Physical Chemistry
35. Surface Chemistry

Ruifeng ZHOU

Faculty of Science &Institute for the Advancement of Higher Education
Hokkaido University2

1. Adsorption
2. Langmuir adsorption model
3. BET theory
4. Surface reactions

3

1. Adsorption• Activated carbon deodorizer removes odours in air.
Valeric acid (pentanoic acid)Benzaldehyde

H2S

1. Adsorption

4• Like 2 molecules, a molecular entity and a solid
surface (both charge neutral) have attractive vander Waals forces when they are farther than 0.4nm
from each other.

5

1. Adsorption• When they get too close, repulsion emerges from
Pauli exclusion principle of their electron clouds.
• 𝑟𝑟e is the equilibrium distance, where the net force is0 (minimum of potential energy).

𝑟𝑟e61. Adsorption• The attachment of molecules to solid surfaces iscalled adsorption. The detachment of molecules tosolid surfaces is called desorption.
• The solid is an adsorbent.
• The attached molecules are adsorbate.

Adsorbate
Adsorbent

71. Adsorption• If the adsorbates form chemical bonds with theadsorbent, the adsorption is called chemisorption.
• Otherwise, the adsorption is called physisorption.
• Chemisorption can be further categorized into
associative and dissociative types.
BA

Physisorption
BA

Associative chemisorption

End onSide on

Dissociativechemisorption

BAA
Adsorbent

BAB

81. Adsorption• The depth of potential well is called the binding
energy (𝐸𝐸bind ).
Energy (a.u.)Transition stateof chemisorption

0𝐸𝐸bind
𝐸𝐸bind𝐸𝐸bind

𝑟𝑟e
𝑟𝑟e

𝑟𝑟e

Molecules

Physisorption
Associative chemisorption
Dissociative chemisorption
0Dissociated atoms

Distance (a.u.)

91. Adsorption• For example, calculated physisorption, transition
state and chemisorption of ethylene on Ir(111).
• The colours represent the electron localization
function.
Physisorption

Transition state

Chemisorption

Chin. J. Chem. Phys., Vol. 32, No. 4

10

1. Adsorption
TypePhysisorption

Chemisorption

Attraction

Van der Waals
forcesChemical bonds

Electronic structure
at the interface

No significant
changeOrbital overlap

Equilibrium distance Large

Small

Binding strength

StrongWeak1. Adsorption

11• The coverage is𝑛𝑛a𝜃𝜃 ≡𝑛𝑛0
• 𝑛𝑛a is the amount of adsorbate.
• 𝑛𝑛0 is the amount of adsorbate in a filled monolayer.

121. Adsorption• The adsorption anddesorption can betreated as a reversiblereaction.
• There is a chemical
equilibrium in certain
condition (e.g., 𝑃𝑃 and 𝑇𝑇).
• The pressure-coverage(𝑃𝑃 − 𝜃𝜃) plot at fixed atemperature is called
the adsorption isotherm.

𝜃𝜃𝑃𝑃

13

2. Langmuir adsorption model• Assumptions in Langmuir adsorption model are
1. The adsorption sites are identical.
2. Each site holds at most one molecule.
3. No interaction between adsorbates.  Theadsorption on one site does not influence theadsorption on the other sites.
4. The adsorption and desorption are elementaryreactions.
AASSAS

SA ASSSA × ASSSS

14

2. Langmuir adsorption model• The adsorption-desorption equilibrium can be
expressed asA+S𝑘𝑘ad𝑘𝑘deAS• The adsorption is a 2nd order reaction.
𝑣𝑣ad = 𝑘𝑘ad A 1 − 𝜃𝜃
• 1 − 𝜃𝜃 is the “concentration” of empty sites.
• The desorption is a 1st order reaction.
𝑣𝑣de = 𝑘𝑘de 𝜃𝜃• 𝜃𝜃 is the “concentration” of occupied sites.

