± 0.0077,

where the uncertainty figure represents 95 percent probability

bounds that at least 95 percent of all measurements on all

samples in this lot would fall within these limits, if measured

by means of the above instrument-man system.

The results of this work and the work on arsenious oxide

analysis are being incorporated into a NBS Monograph (260 series)

on the characterization of Redox Standard Reference Materials

.

4 . Tris - Basimetric Standard

Studies of tris(hydroxymethyl)aminomethane in this

laboratory showed that tris cannot be coulometrically titrated

directly via the anodic reaction

H

2

-* 2H+

+ 2e + 1/2 . The experimentally determined assay was consistently low by

several percent. A systematic survey of the literature from

19^7 to the present revealed no attempts to titrate tris

coulometrically. Its electrochemical behavior in general has

not been investigated. Relevant evidence in the literature

shows that attempts to titrate aromatic amines coulometrically

failed due to oxidation of the amines themselves.

56
This difficulty 3 however, is circumvented by a backtitration procedure which was developed in this laboratory.

The following reaction is used for alkalimetric assay of tris.

n(H0CH o KCNHo + (n+x)H+ > n[ (HOCH ) CNH Q

] + + xH

+

. d 3 d d j 5

The coulometric reaction involves only the reduction

xH

+ + xe ^ x/2 H

2

i

.

Thus, for quantification purposes, the acid solution is

standardized coulometrically , then a known amount of the acid

is added in excess to preweighed samples of tris and the excess

of acid is back-titrated coulometrically.

The material to be issued as a standard reference material

arrived in five cases. Fifteen random samples (three from each

case) were evaluated. Random sampling and the experimental

design furnished by Dr. John Mandel (Statistical Consultant,

NBS) were followed. Duplicate titrations were performed on

each of the random samples in an experiment consisting of two

sets. One sample from each bottle was removed, dried at 70 °C

in a vacuum oven for 24 hours, weighed, corrected to weight in

vacuum, and titrated. This constitutes Set I. The second set

is identical to the first set except the sequence of weighing

and titration of samples was altered at random.

Approximately 1.6 molar sulfuric acid solution, standardized coulometrically, was used in these titrations. Back-titration of the excess sulfuric acid was carried out to a differential potentiometric inflection point. In each titration,

about one gram of tris and about 5°5 grams of HpSCK solution

were used. Using 100 ml of 1M KC1 supporting electrolyte and

the above amounts of tris and H„SO h , the (ApH/AC) occurred

2 4* ^ 'max

in the vicinity of pH = 5o

The results of analyses are summarized in Table 18. Roman

numerals in the Sample Number column indicate the case numbers

and Arabic numerals — the bottle number. The duplicate

57
Table 18. Results of coulometric analysis of tris

basimetric standard.

Sample Number First Set Second Set

1-7 99.9787 99-9559

1-9 99.9683 99.9734

V-6 99.9^61 99.9532

IV-6 99-9699 99.9675

111-12 99.9763 99-9707

11-12 99-9810 99.9709

III-ll 99.9749 99.9665

V-5 99.9690 99.9754

II-9 99-9641 99.9657

IV-2 99-9841 99.9555

III-4 99.9746 99.9727

V-9 99.9695 99-9689

11-10 99.9645 99.9703

IV8

99.9685 99.9750

1-2 99.9690 99.9689

Average 99.9706 99.9674

s = O.OO87 s = 0.0071

samples for each bottle are shown on the same line of the two

corresponding sets.

The mean basimetric assay of this lot of tris is 99.9690

± 0o0030 weight percent. The above uncertainty represents the

95-percent confidence interval for the mean. No evidence was

found for variability between samples beyond that accounted

for by the random error of measurement. Accordingly, the

material is considered to be homogeneous. A pooled estimate

of the random error (standard deviation of a single determination based on all 30 determinations) is o 008l assay units Q

(G. Marinenko)

58
6. CONDUCTIMETRY

The Frequency Extrapolation of Conductance Data for

Aqueous Salt Solutions

A. Introduction

Systematic sources of error in conductivity measurements

are being sought as part of a program for standardizing and

certifying solutions for use in the calibration of conductivity

cells and salinometers . One such source of error is the

frequency-dependent polarization impedance that inevitably

accompanies the measurement of the ac conductance of solutions

in conventional cells

The present study deals with various mathematical means

for extrapolating resistance vs. frequency data in order to

remove polarization effects. Various experimental techniques

for accomplishing the same objective were ruled out for

reasons given below. Seven empirical and theoretical equations

that have been used or proposed for the reduction of conductivity data are critically compared, using data for aqueous salt

solutions in cells with bright platinum electrodes and with

electrodes coated with palladium blacko Robinson and Stokes

[40] discuss polarization models qualitatively and emphasize

that the functional form of the resistance-frequency curve

must be determined whenever polarization is not negligible.

Bo Test Equations

The equations to be compared and their historical or

theoretical bases follow. R represents the observed resistance

of a parallel R-C bridge arm having the same impedance as the

conductivity cell, R-, is the high-frequency limit of R (assumed

to correspond to the electrolytic resistance of the cell), f

is the frequency in Hz, and oj is the angular frequency (27rf)

1, Two-Parameter Equations

R = R + a f" 1/2

(39)

59
Jones and Christian [4l], in a classical study of polarization in conductivity measurements, recommended Eq. (39) as

a practical expedient although it was recognized that this

function led to R values somewhat smaller than the true electrolytic resistance.

R = R

1

+ a f" 1

(40)

Several workers [40,42] have found empirically that Eq

(40) better represented their data than did Eq. (39).

2 Three-Parameter Equations

R = R

1 + a f" 1/2

+ b f" 1

(l|i)

Nichol and Fuoss [43] found that the simpler Eqs. (39)

and (40) were inadequate to represent their data for dipping

electrode designs and used this quadratic function of t ' .

R = R

1 + a f

b

(42)

Because of uncertainty as to the best exponent for f in

Eqs. (39) and (40), Eq. (42) was proposed [44], Although this

equation can provide an excellent fit to experimental data, it

will be seen below that it can introduce a large error in extrapolation. Accordingly, the use of Eq c (42) is not

recommended.

3 Theoretical Equations

These are based on the model for the conductivity cell

shown in Figure 13, where C

n is the geometric capacity of the

cell and C, is the double-layer capacity at the electrode

surface. R_ is the frequency-independent part of the faradaic

impedance and W represents the Warburg impedance. The complex

impedance of W is assumed to be represented by

Z

w

= k(l - i)o)" 1/2

. (43)

R

?

arises from the rate of oxidation or reduction at the electrode and W from the diffusion of the electroactive species

„

60
AAA/W

Figure 13. Equivalent circuit for conductance cell,

according to reference 45.

Feates, Ives, and Pryor [45] solved the bridge balance conditions for this model with the restriction that W is negligible

and obtained Eq „ (44).

R

R = RL +

2

1 + a u' where

a = R-^C 2/^ + R

2

)

(44)

(45)

These authors used an empirical extrapolation formula equivalent

to Eq. (40) for reduction of their data.

The alternate solution for the model of Figure 13 for

the simplifying condition that R

? = was given by Hills and

Djordjevic [46]. Their corrected Eq . 4 in the notation of the

present report is test Eq . (46).

R

s ~ R

l + ~T72

k (46)

i"i. + 2kC

1

oo 1/2

+ 2k 2

C

2

co)

Note that R is the resistance of an equivalent series R-C

s M

61
bridge arm The solution in terms of the parallel combination

is much less tractable.

The bridge balance conditions for the model of Figure 13,

including both the R~ and Warburg impedance lead to the result

[47]

R = R

1 + [R2 (R

1 + R2

) + k(R

1 + 2R

2 )uT 1/2

+ 2k 2oT 1

]/

[R-^C^oo 2 + 2kR

1

R

2

C

2

a) 3/2

+ 2k 2

R

1

C

2

u) + 2kR

1

C

1

oo 1/2

+ R + R

2 + kco" 1/2

] (47)

In order to fit Eq. (47) to experimental data it has been ex-

-1/2 panded in powers of to with the result

R = R + aoj

-2

+ baf 5/2+ cuf 7/2+ • • • (48)

where the coefficients have the theoretical values

a = (R1 + R

2

)/R

1

R

2

C

2

(49)

b = - k/(R

2

C

1

) 2

(50)

c = [2k 3R

1

C

1 - 2kR

2 (R

1 + R2 )]/R

1

R

2

C

3

. (51)

Because of the omission of higher negative powers of oo, Eq

.

(48) is expected to be asymptotically correct at higher

frequencies

.

Chang and Jaffe [48] examined the faradaic process in

detail but did not obtain an explicit function for R in terms

of f. Because of the difficulty of applying their results to

conductivity data the Chang-Jaffe model is not considered

further here.

The essential requirement of an extrapolation formula is

that the high frequency limit R, correspond closely to the

true resistance of the electrolyte in the cello This condition

was judged by the agreement between the value of R-. obtained

62
for the same cell and solution whether the electrodes were

bright platinum or coated with palladium blacko The coating

should change the double-layer parameters greatly without

affecting R_ . Since the palladium black has a finite thickness any effect on the cell constant was reduced by using

capillary cells with relatively large constants (37 and 86)

.

The extrapolation formula should also provide a close fit to

the experimental measurements over an appreciable range of

frequencies. It is also desirable that the theoretically

based equations yield plausible values for the double- layer

parameters

„

Although the use of platinum or palladium black is a familiar and effective means of reducing polarization effects

on conductivity measurements, bare metallic electrodes have

some advantages for checking standard solutions. We prefer to

introduce the sample to a clean, dry cell when only a limited

specimen is available since there may not be enough to rinse

the cell to constant composition as would be required with

the highly adsorptive blacked electrodes. Potentiometric [49]

and inductive [50] cells have been used to avoid polarization

effects completely but these require specialized measuring

instruments and are not suitable to our ultimate objective of

redetermining the Jones and Bradshaw [51] standards on an

absolute basis.

C . Experimental Section

1. Apparatus

Two cells of the conventional Jones design were used.

These had circular platinum electrodes 7o0 square centimeters

in area in enlarged bulbs connected by a sufficient length of

4-mm i.d. tubing to give constants of 37.050 and 86.096, Two

bare copper leads were soldered to each electrode support

close to the outside of the cell for use with the four-terminal

method of measurement „ The uncompensated lead resistance was

calculated from the materials of construction (copper, tungsten,

63
and platinum) to be 0.002 ohm.

A Jones-Dike bridge was modified for use in the fourterminal mode by providing auxilliary switches for reversing

leads and connecting the active potential lead directly to

the detector,. In this configuration the entire slide-wire

circuit of the bridge was in the "Standard" arm and 26.181

ohms was determined to be the correction to be added to the

dial readings to compensate for this modification.

The parallel capacitance required for balance was provided by an external calibrated 1400 pF variable air capacitor,

supplemented as needed by mica capacitors up to o 06 yF„ The

thermostat was a self-lagging oil bath equipped with

proportional j rate, and reset controls „ Temperatures were

measured with two calibrated platinum resistance thermometers

of different time constants (6 and 11 seconds). In 28

measurements the maximum difference between the readings of

_^?

the two thermometers was 3.6 x 10 K, while the standard

deviation of the difference was 1.6 x 10 K and the mean difference was less than one-fifth the standard deviation

2o Solutions and Filling of Cells

Two solutions were used: demal potassium chloride [51]

sealed in 100-cm ampoules and Standard Sea Water, Lot P50,

which is supplied in double-necked 250-cm ampoules [52] . Our

experience has confirmed the observation that a major source

of random error is in the filling of cells [53]. We have

obtained standard deviations less than 50 ppm for the measurement of conductivities of sets of four or five ampoules of

Standard Sea Water and attribute the high degree of precision

largely to the ability to drain the sample directly from the

ampoule into the cell. The potassium chloride solution was

prepared from specially purified and dried salt and contained

71.1435 grams of KC1 per kilogram of solution (corrected to

vacuum weights) . Borosilicate ampoules were filled in a 5 °C

cold room, having first been flushed with nitrogen presaturated

64
with the same solution. The filled ampoules were immersed in

an ice bath above the solution level while the necks were sealed

off.

Cells with bright electrodes were rinsed thoroughly with

distilled water, followed by three portions of spectrographic

grade acetone, dried with nitrogen and filled from freshly

opened ampoules. At the end of this series of measurements,

each electrode was palladized for 4 . 5 minutes at 50 mA, using

a solution prepared by electrolytically dissolving 0.1 g of

3 palladium in 20 cm of constant-boiling hydrochloric acid and

diluting to 100 cm

J

. Palladium black is advantageous in that

it can be stripped completely from the electrode. The coated

electrodes were rinsed thoroughly and electrolyzed in dilute

sulfuric acid for 1„5 hours with frequent reversals of polarity.

The palladized electrodes were never allowed to become dry but

were kept wet with water or aqueous electrolyte,, Before filling, the cells were rinsed several times with a solution of

the approximate composition as that to be measured, and finally

with a small portion from the freshly opened ampoule. After

I the resistance measurement the cell was emptied and immediately

j refilled from another ampoule of the same solution and the

[measurements were repeated. The resistances for the second

series were o 01 to 0.07 percent lower than the first and are

the ones reported here.

3 o Fitting Equations to Data

After applying bridge calibration corrections and adjusting

the data to exactly 25 °C (on the International Temperature

Scale of 1948), the seven equations were fitted by computer

programs. The linear equations (39 and 40) were fitted by conventional least square methods. The polynomials of degree

higher that first (Eqs . 4l and 48) were fitted by orthogonal

polynomials [54] . The non-linear forms (Eqs. 42, 44, and 46)

were fitted by an iteration technique that varied one parameter

until the sum of the squares of deviations was minimized For

each value of the independently adjusted parameter the other

65
two parameters were set by a least-squares fit of a linearized

form of the equation. The step size for the iteration was

varied in a way that guaranteed that the sum of squares of

deviations passed through the minimum at least once and convergence was accepted when successive iterations reduced the

sum of squares less than 0.01 percent.

D . Results and Discussion

The results [47] are summarized in Table 19, where the

calculated values of R, according to the seven equations are

compared for two solutions and two cells, each with bright

and with palladized electrodes. With respect to the requirement that the equations yield the same value for R-, for either

bright or coated electrodes, both theoretical Equations (44)

and (48) are very satisfactory. The relative differences for

all eight comparisons are less that 70 ppm. That these values

of R-, represent the true resistance of the electrolyte is supported by not only the prediction from the theoretical models,

but also by the fact that nearly all the extrapolation formulas

yield the same results for the palladium blacked electrodes.

A notable exception is the exponential Equation (42) in the

case for the cell (constant 37) with demal potassium chloride

Here the best fit yielded a large exponent (b = -1.47) and a

value of R, some 70 ohms too low.

The simple, two-parameter equation in reciprocal frequency

(Eq. 40) provides very satisfactory agreement between the

measurements obtained with bright and coated electrodes but

this agreement appears to be the result of a cancellation of

errors. The comparison of several of these functions in

Figure 14 shows that Equation (40) actually reproduces the

experimental data quite poorly. Over a limited range of

frequencies (approximately 1 to 10 kHz) a good fit can be obtained with Equation (40) but it then extrapolates to too low

a value for R-, .

66
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334 -

333 -

932

Figure 14 . Comparison of test equations. Data points are

for demal KC1, bright platinum electrodes, cell

constant 37-

Key: Equation 39 3 straight line; 40, solid

curve; 44, broken curve.

The equations that provide the best extrapolation do not

necessarily fit the data most closely In Figure 15 , deviations

-1/2 from Equation (44) are plotted as a function of f . This

scale expands the high frequency region were the extrapolation

behavior is crucial It appea s that none of the functions

fits the data within experimental precision although Equation

(4l) gives the smallest standard deviation of fit (Table 19).

Equation (42) yields essentially the same result as Equation

(4l). It is well known that the close fit of an empirical

equation to a set of data does not provide a sound basis for

extrapolating beyond the range of the measurements and this

caution applies to the four empirical forms considered in the

present report.
03

0.2

0.1 z

o

<

>

UJHZ

UJO

£

UJ

Q.-0.1

-0.2

1f«2

Figure 15. Percentage deviations from test equation 44.

Data points are for demal KC1, bright platinum

electrodes, cell constant 37. The solid rectangle

at the origin of the coordinates represents the

probable limiting resistance for palladized electrodes . Key: Equation 41, solid; 48 broken; 48 plus

next higher term dotted.

Equation (46) has not been mentioned in the foregoing

discussion because it was not tested on a strictly comparable

basis. The measurements were made with a parallel R-C bridge

arm and had to be recalculated to the equivalent series values

by Equations (52) and (53) in order to apply Equation (46).

R

s = R /(I + .W)

c

s = cci + i/(wW)]

(52)

(53)

6 9
Capacitances were measured with much less accuracy than resistances and the application of Equations (52) and (53)

introduced an undetermined error. Although Equation (46) is

a fit of R vs o oo j points were omitted when the corresponding

value of the series capacitance appeared clearly discordant

„

Equation (46) reproduces the data points more closely than

Equation (44) but extrapolates to FL values that seem uniformly

nearly 0.2 ohm too low. These functions (Eqs. 44 and 46) are

compared in Figure 16

.

It is apparent from Figure 15 that Equation (48) behaves

very poorly at the lower frequencies, probably due to the

neglect of higher terms in the polynomial expansion of Equation

-4

(Jj7). The next higher term is d w , where

(m

;io

20

tl

K

0.1

z

oH

>

uiQ O

H

Z

UJU

K

ui

Q.

-0.1

1

Figure 16. Percentage deviations from test equation 39-

Data points are for demal KC1, bright platinum

electrodes , cell constant 37

Key: R , open circlesj R 3 filled circles;

Equation 44 3 broken line; 46, solid curve.

70
d = - 4k - 2k 2 (3R i + Rz) + (R i + R ^ . (54)

5a R C

2 HiRjcf R

Z R^C7

-4 Inclusion of the term in oo improves the fit appreciably reducing the standard deviation from 0.047 to 0.015 ohm. However, the behavior between the two lowest experimental frequencies is even more extreme, as shown in Figure 15.

The fundamental parameters of the faradaic impedance and

double layer for the theoretical models are compared in Table

20. The parameters are at least plausible in magnitude although it is questionable how much physical significance should

be attached to them. The coefficients for one example are

shown in Table 21. Their standard deviations are sufficiently

Table 20. Fundamental parameters of conductance cell derived

from frequency dependence of resistance

Demal KC1, bright platinum electrodes, cell constant 37

Eq. 44 Eq. 46 Eq . 48

R 1 (ohm) 332.895 332.644 332.872

R 2 (ohm) 2.107 — 8.44

C x (uF) 102.8 15.58 35.3

k (ohm-sec"

1/2

) — 96.3 W

Table 21. Polynomial coefficients and their standard deviations

Test equation 48 fitted to data for demal KC1, bright

platinum electrodes, cell constant 37-

4-term eq

.

