Multicomponent Equilibrium Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 81

Solute transfer

Cavity formation Solute accommodation and

solute-solvent interactions

Δ G = G c + G i

FIGURE 3.10 Molecular description of the solubility of a nonpolar solute in water. The first
stage is the formation of a cavity to accommodate the solute and the second stage involves
establishing molecular interactions between the solute and water molecules.

microscopic cavity was found to be approximately one third of the value for a plane
surface.
Hermann (1972) obtained the free energy associated with the formation of a
cavity in water and the introduction of various hydrocarbons into water. Table 3.12
summarizes some of his calculations. It gives the values of G c and G t for a vari-
ety of hydrocarbons in water. The agreement between the experimental values and
predicted values is satisfactory considering the fact that an approximate structure
for water was assumed. The most important aspect is that the values of cavitation
free energies are all positive whereas those for the interactions are all negative. The
major contribution toward the unfavorable free energy of dissolution of hydrophobic
molecules results from the work that has to be done against perturbing the structure
of water. Practically all molecules have interaction energies that are favorable toward
dissolution. Thus the term hydrophobic molecule is a misnomer. It is not that the
molecules have any phobia toward water but, in fact, it is the water that rejects the
solute molecule .

E XAMPLE 3.13 H ENRY'S C ONSTANT FROM F REE E NERGY OF S OLUTION

K aw = exp Δ G
RT

.

(3.68)

Knowledge of the free energy of transfer of a mole of solute i from the gas phase
to water from theory allows a direct estimation of Henry's constant, K aw , from the
equation. For methane the free energy change at 298 K is 6.7 kJ/mol. Hence Henry's
constant is estimated to be 14.9. The experimental value is 28.6.