2. Langmuir adsorption model• At equilibrium,

15𝑣𝑣ad = 𝑣𝑣de𝑘𝑘ad A 1 − 𝜃𝜃 = 𝑘𝑘de 𝜃𝜃A𝜃𝜃 =𝑘𝑘de
A +𝑘𝑘ad• For ideal gas, the concentration can be converted
to pressure.
𝑛𝑛𝑃𝑃
A = =𝑉𝑉 𝑅𝑅𝑅𝑅

16

2. Langmuir adsorption model𝑘𝑘de𝑃𝑃 + 𝑅𝑅𝑅𝑅
𝑘𝑘adCoverage• Define𝜃𝜃 =𝑃𝑃

1.0

Henry’s law
𝑃𝑃 = 𝜃𝜃𝑃𝑃0

0.8

0.6

𝑘𝑘d𝑃𝑃0 ≡ 𝑅𝑅𝑅𝑅
𝑘𝑘a𝑃𝑃
𝜃𝜃 =
𝑃𝑃 + 𝑃𝑃0• This the Langmuir adsorption isotherm. P/P• Langmuir adsorption isotherm can bederived using canonical ensemble.
0.4

0.2

0.00123045

17

2. Langmuir adsorption model• For dissociative chemisorption,
A2 + 2S𝑘𝑘ad

𝑘𝑘de2AS𝑣𝑣ad = 𝑘𝑘ad A2 1 − 𝜃𝜃 2𝑣𝑣de = 𝑘𝑘de 𝜃𝜃 2
• At equilibrium,
𝑘𝑘ad A2 1 − 𝜃𝜃 2 = 𝑘𝑘de 𝜃𝜃 21𝜃𝜃 =𝑘𝑘de+1𝑘𝑘da A2

18

2. Langmuir adsorption model• Adsorption isotherms are usually used to determine
the surface area of samples.
Data collection

HeN2𝑃𝑃𝑃∆𝑉𝑉𝑇𝑇′Injection
piston𝑃𝑃PumpV
Dead spaceAdsorbent
Liquid N2 Dewar
𝑇𝑇 = 77KP

2. Langmuir adsorption model

19• Let 𝑉𝑉a be the volume of 𝑛𝑛a ideal gas at 𝑃𝑃′ and 𝑇𝑇′.
𝑛𝑛a 𝑅𝑅𝑇𝑇𝑇 𝑛𝑛0 𝜃𝜃𝜃𝜃𝜃𝜃′
𝑛𝑛0 𝑅𝑅𝑇𝑇𝑇𝑃𝑃
𝑉𝑉a ===𝑃𝑃′𝑃𝑃′
𝑃𝑃𝑃 𝑃𝑃 + 𝑃𝑃0• Rearrange
𝑅𝑅𝑇𝑇𝑇𝑃𝑃− 𝑃𝑃0
𝑃𝑃 = 𝑛𝑛0
𝑉𝑉a 𝑃𝑃′•𝑅𝑅𝑇𝑇𝑇𝑃𝑃Linear fitting 𝑃𝑃 vs, the slope is 𝑛𝑛0 .
𝑉𝑉a 𝑃𝑃′• This is used to calculate the amount of adsorption
sites or surface area.

20

2. Langmuir adsorption model• For example,
𝑉𝑉a 10−12 m3
determine the2.5
number ofadsorption sites
2.0from given data.
1.5𝑇𝑇𝑇 = 273.15K and
1.0′ = 1bar.
𝑃𝑃P (10-12torr)

𝑃𝑃 10−12 torr

2.55 1.79 1.30 0.98 0.71 0.46 0.30 0.21
3.39 3.17 2.89 2.62 2.45 1.95 1.55 1.23

0.50.0• The slope is 𝑛𝑛0 =1.77 × 10−6 mol.

-0.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

RTP/P°Va (10-6torr/mole)2. Langmuir adsorption model• Define the adsorption equilibrium constant.
𝜃𝜃𝐾𝐾ad ≡ 𝑃𝑃𝑃𝑃𝑃• When 𝜃𝜃 is fixed, the adsorption enthalpy is called
the isosteric enthalpy of adsorption (Δad 𝐻𝐻°).
• According to van’t Hoff equation,
𝑑𝑑 ln 𝐾𝐾 ∆𝐻𝐻°
=𝑑𝑑𝑑𝑑
𝑅𝑅𝑇𝑇 2
𝑃𝑃𝑑𝑑 ln𝑑𝑑ln
𝐾𝐾ad𝑃𝑃°= 𝑅𝑅Δad 𝐻𝐻° = 𝑅𝑅𝑇𝑇 2
1𝑑𝑑𝑇𝑇𝑑𝑑𝑇𝑇

21

22

2. Langmuir adsorption modelln(P/P°)

𝑇𝑇 K
200
• For example,
𝑃𝑃 kPa4
determine ∆ad 𝐻𝐻°-2.2
from given data.
-2.4
3 ideal gas• 10cm-2.6
is adsorbed at 𝑃𝑃.

300

4.95

400

6.03

500

600

7.2

8.47

0.00420.00440.00460.0048

700

9.85

-2.8

-3.0

Δad 𝐻𝐻°= −7.5kJ � mol−1-3.2
0.00401/T (K-1)

0.00503. BET theory

23• Stephen Brunauer-Paul Emmett-Edward Teller(BET) isotherm is widely used in material science.
• The assumptions in BET theory are
1. Physisorption of molecule entities in infinite layers.
2. There is interaction (enthalpy) between theadsorbates in different layers.
3. The enthalpy of attachment for the 2nd and outerlayers is the same as the enthalpy of condensation(Δcon 𝐻𝐻 = −Δvap 𝐻𝐻).
4. The enthalpy of adsorption for the 1st layer (Δad 𝐻𝐻)
is lower than the other layers (Δad 𝐻𝐻 < Δcon 𝐻𝐻).

24

3. BET theory

5. The Langmuir theory can be applied to each layer.
A

Δcon 𝐻𝐻

A
A

A
A

A

A

A

A

A
A
A

Δcon 𝐻𝐻
Δcon 𝐻𝐻A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

A

S

SSSSSSSSSS• Suppose the 𝑛𝑛th layer’s coverage is 𝜃𝜃𝑛𝑛 .

Δcon 𝐻𝐻

Δcon 𝐻𝐻
Δcon 𝐻𝐻

Δcon 𝐻𝐻
Δad 𝐻𝐻25

3. BET theory• The rate of the change of the 𝑛𝑛th layer (𝑛𝑛 ≥ 2) is𝑑𝑑𝜃𝜃𝑛𝑛= 𝑘𝑘con 𝑃𝑃 𝜃𝜃𝑛𝑛−1 − 𝜃𝜃𝑛𝑛 − 𝑘𝑘vap 𝜃𝜃𝑛𝑛 − 𝜃𝜃𝑛𝑛+1
𝑑𝑑𝑑𝑑•𝑑𝑑𝜃𝜃𝑛𝑛
At equilibrium,
= 0.
𝑑𝑑𝑑𝑑

𝑘𝑘con 𝑃𝑃 𝜃𝜃𝑛𝑛−1 − 𝜃𝜃𝑛𝑛 = 𝑘𝑘vap 𝜃𝜃𝑛𝑛 − 𝜃𝜃𝑛𝑛+1• 𝜃𝜃𝑛𝑛 is a geometric progression.
𝑘𝑘con 𝑃𝑃
𝜃𝜃𝑛𝑛
𝜃𝜃𝑛𝑛+1 =𝑘𝑘vap
liq

𝜃𝜃1vap

𝜃𝜃2

⋮

𝜃𝜃4

𝜃𝜃3

3. BET theory• When 𝑃𝑃 is the vapour pressure (𝑃𝑃∗ ) of the liquid,
the gas liquifies indefinitely.
𝜃𝜃𝑛𝑛+1 = 𝜃𝜃𝑛𝑛 = 1𝑘𝑘vap= 𝑃𝑃∗𝑘𝑘con• Define
𝑃𝑃𝑧𝑧 ≡ ∗𝑃𝑃• Then,𝜃𝜃𝑛𝑛 = 𝑧𝑧𝜃𝜃𝑛𝑛−1 = 𝑧𝑧 𝑛𝑛−1 𝜃𝜃126