Const. 332.872 ± 0.019

2nd (97.6 ± 7.8) x 10 6

3rd -(58.1 ± 5.7) x 10 8

4th (33-6 ± 4.2) x 10 11

48 F lus

h:Lgher term

332. 826

4. 17

34. 5

324

5th

5- term eq.

332.828 ± 0.008

(20.4 ± 1.2) x 10 7 -(18.2 ± 1.3) x 10 9

(41.9 ± 4.1) x 10 12

-(10.2 ± 1.1) X 10 14

71
large to suggest considerable uncertainty in any derived

parameters. It is interesting that the inclusion of an additional term to Equation (48) greatly changes the polynomial

coefficients but appreciably affects only the R parameter.

E . Recommendations

Although the frequency dependence of the measured resistance should be determined when polarization is not negligible,

this step is not sufficient to insure accuracy. The Grahame

model of Figure 13 and its simplifications predict that the

limiting resistance is approached horizontally. Consequently,

any of the simple extrapolation formulas that have been proposed will give low results. In many cases, an experimental

value in the range 5 to 10 kHz is more accurate than an

empirical extrapolation. Either Equation (44) or (46) is

sufficiently accurate for extrapolation purposes „ These

equations are solved by essentially the same program and the

choice depends upon the experimental set-up accordingly as

the equivalent parallel or series R-C combination is measured.

In solution conductivity work, it is usually preferable to

use the parallel configuration in order to avoid the need for

large capacitors

.

(T. B. Hoover)

72
7. FOREIGN-CURRENCY PROGRAMS

The two projects, sponsored by the Electrochemical

Analysis Section at universities in India and financed through

the provisions of Public Law 480, continued actively during

the reporting year. A brief description of these programs

follows .

A. Properties of Electrolytes in Nonaqueous Media, Dr. M. N.

Das and Dr. K. K. Kundu, Jadavpur University , Calcutta

(1) Studies on the behavior of some uncharged bases in

aquo-glycolic and aquo-methanolic solvent systems.

(2) Standard potentials of Li/Li and Cs/Cs electrodes

in ethylene glycol-water systems.

(3) Acidity function (H ) '^ for solutions of sodium and

lithium glycoxides in ethylene glycol at 25 °C.

(4) Studies in isodielectric media: standard potentials

(E° ) of Ag-AgCl electrode in methanol-propylene glycol solvent

system at different temperatures and the related thermodynamic

quantities

.

Publications resulting from the above programs are:

K. K. Kundu, D. Jana, and M. N. Das, "Standard Potentials

of the Silver-Silver Bromide Electrode in Propylene Glycol and

the Silver-Silver Iodide Electrode in Ethylene and Propylene

Glycols at Different Temperatures and Related Thermodynamic

Quantities", J. Phys . Chem. 7_4 (13), 2625 (1970).

K. K. Kundu, P. K. Chattopadhyay , D c Jana, and M. N. Das,

"Thermodynamics of Self-Ionization of Ethylene and Propylene

Glycols", J. Phys. Chem. 7_4 (13), 2633 (1970).

K. K. Kundu, P. K. Chattopadhyay, D. Jana, and M. N. Das,

"Standard Potentials of Ag-AgX (X = CI or Br) Electrodes in

Glycolic Solvents at Different Temperatures and Related

Thermodynamic Quantities", J. Chem. Eng . Data 15_, 209 (1970).

73
B. Physicochemical Studies in Nonaqueous Solvents, Prof. R. C.

P aul, Panjab University, Chandigarh

Recent work is described in the following manuscripts:

R. C. Paul, D. S. Gill, and S. P. Narula,

"Physicochemical Studies in Nonaqueous Solvents.

Part I. Conductance and Thermochemical Studies

of Some Perchlorates in N,N-Dimethylformamide"

,

J. Chem. Soc. (A) (in press).

R. C. Paul, D. S. Gill, J. P. Singla, and S. P.

Narula, "Physicochemical Studies in Nonaqueous

Solvents. Part II. Conductance and Solvation

Studies in N-Methy Iformamide ", J. Phys . Chem.

(submitted)

.

(R. A. Durst)

n
8. PERSONNEL AND ACTIVITIES

A. Personnel Listing

Richard A. Durst, Acting Section Chief

Carolyn E. Smith, Section Secretary

Acidity Scales —

Maya Paabo

Conductimetry —

Thomas B. Hoover (to January 1970)

Coulometry —

George Marinenko

Ion-Selective Electrodes -- Bert R. Staples

Robert G. Hayman (Guest worker September to Feburary)

Duane Wood (Guest worker February to June)

Potentiometry —

Benjamin T. Duhart (part time)

Consultant —

Roger G. Bates

B. Publications and Manuscripts

1. R. G. Bates, "Solute-Solvent Interactions" in Medium

Effects and pH in Nonaqueous Solvents , Marcel Dekker,

New York, 1969, pp. 45-96.

2. M. Paabo and R. G. Bates, "Dissociation of Deuteriocarbonate Ion in Deuterium Oxide from 5 to 50°", J.

Phys. Chem 73, 3014 (1969)

.

3. R. A. Robinson, "An Isopiestic Vapor Pressure Study of

the System Potassium Chloride-Sodium Chloride in Deuterium

Oxide Solutions at 25°" , J. Phys. Chem. 73, 3165 (1969).

75
4. R. A. Durst, "Fluoride Microelectrode—Fabrication and

Characteristics", Anal Chem. 4l, 2089 (1969).

5. R. G. Bates, Editor, NBS Technical Note 503, "Electrochemical Analysis Section: Summary of Activities,

July 1968 to June 1969" 9 U. S. Government Printing Office,

August 1969.

6. R. G. Bates, "Proposal for the Practical Measurements of

pH in Amphiprotic and Mixed Solvents", Pure & Appl . Chem.

18, 419-425 (1969).

7. G. Marinenko and C. E. Champion, "Difference between the

Inflection Point and the Equivalence Point in Coulometric

Titrations of Weak Acids", Anal. Chem. 4l, 1208 (1969).

8. R. G. Bates and M. Alfenaar, "Activity Standards for

Ion-Selective Electrodes", in Ion-Selective Electrodes , NBS Special Publication 314, U. S. Government Printing

Office, 1969, p. 191.

9. R. A. Durst, "Analytical Techniques and Applications of

Ion-Selective Electrodes" in Ion-Selective Electrodes , NBS Special Publication 314 , U. S. Government Printing

Office, 1969, P. 375.

10. R. A. Durst, Editor, Ion-Selective Electrodes , NBS Special

Publication 314, U. S. Government Printing Office, 1969.

11. R. G. Bates, B. R. Staples, and R. A. Robinson, "Ionic

Hydration and Single Ion Activities in Unassociated Chlorides at High Ionic Strengths", Anal. Chem. 4_2, 867 (1970).

12. M. Paabo and R. G. Bates, "Dissociation Constant of

Protonated 2,2-Bis(hydroxymethyl)-2, 2

' ,2"-nitrilotriethanol

(Bis-tris) and Related Thermodynamic Functions from to

50°", J. Phys. Chem. 74, 702 (1970).

13. M. Paabo and R. G. Bates, "Deuterium Isotope Effects and

the Dissociation of Deuteriophosphoric Acid from 5 to

50°", J. Phys. Chem. 74, 706 (1970).

14. E. J. Catanzaro, C. E. Champion, E. L. Garner,

G. Marinenko, K. M. Sappenfield, and W. R. Shields,

"Boric Acid; Isotopic and Assay Standard Reference

Materials". NBS Special Publication 260-17, U.S.

Government Printing Office, 1970.

15- R. A. Robinson, "The Dissociation Constant of m-Nitroanilinium Ion in Water-Tetrahydrofuran Solvents at 25 °C",

J. Res. NBS (in press).

76
16. M. Paabo and R. G. Bates, "Acidic Dissociation of

Diprotonated Piperazine in Methanol-Water Solvents from

10 to 40 °C", J. Res. NBS (in press).

17. R. A. Durst and B. T. Duhart, "Ion-Selective Electrode

Study of Trace Silver-Ion Adsorption on Selected

Surfaces", Anal. Chem. (in press).

18. H. P. Thun, B. R. Staples, and R. G. Bates, "Thermodynamics of Hydrochloric Acid in 80 Weight Percent

2-Methoxyethanol and 20 Weight Percent Water from 10 to

50 °C", J. Res. NBS (in press).

19. T. B. Hoover, "Frequency Extrapolation of Conductance

Data for Aqueous Salt Solutions", J. Phys . Chem. (in press)

20. R. A. Robinson, "The System: Potassium Chloride-Sodium

Chloride in Deuterium Oxide Solution at 25°", J. Phys.

Chem. (submitted).

21. R. A. Durst, "Ion-Selective Electrodes in Science,

Medicine, and Technology", Amer. Scientist (submitted).

C. Talks

1. G. Marinenko, "Coulomb - the Absolute Chemical Standard",

The American University, Washington, D. C., September

22, 1969.

