Surface and Interface Chemistry

Solid/gas Interface
Valentim M. B. Nunes
Engineering Unit of IPT
2014
Adsorption of gases in solids
When a gas or vapor comes into contact with a solid part of it
adsorbs in the surface.
Physical: interaction by
van der Waals forces;
energies of adsorption 
300 a 3000 J.mol-1
There are two types
of adsorption:
Chemical: small range
interactions; heat of
chemical adsorption
increased  40 a 400
kJ.mol-1
Method of measurement
The gas to be adsorbed
occupies a calibrated
burette and the pressure
is read on a manometer.
When the gas comes into contact with the adsorbent sample, the
quantity adsorbed can be calculate from the pressure reading,
when equilibrium is achieved.
Adsorption isotherms: amount of gas adsorbed as a function of
p/ps, where ps is the vapor pressure of adsorbed at the
temperature of the isothermal.
Volume of adsorbed gas / g of
adsorbent
N2 in silica at 77 K
(physical adsorption)
0
p/ps
O2 in activated
carbon at 150 K
(chemical adsorption
limited to a
monolayer)
1
Adsorption Isotherms – BRUNAUER’s Classification
Type I: Solids with small pores – activated carbon.
Type II: Solids that do not have internal networks of holes –
silica or alumina.
Type III: Non porous adsorbent – Cl2 in silica gel; CCl4 in kaolin.
Type IV and V: fairly rare.
Physical adsorption
When p = ps gas condensation occurs on the surface of the solid.
The amount of vapor adsorbed to a given adsorbent depends on
several variables.
xads  f ( p, T , gás, sólido )
The increase in temperature decreases the amount of adsorbed
gas, since the physical adsorption is an exothermic process,
Hads < 0
IUPAC Technical Reports and Recommendations
Reporting physisorption data for gas/solid systems with special
reference to the determination of surface area and porosity
(Recommendations 1984). K. S. W. Sing
Due to the weak bonds involved between gas molecules and the
surface (less than 15 KJ/mole), adsorption is a reversible
phenomenon!
However, from the theoretical point of view, it is very difficult to
predict the form of the isotherms. Most of the theories are
based on the appearance of monolayer’s at low pressures,
forming multilayer's when p  ps.
LANGMUIR ISOTHERM
Hypothesis:
a) Solid surface has a fixed number of centers for adsorption.
The equilibrium between the gas and the solid is dynamic.
At a given temperature and pressure a fraction of centers, ,
is occupied, and a fraction 1- are unoccupied.
b) Each center is occupied only by one molecule.
c) The heat of adsorption is the same for all centers and does
not depend on .
d) There is no interaction between the molecules of different
centers.
The rate at which the molecules occupy the centers is equal to
the rate at which they vacate the centers.
At pressure p, the velocity of occupation of centers is:
va  ka pN (1   )
where N is the total number of centers.
the rate at which the molecules vacate the centers is:
vd  kd N
At equilibrium, equalizing the speed of occupation and vacation,
we obtain :
kp

1  kp
with k = ka/kd.
Reorganizing the expression:
Considering now,
kp    kp
V

Vm
where Vm is the volume corresponding to all the surface occupied
(or volume of monolayer):
V
V
kp 
 kp
Vm Vm
We obtain the Langmuir’s Isotherm:
p
p
1


V Vm kVm
Representing p/V as a function of p, we obtain a straight line
whose slope equals 1/Vm and whose ordinate at the origin is
1/kVm.
The rate of absorption depends on the number of collisions of
the molecules by the molecules (kinetic theory of gases)
NA p
(1   )
1/ 2
2MRT 
The velocity of vacation depends on an activation process:
Z me
H / RT
Where ΔH is the heat of adsorption, Zm is the number of
molecules adsorbed by area and ν is the frequency of oscillation
of the molecules perpendicular to the surface.
Equalizing both expressions we obtain:
NA p
1/ 2

2MRT 

NA p
H / RT

Z

e
2MRT 1/ 2 m
or
1
1
 1

kp
with

H
RT
N Ae
k
1/ 2
Z m 2MRT 
For low pressure (kp << 1):
  kp
V  kpVm
For high pressures (kp >> 1):
 1
V  Vm
K behaves as an equilibrium constant:
H
1
H
  ln k 



 
2
2

T
RT
2
T
RT

p
van’t Hoff equation
Freundlich Isotherm:
V  kp
1/ n
1
log V  log k  log p
n