27

3. BET theory• The rate of the change of the 1st layer is𝑑𝑑𝜃𝜃1= 𝑘𝑘ad 𝑃𝑃 1 − 𝜃𝜃1 − 𝑘𝑘de 𝜃𝜃1 − 𝜃𝜃2𝑑𝑑𝑑𝑑•𝑑𝑑𝜃𝜃1At equilibrium,= 0.
𝑑𝑑𝑑𝑑

𝑘𝑘ad 𝑃𝑃 1 − 𝜃𝜃1 = 𝑘𝑘de 1 − 𝑧𝑧 𝜃𝜃1𝑘𝑘ad 𝑃𝑃
𝜃𝜃1 =𝑘𝑘de 1 − 𝑧𝑧 + 𝑘𝑘ad 𝑃𝑃adde

𝜃𝜃1

𝜃𝜃2

⋮𝜃𝜃4

𝜃𝜃3

28

3. BET theory• Multiply the numerator and denominator by𝑘𝑘ad 𝑃𝑃∗
𝑘𝑘de𝜃𝜃1 =𝑃𝑃∗ 𝑘𝑘ad 𝑃𝑃∗
1 − 𝑧𝑧+𝑃𝑃𝑘𝑘de• Define the BET constant, 𝑐𝑐.
𝑘𝑘ad 𝑃𝑃∗𝑐𝑐 ≡𝑘𝑘de𝑐𝑐𝑐𝑐𝑐𝑐
𝜃𝜃1 ==
1
1 − 𝑧𝑧 + 𝑐𝑐 1 + 𝑧𝑧 𝑐𝑐 − 1𝑧𝑧𝑃𝑃∗

𝑘𝑘de 𝑃𝑃.

29

3. BET theory• The overall coverage is∞∞

𝜃𝜃1
𝑛𝑛−1=
𝜃𝜃 = � 𝜃𝜃𝑛𝑛 = � 𝑧𝑧
𝜃𝜃1 =1 − 𝑧𝑧𝑛𝑛=1
𝑛𝑛=1• At low pressure, 𝑃𝑃 ≪ 𝑃𝑃∗ .

𝑐𝑐𝑐𝑐
1 + 𝑧𝑧 𝑐𝑐 − 1𝑐𝑐
lim 𝜃𝜃 = 𝑧𝑧𝑧𝑧 = ∗ 𝑃𝑃𝑧𝑧→0𝑃𝑃• It is Henry’s law again.
• At high pressure, 𝑃𝑃 ≈ 𝑃𝑃∗ .
lim 𝜃𝜃 = ∞𝑧𝑧→1• The gas liquifies indefinitely.

1 − 𝑧𝑧3. BET theory30• Suppose 𝑉𝑉 is the volume of adsorbed gas in somecondition (𝑃𝑃𝑃 and 𝑇𝑇′).
• 𝑉𝑉m is the volume of monolayer adsorbed gas in thesame condition.
𝑉𝑉𝜃𝜃 =𝑉𝑉m• The coverage can be rearranged as follows.
𝑧𝑧
𝑐𝑐 − 1
1=𝑧𝑧 +
1 − 𝑧𝑧 𝑉𝑉
𝑐𝑐𝑉𝑉m𝑐𝑐𝑉𝑉m• By linearly fitting

𝑧𝑧vs 𝑧𝑧, 𝑐𝑐 and 𝑉𝑉m can be found.
1−𝑧𝑧 𝑉𝑉31

3. BET theory• On the other hand,
𝑘𝑘ad 𝑃𝑃∗ 𝑘𝑘ad 𝑘𝑘vap
𝐾𝐾ad
𝑐𝑐 ====𝑘𝑘de
𝑘𝑘de 𝑘𝑘con 𝐾𝐾con
Δcon 𝐻𝐻°−𝑇𝑇Δcon 𝑆𝑆°−Δad 𝐻𝐻°+𝑇𝑇Δad 𝑆𝑆°
𝑅𝑅𝑅𝑅= 𝑒𝑒

