Handbook of Solvents - George Wypych - ChemTech - Ventech!

5.5 The phenomenological theory of solvent effects 293
Figure 5.5.8. Thermodynamic cycles for bimolecular association. The symbols s, l, g represent solid, liquid, and
gas phases; the superscripts refer to substrate S, ligand L, and complex C. (Reproduced with permission from the
Journal of Solution Chemistry, reference 18.)
C
C
() + ( + ) − ()
ΔG g ΔG ΔG ΔG
l
comp cav
solv
comp
L
L
S
S
( ΔGcav ΔGsolv ) ( ΔGcav ΔGsolv
)
− + − + = 0 [5.5.39]
We apply the δ M operator to eq. [5.5.39]
C
S
L
C
δ ΔG −δ ΔG − δ ΔG + δ ΔG −δ
ΔG
M cav
M cav
M cav
()
M solv
S
M solv
L
− δ ΔG = δ Δ G l
[5.5.40]
M solv
M comp
where we have assumed δ MΔG comp(g) = 0, which is equivalent to supposing that the structure
of the complex (the spatial relationship of S and L) does not depend upon solvent composition,
or that the intersolute effect is composition independent.
Also applying the δ M treatment to eq. [5.5.4] gives
δ ΔG = δ ΔG + δ ΔG
[5.5.41]
M soln M cav M solv
for each species; recall that ΔG gen med and ΔG cav are identical. Use eq. [5.5.41] in [5.5.40]:
()
C
L
δ ΔG l = δ ΔG −δ ΔG −δ
ΔG
M comp M soln M soln M
S
soln
[5.5.42]
Eq. [5.5.42] says that the solvent effect on complex formation is a function solely of the solvent
effects on the solubilities of reactants (negative signs) and product (positive sign). This
is a powerful result, because we already have a detailed expression, eq. [5.5.23], for each of