Handbook of Solvents - George Wypych - ChemTech - Ventech!

5.5 The phenomenological theory of solvent effects 283
5.5.2.3 The solvation effect: solute-solvent interaction
Our approach is to treat solvation as a stoichiometric equilibrium process. Let W symbolize
water, M an organic cosolvent, and R the solute. Then we postulate the 2-step (3-state) system
shown below.
[5.5.5]
[5.5.6]
In this scheme K 1 and K 2 are dimensionless solvation equilibrium constants, the concentrations
of water and cosolvent being expressed in mole fractions. The symbols RW 2, RWM,
RM 2 are not meant to imply that exactly two solvent molecules are associated with each solute
molecule; rather RW 2 represents the fully hydrated species, RM 2 the fully cosolvated
species, and RWM represents species including both water and cosolvent in the solvation
shell. This description obviously could be extended, but experience has shown that a 3-state
model is usually adequate, probably because the mixed solvate RWM cannot be algebraically
(that is, functionally) differentiated into sub-states with data of ordinary precision.
Now we further postulate that the solvation free energy is a weighted average of contributions
by the various states, or
ΔG = ΔG F + ΔG F + ΔG
F
[5.5.7]
solv WW WW WM WM MM MM
where F WW,F WM, and F MMare fractions of solute in the RW 2, RWM, and RM 2 forms, respectively.
Eq. [5.5.7] can be written
( ) ( )
ΔG = ΔG − ΔG F + ΔG − ΔG F + ΔG
[5.5.8]
solv WM WW WM MM WW MM WW
By combining definitions of K 1,K 2,F WM, and F MM we get
F
K 1
RW2 + M RWM + W
K 2
RWM +
M RM2 + W
Kxx 1 1 2
=
2
x + K x x + K K x
WM 2 MM
1 1 1 2 1 2 2
for use in eq. [5.5.8]
Now observe this thermodynamic cycle [5.5.10]:
From this cycle we get
F
2
KK 1 2x2 =
2
2
x + K x x + KK 1 2x2 1
1 1 2
[5.5.9]
ΔG = ΔG − ΔG
=−kTln K
[5.5.11]
1 WM WW
1