• Note that,• Thus,Δcon 𝑆𝑆° ≈ Δad 𝑆𝑆° ≈ −𝑆𝑆 gΔcon 𝐻𝐻°−Δad 𝐻𝐻°
𝑅𝑅𝑅𝑅
𝑐𝑐 = 𝑒𝑒Δad 𝐺𝐺°𝑒𝑒 − 𝑅𝑅𝑅𝑅𝑒𝑒Δ𝐺𝐺°− con𝑅𝑅𝑅𝑅

32

3. BET theory• For example, determine the surface area of TiO2and Δad 𝐻𝐻° of N2 by the data at 75K.
• At 75K, for N2,
𝑃𝑃∗ = 76kPa
Δcon 𝐻𝐻° = −5.577kJ � mol−1• Each N2 molecule covers an area of 𝐴𝐴 = 0.16nm2 .
• The adsorbed volumes are measured at 𝑃𝑃′ = 1atm
and 𝑇𝑇𝑇 = 273K.
𝑃𝑃 kP

𝑉𝑉 mm30.16
601

1.87
720

6.11822

11.67
935

17.02104621.92114627.291254

33

2500

0.5

20000.4

1500

1000

Vm

500

0z/[(1-z)V] (cm-3)

V (mm3)

3. BET theory
0.05<z<0.35

0.3

0.2

0.1

0102030

P (kPa)

4050

0.0
0.00

0.05

0.10

0.15

0.20

0.25

0.30z

𝑐𝑐 − 1
1−3= 1.225cm= 4.07 × 10−3 cm−3𝑐𝑐𝑉𝑉m𝑐𝑐𝑉𝑉m𝑐𝑐 = 302𝑉𝑉m = 0.814cm3

0.350.40

3. BET theory

𝑉𝑉m 𝑃𝑃𝑃= 3.59 × 10−5 mol
𝑛𝑛a =𝑅𝑅𝑇𝑇𝑇• The surface area is
𝐴𝐴 = 𝑁𝑁A 𝑛𝑛a × 0.16nm2 = 3.46m2• Finally,
Δcon 𝐻𝐻° = Δliq 𝐻𝐻° − 𝑅𝑅𝑅𝑅 ln 𝑐𝑐 = −18.538kJ � mol−134• Δad 𝐻𝐻° has the same order of magnitude as Δliq 𝐻𝐻°
but is lower due to stronger absorbent-absorbateinteraction.
• BET adsorption model is usually accurate and usedin the range of 0.05 < 𝑧𝑧 < 0.35.

35

3. BET theory• When the surface is not flat…

𝐻𝐻ad is affected by curvaturethat changes surface tension.

Monolayer
Lowpressure

BJH isotherm can beused to determine
pore size distribution.

Chemical potentials of different
coverage can be identical(hysteresis in isotherm).

3. BET theory• The IUPAC classification ofadsorption isotherms.
I. Microporous with small externalsurface. The limiting uptake being
governed by the accessible
micropore. e.g., active carbon-N2.
II. Non-porous or macroporous
adsorbent. Typical BET isotherm.
Point B: start of multilayer
adsorption. e.g., silica-N2.

36

3. BET theory

III. Weak interaction. Δad 𝐻𝐻 > Δcon 𝐻𝐻.
The monolayer adsorption ismissing. e.g., carbon-water.
IV. At low pressure, like type II. At
high pressure, capillary
condensation in mesoporescauses hysteresis loop. e.g.,
mesoporous carbon-N2.
V. Type III at low pressure and typeIV at high pressure.
VI. Stepwise from hierarchy pores.

