Gas-Solid Interactions
Light bulbs, Three way catalysts,
Cracking, Corrosion, Electronic
Devices etc.
Adsorption-the key step
Extent of adsorption usually given by fractional coverage
number of surface sites occupied (N s )

total number of surface sites (N )
V

V
N is often
equivalent to
number of
surface atoms of
the substrate
when   1 we have monolayer coverage
Associative (or non-dissociative) adsorption is when a
molecule adsorbs without fragmentation
Dissociative adsorption is when fragmentation occurs
during the adsorption process
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
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.
http://www.nobel.se/chemistry/laureates/1932/langmuir-bio.html
Langmuir Isotherm
Simplifying assumptions
• Adsorption proceeds to
monolayer formation
only
• All sites are equivalent
and the surface is
uniform
• Molecule adsorption is
independent of
occupation of
neighbouring sites
M g  S surface
ka
kd
M  S surface
d
adsorption rate 
 k a p (1   )
dt
d
desorption rate 
 k d
dt
At equilibriu m
k a p (1   )  k d
ka
Kp

,K 
1  Kp
kd
Langmuir Isotherms
Ns
m
V
Kp




N m V 1  Kp
Can write
p
1
p

 ,
N s NK N
p
1
p
p
1
p


,


m m K m V V K V
p p p
Plot
, , vs p
Ns m V
to determine N, m , V
Using the isotherm
From m or V
we may determine N
m
N
nm 

molar mass L
pV  nm RT
SA = N x Am
Specific surface area
SA/(mass of substrate)
Atkins & dePaula 8th p. 918
Attard & Barnes p. 4
Dissociative Adsorption
M 2 g  2 S surface
ka
kd
2( M  S surface)
d
adsorption rate 
 k a p (1   ) 2 ,
dt
d
desorption rate 
 k d 2
dt
At equilibriu m
k a p (1   ) 2  k d 2
ka p
2

 Kp ,
2
(1   )
kd


(1   )
Kp
1  Kp
 Kp
Typical Langmuir isotherms
Associative adsorption isotherms
Dissociative adsorption isotherms
http://www.oup.com/uk/orc/bin/9780199271832/01student/graphs/lg_16_17_18_20.htm
Heats of Adsorption
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.
Q
qi   
 n V
qi = integral heat of
adsorption
 Q  q = differential heat of
qD  
 adsorption
 n V ,T
D
Enthalpy of Adsorption
Heats of adsorption change as a function of surface coverage
M g  S surface  M  S surface
0
0
0
G AD
  RT ln K 0  H AD
 TS AD
differentiate
0
0

H

S
AD
AD
ln K 0  

RT
R
0
H AD

0
 T ln K   RT 2


Van’t Hoff equation
Isosteric enthalpy of adsorption
Re-arranging Langmuir
Differentiate & re-arrange
Kp 

1
  
ln K  ln p  ln 

 1 




 T ln K     T ln p 




H AD


 T ln p    RT 2


0
Use van’t Hoff
0
 p1 
1 1
H AD
  
ln  
R  T1 T2 
 p2  
Measuring isosteric enthalpies
Attard &
Barnes p. 83
0
 p1 
1 1
H AD
  
ln  
R  T1 T2 
 p2  
Isosteric HEATS of adsorption
sometimes used instead of enthalpies
qST   H
0
AD
 qD  RT
Measuring isosteric enthalpies
Atkins & de
Paula, 8th p.
919-920
Note
d 1 / T 
1
 2
dT
T
0
  ln p 
H AD
  1 / T    R


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, ΔH0AD = -Δ H0VAP
BET
p
1 c 1 p 


 * 
*
N s  p  p  Nc Nc  p 
p/ p
1 c 1 p 


 * 
*
1  p / p N s Nc Nc  p 
*

 H
ce
0
0


H
AD
VAP
/ RT
As before, we can replace N with masses or volumes.
BET
“knee” in some
isotherms represents
monolayer coverage

0
0
c   H AD
 H VAP
V
1

*
V 1  p / p
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 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
  c1 ln c2 p 
  c1 p
1 / c2
Try example in Attard & Barnes, p.83