2. R. A. Durst, "Ion-Selective Electrodes", NBS Analytical

Chemistry Division Scientific Discussion, October, 1969.

3. M. Paabo, "Thermodynamics of the Dissociation of

Protonated Bis-Tris from to 50 °C", Southeastern

Regional Meeting, American Chemical Society, Richmond,

Virginia, November 1969.

4. R. A. Durst, "Microanalysis Using Ion-Selective

Electrodes", Southeastern Regional Meeting, American

Chemical Society, Richmond, Virginia, November 1969.

5. T. B. Hoover, "Frequency Extrapolation of Conductance

Data for Aqueous Solutions, Southeastern Regional

Meeting, American Chemical Society, Richmond, Virginia,

November 1969.

6. R. G. Bates, "Proton Medium Effects and the Measurement

of Acidity in Nonaqueous and Mixed Solvents", Eastern

Analytical Symposium, New York, New York, November 1969.

77
7. Ro A. Durst, "Ion-Selective Electrodes and Their

Applications", Analytical Section, New York Chemical

Society, New York, New York, January 1970.

8. R. A. Durst, "Electrochemical Analysis Capabilities

in Chemical Oceanography" (panel), NBS Analytical

Chemistry Division Scientific Discussion, January 1970.

9. G. Marinenko, "Ion-Selective Electrodes", Department of

Chemistry, The American University, February 1970.

10. R. A. Durst, "Ion-Selective Electrode Study of Trace

Silver Adsorption on Selected Surfaces", 159th National

Meeting, American Chemical Society, Houston, Texas,

February 1970.

11. R. A. Durst, "Ion-Selective Electrodes in Science,

Medicine, and Technology", Sigma Xi National Lecture

Tour, New York area, March 9-19, 1970.

12. M. Paabo, "Acid-Base Behavior of Piperazinium Ion in

Methanol-Water Solvents", Fifth Middle Atlantic Regional

Meeting, American Chemical Society, University of

Delaware, Newark, Delaware, April 1970.

13. B. R. Staples, "Thermodynamics of Hydrochloric Acid in

a Mixed Solvent Containing 80 Weight Percent 2-Methoxyethanol and 20 Weight Percent Water from Emf Measurements

at 10 to 50 °C", Fifth Middle Atlantic Regional Meeting,

American Chemical Society, University of Delaware, Newark,

Delaware, April 1970.

14. R. A. Durst, "Ion-Selective Electrode Studies at NBS",

Chemistry Department Colloquium, University of

Connecticut, Storrs, Connecticut, May 1970.

15. M. Paabo, "Acid-Base Behavior of Piperazinium Ion in

Methanol-Water Solvents", Joint Meeting of the Canadian

Institute of Chemistry and the American Chemical Society,

Toronto, Canada, May 1970.

16. R. A. Durst, "Ion-Selective Electrodes", Food and Drug

Administration, U. S. Department of Health, Education,

and Welfare, Washington, D. C, June 1970.

17. R. A. Durst, "Analytical Applications of Ion-Selective

Electrodes", 23rd Annual Summer Symposium on Analytical

Chemistry, American Chemical Society, New Mexico State

University, Las Cruces, New Mexico, June 1970.

78
9 . REFERENCES

[1] R. A. Durst, Editor, Ion-Selective Electrodes , NBS

Special Publication 314, U. S. Government Printing

Office, Washington, D. C, 1969.

[2] R. G. Bates and H. B. Hetzer, J. Phys . Chem. 6_5, 667 (1961)

[3] R. G. Bates and V. E. Bower, J. Res. NBS 53, 283 (1954).

[4] R. G. Bates and E. A. Guggenheim, Pure Appl. Chem., 1,

163 (I960).

[5] D. D. Van Slyke, J. Biol. Chem. 52, 525 (1922).

[6] R. G. Bates, G. D. Pinching, and E. R. Smith, J. Res.

NBS 4_5, 418 (1950) . [7] R. G. Bates and S. P. Acree, J. Res. NBS 34_, 373 (1945).

[8] M. Paabo and R. G. Bates, J. Phys. Chem. 74, 702 (1970).

[9] R. G. Bates and H. B. Hetzer, J. Phys. Chem. 6J5, 667

(1961).

R. G. Bates, Editor, NBS Technical Note 503, August 1969.

P. Schlindler, R. A. Robinson, R. G. Bates, J. Res. NBS

72A , 141 (1968).

R. M. Fuoss, J. Amer. Chem. Soc, 8_0, 5059 (1958).

R. G. Bates, Editor, NBS Technical Note 400, September

1966.

R. G. Bates, E. A. Guggenheim, H. S. Harned, D. J. G. Ives,

J. J. Janz, C. B. Monk, R. A. Robinson, R. H. Stokes,

and W. J. K. Wynne-Jones, J. Chem. Phys. 25, 361 (1956).

R. G. Bates and M. Alfenaar, in Ion-Selective Electrodes , R. A. Durst, Editor, NBS Special Publication 314, 1969,

Chapter 6

.

R. H. Stokes and R. A. Robinson, J. Amer. Chem. Soc., 70

,

1870 (1948) . R. G. Bates, B. R. Staples, and R. A. Robinson, Anal.

Chem. 42, 867 (1970).

R. A. Robinson and R. H. Stokes, Electrolyte Solutions , 2nd Edition, Butterworths , London, 1959-

79
[19] Y.-C. Wu and W. J. Hamer, Electrochemical Data, Part XI,

NBS Report 9908, September 6, 1968.

[20] C. W. Chambers and C. M . Proctor, Public Health Service

Technical Report W60-4 (i960).

[21] C. W. Chambers, C. M. Proctor, and P. W. Kabler, J. Amer.

Water Works Assoc. 5_4 3 208 (1962).

[22] F. K. West, P. W. West, and F. A. Iddings , Anal. Chern.

38, 1566 (1966).

[23] ibid., Anal. Chim. Acta 31, 112 (1967).

[24] J. K. Taylor, Editor, NBS Technical Note 403, September

1966.

[25] International Commission on Atomic Weights, Comptes

Rendus XXIV IUPAC Conference, Prague, 4 to 10 Sept. 1967,

pp. 130-141.

[26] A. E. Cameron and E. Wlchers, J. Amer. Chem. Soc, 84_,

417? (1962) . [27] 0. Honigschmid and M. von Mack, Z. anorg. und Allgem.

Chem. , 2_46, 363 (194l) . [28] G. P. Baxter and M. R. Grose, J. Amer. Chem. Soc . , 38.,

868 (1916)

.

[29] G. P. Baxter and J. H. Hodges, J. Amer. Chem. Soc, 43.,

1242 (1921) . [30] W. T. Leland and A. 0. Nier, Phys . Rev., 73., 1206 (1948).

[31] D. C. Hess, M. G. Inghram and R. J. Hayden, Phys. Rev.,

74, 1531 (1948).

[32] M. Faraday, Phil. Trans., Series 2, 3, 23 (1833).

[33] J. S. Laird and G. A. Hulett, Trans. Amer. Electrochem.

Soc, 22, 385 (1913).

[34] J. H. Gladstone and W. Hibbert, J. Chem. Soc, 55, 443

(1889).

[35] W. J. Hamer, J. Res. NBS, 72A 3 435 (1968).

[36] D. N. Craig, J. I. Hoffman, C. A. Law and W. J. Hamer,

J. Res. NBS, 64A, 381 (I960).

[37] G. Marinenko and J. K. Taylor, Anal. Chem., 40, 1645

(1968).

80
[38] G. Marinenko and J. K. Taylor, J. Res. NBS, 67A, 453

(1963).

[39] Private communication, Dr. H. Ku, NBS Statistical

Engineering Section, February 1970.

[40] R. A. Robinson and R. H. Stokes, Electrolyte Solutions,

2nd ed . , Butterworth Publications Ltd., London pp. 93-95,

(1959) • [41] G. Jones and S. M. Christian, J. Amer. Chem. Soc . , 57,

272 (1935) . [42] J. C. Nichol and R. M. Puoss, ibid., 77, 198 (1955).

[43] J. C. Nichol and R. M. Puoss, J. Phys. Chem., 5_8, 696

(1954).

[44] T. B. Hoover, ibid., 68, 876 (1964).

[45] P. S. Feates, D. J. G. Ives and J. H. Pryor, J. Electrochem. Soc, 103, (10), 580 (1956).

[46] G. J. Hills and S. Djordjevic, Electrochim. Acta, 13 , 1721 (1968) . [47] T. B. Hoover, J. Phys. Chem., Jk_ 3 2667 (1970).

[48] H. C. Chang and G. Jaffe, J. Chem. Phys., 20_, (7), 1071

(1952).

[49] F. P. Anderson, H. C. Brookes, M. C. B. Hotz and

A. H. Spong, J. Sci. Instr., [2] 2, 499 (1969).

[50] S. R. Gupta and G. J. Hills, ibid., 33, 313 (1956).

[51] G. Jones and B. C. Bradshaw, J. Amer. Chem. Soc., 55 , 1780 (1933).

[52] Available from I. A. P.O. Standard Sea-Water Service,

Charlottenlund Slot, Charlottenlund, Denmark.

[53] R. W, Bremner, T. G. Thompson and C. L. Utterback,

J. Amer. Chem. Soc, 6l_, 1219 (1939).

[54] J. W. Bright and G. S. Dawkins , Ind. Eng . Chem. Fundam.,

4, 93 (1965).

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