37

38

4. Surface reactions• Consider a simple
heterogenous catalysis.
A g

𝑘𝑘ad

𝑘𝑘de𝑘𝑘I ads → P g

𝑑𝑑𝜃𝜃= 𝑘𝑘ad 1 − 𝜃𝜃 A − 𝑘𝑘de + 𝑘𝑘 𝜃𝜃𝑑𝑑𝑑𝑑
• SSA:
𝑘𝑘ad 1 − 𝜃𝜃 A = 𝑘𝑘de + 𝑘𝑘 𝜃𝜃𝑘𝑘ad A𝜃𝜃 =𝑘𝑘 + 𝑘𝑘de + 𝑘𝑘ad A𝑘𝑘ad

𝑘𝑘de𝑘𝑘Catalyst

39

4. Surface reactions• The reaction rate is𝑘𝑘𝑘𝑘ad A𝑣𝑣 = 𝑘𝑘𝜃𝜃 =𝑘𝑘 + 𝑘𝑘de + 𝑘𝑘ad A• If A 𝑘𝑘ad is small,𝑘𝑘ad A𝜃𝜃 ≈𝑘𝑘 + 𝑘𝑘de𝑘𝑘𝑘𝑘ad A𝑣𝑣 ≈𝑘𝑘 + 𝑘𝑘de
• The reaction is 1storder. The rate islimited by coverage.

• For example,
2H + aq→ H2 g+ 2e−

Catalyst

Au s2H∗40

4. Surface reactions• If both 𝑘𝑘 and 𝑘𝑘de aresmall,𝜃𝜃 ≈ 1𝑣𝑣 ≈ 𝑘𝑘
• Catalyst surface issaturated by theproduct (selfpoisoning).
• The reaction is 0thorder.

• For example,
2H + aq→ H2 g+ 2e−

Catalyst

Ni s

2H ∗41

4. Surface reactions

Free energy• Sabatier principle: the interactions between theadsorbate and the catalyst should be “just right”.
• If the interaction is too weak, the reactant will fail tobind to the catalyst.
• If the interaction is too strong, the product fails todissociate.
Too weak• For example,
2H + + 2e

H − AuH − PtH − Ni

Just rightH2

Too strong42

4. Surface reactions• For bimolecular reaction,
𝑘𝑘obs

A g +B g
AB g• Langmuir-Hinshelwood mechanism:A g
B g

𝑘𝑘1

→𝑘𝑘−1
𝑘𝑘2→𝑘𝑘−2A ads
B ads
𝑘𝑘3

A ads + B ads → AB g

𝑘𝑘1 𝑘𝑘−1

𝑘𝑘2 𝑘𝑘−2

Langmuir-Hinshelwood

𝑘𝑘3

43

4. Surface reactions• For example,Pt

2CO + O2 → 2CO2• The mechanism isCO g ⟹ CO ads Associative
O2 g ⟹ 2O ads Dissociative
CO ads + O ads ⟹ CO2 g• Other examples:
CO + 2H2ZnO

CH2 CH2 + H2
N2 O + H2Cu

CH3 OHCu

CH3 CH3N2 + H2 O

4. Surface reactions

44• Suppose the coverages of A, B and empty sites are𝜃𝜃A , 𝜃𝜃B and 𝜃𝜃E .
𝜃𝜃A + 𝜃𝜃B + 𝜃𝜃E = 1• At equilibrium,
𝑑𝑑𝜃𝜃A= 𝑘𝑘1 A 𝜃𝜃E − 𝑘𝑘−1 𝜃𝜃A − 𝑘𝑘3 𝜃𝜃A 𝜃𝜃B = 0𝑑𝑑𝑑𝑑
𝑑𝑑𝜃𝜃B= 𝑘𝑘2 B 𝜃𝜃E − 𝑘𝑘−2 𝜃𝜃B − 𝑘𝑘3 𝜃𝜃A 𝜃𝜃B = 0𝑑𝑑𝑑𝑑• To simplify the problem, suppose 𝑘𝑘3 is small.
𝑘𝑘1 A 𝜃𝜃E = 𝑘𝑘−1 𝜃𝜃A𝑘𝑘2 B 𝜃𝜃E = 𝑘𝑘−2 𝜃𝜃B4. Surface reactions• Define the adsorption-desorption equilibrium
constants.
𝑘𝑘1
𝐾𝐾1 ≡
𝑘𝑘−1
𝑘𝑘2
𝐾𝐾2 ≡𝑘𝑘−2• Then,𝐾𝐾1 A 𝜃𝜃E = 𝜃𝜃A𝐾𝐾2 B 𝜃𝜃E = 𝜃𝜃B• And,𝐾𝐾1 A 𝜃𝜃E + 𝐾𝐾2 B 𝜃𝜃E = 𝜃𝜃A + 𝜃𝜃B = 1 − 𝜃𝜃E45

