1.
Gas-Solid Interactions
Light bulbs, Three way catalysts,
Cracking, Corrosion, Electronic
Devices etc.

2.
Adsorption-the key step
Extent of adsorption usually given by fractional coverage
coverage
monolayer
have
we
1
when
)
(N
sites
surface
of
number
total
)
(N
occupied
sites
surface
of
number 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

3.
Adsorption Isotherms
Models 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, 1881
Graduated from Columbia University in 1903
Postgraduate under Nernst in Göttingen
Post at Stevens Institute of Technology New Jersey
1909 hired by General Electric Company
Studies 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.

4.
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
d
a
d
a
surface
d
a
surface
g
k
k
p
p
k
p
k
k
dt
d
p
k
dt
d
S
M
k
k
S
M












K
,
K
1
K
)
1
(
m
equilibriu
At
rate
desorption
)
1
(
rate
adsorption








5.
Langmuir Isotherms



















V
m
p
V
p
m
p
N
p
V
p
V
V
p
m
p
m
m
p
N
p
N
N
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
K
1
K


6.
Using the isotherm
RT
n
pV
L
N
m
n
N
V
m
m
m







mass
molar
determine
may
we
or
From
Atkins & dePaula 8th p. 918 Attard & Barnes p. 4
SA = N x Am
Specific surface area
SA/(mass of substrate)

7.
Dissociative Adsorption
p
p
p
p
k
p
k
k
p
k
k
dt
d
p
k
dt
d
S
M
k
k
S
M
d
a
d
a
d
a
surface
d
a
surface
g
K
1
K
K
)
1
(
,
K
)
1
(
)
1
(
m
equilibriu
At
rate
desorption
,
)
1
(
rate
adsorption
)
(
2
2
2
2
2
2
2
2
2




























8.
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

9.
Heats of Adsorption
V
i
n
Q
q 






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
T
V
D
n
Q
q
,








 qD = differential heat of
adsorption

10.
Enthalpy of Adsorption
Heats of adsorption change as a function of surface coverage
2
0
0
0
0
0
0
0
0
0
K
ln
K
ln
K
ln
RT
H
T
R
S
RT
H
S
T
H
RT
G
S
M
S
M
AD
AD
AD
AD
AD
AD
surface
surface
g


























differentiate
Van’t Hoff equation

11.
Isosteric enthalpy of adsorption



















































2
1
0
2
1
2
0
1
1
ln
ln
ln
K
ln
1
ln
ln
K
ln
1
K
T
T
R
H
p
p
RT
H
p
T
p
T
T
p
p
AD
AD














Re-arranging Langmuir
Differentiate & re-arrange
Use van’t Hoff

12.
Measuring isosteric enthalpies

















2
1
0
2
1 1
1
ln
T
T
R
H
p
p AD

Attard &
Barnes p. 83
Isosteric HEATS of adsorption
sometimes used instead of enthalpies
RT
q
H
q D
AD
ST 



 0

13.
Measuring isosteric enthalpies
 
  R
H
T
p
T
dT
T
d
AD
0
2
/
1
ln
1
/
1













Atkins & de
Paula, 8th p.
919-920
Note

14.
BET Isotherm
When 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, ΔH0
AD = -Δ H0
VAP

15.
BET
 
 
  RT
H
H
s
s
VAP
AD
e
c
p
p
Nc
c
Nc
N
p
p
p
p
p
p
Nc
c
Nc
p
p
N
p
/
*
*
*
*
*
0
0
1
1
/
1
/
1
1





























As before, we can replace N with masses or volumes.

16.
BET
“knee” in some
isotherms represents
monolayer coverage
 
*
0
0
/
1
1
p
p
V
V
H
H
c VAP
AD








BET underestimates
adsorption at low p
and overestimates
adsorption at high p

17.
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

18.
IUPAC Classification

19.
Other isotherms
When 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
/
1
1
2
1 ln
c
p
c
p
c
c




Try example in Attard & Barnes, p.83