Page 55 - Adsorption by Powders and Porous Solids

40 ADSORPTION BY POWDERS AND POROUS SOLIDS

The drfferential standard entropy of adsorption, A ,, J;,,, is:
A~~~S';,~=~';,,- (2.55)
SF'
The differential entropy of adsorption can be readily calculated from the differential
enthalpy of adsorption since from Equations (2.46), (2.5 1) and (2.54) we obtain:

A ads T. f =-
T
It is important not to confuse the differential (or isosteric) enthalpy of adsorption with
the transformed differential enthalpy of adsorption A ,hT,, which is derived from
Equation (2.45):

so that:

2.5.2. Definitions of the integral molar quantities of adsorption
The difference between a molar surface excess thermodynamic quantity x;, , and the
corresponding molar quantity x;,, for the gaseous adsorptive at the same equilibrium
T and p is usually called the integral molar quantity of adsorption, and is denoted
A4SxT.r:
AadsxT,r= ';,f - 'tSp
We can thus define the integral molar energy of adrorption:
A,su~,r= 4.r- ~8
and the integral molar entropy of adsorption:

Aa&sT,r=s;,r- (2.60)
We may derive the relation between these integral molar quantities of adsorption
from Equations (2.20) using the expression of surface excess chemical potential y"
given by Equation (2.41) and assuming the gas to be ideal:

Then, from Equation (2.40), the transformed integral molar enthalpy of adsorption is
obtained: