1. Surface and Interface Chemistry  Solid/gas Interface
Valentim M. B. Nunes
Engineering Unit of IPT
2014

2. 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

3. 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.

4. (physical adsorption)
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.
N2 in silica at 77 K
(physical adsorption)
O2 in activated carbon at 150 K (chemical adsorption limited to a monolayer)
Volume of adsorbed gas / g of adsorbent 1
p/ps

5. Adsorption Isotherms – BRUNAUER’s Classification

6. 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.

7. 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.
The increase in temperature decreases the amount of adsorbed gas, since the physical adsorption is an exothermic process,
Hads < 0

8. 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

9. 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.

10. LANGMUIR ISOTHERM
Hypothesis:
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.
Each center is occupied only by one molecule.
The heat of adsorption is the same for all centers and does not depend on .
There is no interaction between the molecules of different centers.

11. 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:
where N is the total number of centers.
the rate at which the molecules vacate the centers is:

12. At equilibrium, equalizing the speed of occupation and vacation, we obtain :
with k = ka/kd.

13. Reorganizing the expression:
Considering now,
where Vm is the volume corresponding to all the surface occupied (or volume of monolayer):

14. We obtain the Langmuir’s Isotherm:
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.

17. The rate of absorption depends on the number of collisions of the molecules by the molecules (kinetic theory of gases)
The velocity of vacation depends on an activation process:
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.

18. Equalizing both expressions we obtain:or
with

19. For low pressure (kp << 1):
For high pressures (kp >> 1):

20. K behaves as an equilibrium constant:
van’t Hoff equation

21. Freundlich Isotherm: