Gas-Solid Interactions

Light bulbs, Three way catalysts, Cracking, Corrosion, Electronic

Devices etc.

Adsorption-the key stepExtent of adsorption usually given by fractional coverage

coveragemonolayer have we1when

)(N sites surface ofnumber total

)(N occupied sites surface ofnumber s

V

V

N is often equivalent to number of surface atoms of the substrate

Associative (or non-dissociative) adsorption is when a molecule adsorbs without fragmentation

Dissociative adsorption is when fragmentation occurs during the adsorption process

Adsorption IsothermsModels describing equilibrium between the gaseous and the

adsorbed phases at a given fixed temperature

Simplest is that based on Irving Langmuir’s proposals

http://www.nobel.se/chemistry/laureates/1932/langmuir-bio.html

Born in Brooklyn January 31, 1881Graduated from Columbia University in 1903

Postgraduate under Nernst in Göttingen Post at Stevens Institute of Technology New Jersey

1909 hired by General Electric CompanyStudies embraced chemistry, physics, and engineering

Investigated properties of adsorbed films and the nature of electric discharges in high vacuum and in certain gases at

low pressures.

Langmuir Isotherm

• Adsorption proceeds to monolayer formation only

• All sites are equivalent and the surface is uniform

• Molecule adsorption is independent of occupation of neighbouring sites

Simplifying assumptions

d

a

da

d

a

surface

d

a

surfaceg

k

k

p

p

kpk

kdt

d

pkdt

d

SMk

kSM

K ,K1

K

)1(

mequilibriuAt

rate desorption

)1( rate adsorption

Langmuir Isotherms

Vm

pV

p

m

p

N

p

V

p

VV

p

m

p

mm

p

N

p

NN

p

p

p

V

V

m

m

N

N

s

s

s

, N, determine to

vs,,Plot

K

1 ,

K

1 ,

K

1

Can write

K1

K

Using the isotherm

RTnpVL

Nmn

N

Vm

m

m

massmolar

determinemay we

or From

Atkins & dePaula 8th p. 918 Attard & Barnes p. 4

SA = N x Am

Specific surface area

SA/(mass of substrate)

Dissociative Adsorption

p

p

ppk

pk

kpk

kdt

dpk

dt

d

SMk

kSM

d

a

da

da

surface

d

a

surfaceg

K1

K

K)1(

,K)1(

)1(

mequilibriuAt

rate desorption ,)1( rate adsorption

)(22

2

2

22

22

2

Typical Langmuir isotherms

http://www.oup.com/uk/orc/bin/9780199271832/01student/graphs/lg_16_17_18_20.htm

Associative adsorption isotherms Dissociative adsorption isotherms

Heats of Adsorption

Vi n

Qq

Gas adsorption to a solid is exothermic.The magnitude and variation as a function of coverage may

reveal information concerning the bonding to the surface.

Calorimetric methods determine heat, Q evolved.

qi = integral heat of adsorption

TVD n

Qq

,

qD = differential heat of

adsorption

Enthalpy of Adsorption

Heats of adsorption change as a function of surface coverage

2

00

000

0000

Kln

Kln

Kln

RT

H

T

R

S

RT

H

STHRTG

SMSM

AD

ADAD

ADADAD

surfacesurfaceg

differentiate

Van’t Hoff equation

Isosteric enthalpy of adsorption

21

0

2

1

2

0

11ln

ln

lnKln

1lnlnKln

1K

TTR

H

p

p

RT

Hp

T

pTT

p

p

AD

AD

Re-arranging Langmuir

Differentiate & re-arrange

Use van’t Hoff

Measuring isosteric enthalpies

21

0

2

1 11ln

TTR

H

p

p AD

Attard & Barnes p. 83

Isosteric HEATS of adsorption sometimes used instead of enthalpies

RTqHq DADST 0

Measuring isosteric enthalpies

R

H

T

p

TdT

Td

AD0

2

/1

ln

1/1

Atkins & de Paula, 8th p. 919-920

Note

BET IsothermWhen adsorption of a gas can occur over a previously

adsorbed monolayer of the gas

Brunauer, Emmett & Teller extends the Langmuir isotherm model to multilayer adsorption

Assumptions:

Adsorption of 1st layer takes place on a surface of uniform energy

2nd layer only adsorbs on 1st, 3rd on 2nd, etc. When p=p*, infinite layers form.

At equilibrium, rates of condensation & evapouration are same for each individual layer

For layers ≥ 2, ΔH0AD = -Δ H0

VAP

BET

RTHH

s

s

VAPADec

p

p

Nc

c

NcNpp

pp

p

p

Nc

c

NcppN

p

/

**

*

**

00

11

/1

/

11

As before, we can replace N with masses or volumes.

BET

“knee” in some isotherms represents monolayer coverage

*

00

/1

1

ppV

V

HHc VAPAD

BET underestimates adsorption at low p and overestimates adsorption at high p

Using the BET

Atkins & dePaula 8th

p. 921

Principle behind the surface area and pore size analyzers on the market. Use nitrogen at 77K as adsorbate. Knowing size of molecule, the surface area and/or pore size can be determined from the isotherm.

http://www.beckman.com/products/instrument/partChar/pc_sa3100.asp

IUPAC Classification

Other isothermsWhen adsorption sites are not equivalent, enthalpy of adsorption

changes as a function of coverage

Temkin: Assumes enthalpy changes linearly with pressure

Freundlich: Assumes enthalpy changes logarithmically with pressure

2/11

21 ln

cpc

pcc

Try example in Attard & Barnes, p.83