Page 60 - Partition & Adsorption of Organic Contaminants in Environmental Systems

ISOSTERIC HEAT OF ADSORPTION 51

The isosteric-heat data describe how sensitively the molar heat of adsorp-
tion of a vapor or a solute varies with the amount adsorbed by a solid. To
determine the isosteric heat of adsorption at a given Q (say, Q A in Figure 4.3),
one accounts for the variation of P (or C e) with T at a fixed Q using the general
form of the Clausius–Clapeyron equation:

d log P D H d -D H a
= = (4.14)
dT . 2 303 RT 2 . 2 303 RT 2

or

d log P -D H d
= (4.15)
d 1 ( T) . 2 303 R

Similarly,

d log C e D H d -D H a
= = (4.16)
dT . 2 303 RT 2 . 2 303 RT 2

or

d log C e -D H d
= (4.17)
d 1 ( T) . 2 303 R

where DH d is the molar heat of desorption and DH a is the molar heat of
adsorption (DH d =-DH a ). By repeating the calculations for DH a at other fixed
on Q can then be determined. For vapor or solute
Q, the dependence of DH a
should have the largest negative value (i.e., the molar
adsorption, the DH a
exothermic heat) at the lowest Q and hence the smallest negative value at the
highest Q. As stated before, if the adsorbed vapor forms a condensed phase
should be more exothermic than the molar heat of
on the adsorbent, the DH a
vapor condensation (i.e., -DH evap or -DH sub ). Similarly, if the adsorbed solute
displaces the solvent to form a separate phase on the adsorbent surface, D H a
should be more exothermic than the reverse molar heat of solute solution (i.e.,
-DH sol ). When the adsorption reaches the maximum on an adsorbent, the net
is equal to the heat of adsorbate con-
adsorption heat is zero and thus DH a
densation. In systems where the adsorption energy is not high enough to con-
dense the vapor into a separate phase or to condense the solute by displacing
the solvent, the adsorption will be weak. In this case, the thermicity of adsorp-
tion would be small and notably less exothermic than the heat of adsorbate
condensation. However, as long as a net adsorption occurs, the system will
nevertheless exhibit an exothermic effect, despite the fact that it may be very