4. Surface reactions

1𝜃𝜃E =𝐾𝐾1 A + 𝐾𝐾2 B + 1• Thus,• Finally,

𝐾𝐾1 A
𝜃𝜃A = 𝐾𝐾1 A 𝜃𝜃E =𝐾𝐾1 A + 𝐾𝐾2 B + 1
𝐾𝐾2 B𝜃𝜃B = 𝐾𝐾2 B 𝜃𝜃E =𝐾𝐾1 A + 𝐾𝐾2 B + 1𝑘𝑘3 𝐾𝐾1 𝐾𝐾2 A B
𝑣𝑣LH = 𝑘𝑘3 𝜃𝜃A 𝜃𝜃B =𝐾𝐾1 A + 𝐾𝐾2 B + 1 246

4. Surface reactions• If both A and B are small,
𝑣𝑣LH ≈ 𝑘𝑘3 𝐾𝐾1 𝐾𝐾2 A B• The reaction is 1st order toA and B .
• If A is with large excess,𝑘𝑘3 𝐾𝐾2 B
𝑣𝑣LH ≈𝐾𝐾1 A• The reaction is 1st order toB, but poisoned by A, viceversa.

47

48

4. Surface reactions• Eley-Rideal mechanism:
A g
B g

𝑘𝑘1

→

𝑘𝑘−1
𝑘𝑘2

→

𝑘𝑘−2

A ads

Competitive adsorption

B ads
𝑘𝑘3

A ads + B g → AB g
• For example,
CO2 + H2 → 2CO + H2 O

𝑘𝑘1 𝑘𝑘−1

𝑘𝑘2 𝑘𝑘−2
Eley-Rideal

𝑘𝑘3

4. Surface reactions• The mechanism isH2 g ⟹ 2H ads
H ads + CO2 g ⟹ CO2 H ads
H ads + CO2 H ads ⟹ CO g + H2 O g• At equilibrium,
𝑘𝑘1 A 𝜃𝜃E − 𝑘𝑘−1 𝜃𝜃A − 𝑘𝑘3 𝜃𝜃A B = 0𝑘𝑘2 B 𝜃𝜃E − 𝑘𝑘−2 𝜃𝜃B − 𝑘𝑘3 𝜃𝜃A B = 0• Suppose 𝑘𝑘3 is small.
𝑘𝑘3 𝐾𝐾1 A B
𝑣𝑣ER = 𝑘𝑘3 𝜃𝜃A B =𝐾𝐾1 A + 𝐾𝐾2 B + 149

4. Surface reactions• If both A and B aresmall,
𝑣𝑣ER ≈ 𝑘𝑘3 𝐾𝐾1 A B• The reaction is 1st order toA and B .
• When A is with large
excess,𝑣𝑣ER ≈ 𝑘𝑘3 𝜃𝜃A B ≈ 𝑘𝑘3 B• The reaction 1st order to Band 0th order to A.

50

51

4. Surface reactions• The reaction is 1storder to A and 0thorder to B.
• The rate at constant
A isv• If B is with large
excess,𝑘𝑘3 𝐾𝐾1𝑣𝑣ER ≈A
𝐾𝐾2

Langmuir-Hinshelwood
Eley-Rideal[B]4. Surface reactions

52• For example, the Haber-Bosch process is theproduction of ammonia on metal surface.
H2 g ⟺ 2H ads
N2 g ⟺ N2 ads Physisorption
N2 ads ⟺ 2N ads Dissociative chemisorption
N ads + H ads ⟺ NH ads
NH ads + H ads ⟺ NH2 ads
NH2 ads + H ads ⟺ NH3 adsNH3 ads ⟺ NH3 g• The activation energy depends on chemisorptionenergy of N2.

53

4. Surface reactions• Reaction energy diagram.

Volcano plot