Handbook of Solvents - George Wypych - ChemTech - Ventech!

528 Y. Y. Fialkov, V. L. Chumak
ΔG = σ −σ −ΔG
solv, E solv, F
( v )
[9.48]
The variation of free energy due to any chemical process consists of both covalent and
electrostatic components:
ΔG ΔG ΔG
el
= −
(cov) ( )
[9.49]
Substituting [9.49] in [9.48], we come to an equation that in general describes the
mixed solvent effect on the equilibrium chemical process:
(cov) (cov) ( ,
, )
( el )
solv E solv F ( solv, E solv,
F)
ΔG ΔG
v ( )
( el )
=− + σ − σ + σ −σ
[9.50]
(el) (cov)
For universal (chemically indifferent) solvents where σ >> σ , it may by assumed
that
ΔG ΔG
v ( ) ( el ) ( el )
=− + σ −σ
[9.51]
solv, E
solv, F
Thus the mixed solvent effect on the equilibrium of the chemical process [9.45] is determined
not only by the vacuum component but also by the solvation energy of each of the
chemical forms of equilibrium members.
From free energy to equilibrium constants, one can obtain the equation describing
mixed solvent effect on the equilibrium constant of the [9.45] process:
( ) (cov) (cov)
( el ) ( el )
[ Δ ( σ σ solv, F solv, E ) ( σ σ
solv, F solv,
E ) ]
lnK
G v
= + − + −
/ RT [9.52]
In the special case of universal media, i.e., mixed solvent formed by both solvation-inert
components, this equation can be presented as:
( el ) ( el )
[ solv, f solv, E ]
( univ ) ( v )
ln K = ΔG + σ −σ
/ RT
[9.53]
Because the energy of all types of electrostatic interaction is inversely proportional to
permittivity, these equations can be rewritten in the form:
and
( ) (cov) (cov)
[ Δ ( σ σ solv, F solv, E ) ( βsolv, F βsolv,
E)
]
lnK
G v
= + − + −
[ ( solv, F solv, E ) ]
/ ε / RT [9.52a]
( univ ) ( v )
ln K = ΔG + β −β
/ ε / RT
[9.53a]
where:
β the multipliers of the magnitudes of reciprocal permittivity in equations of energy of the
main types of electrostatic interactions such as dipole-dipole, ion-dipole, and ion-ion
interactions
As follows from [9.52a], in binary mixed solvents formed from solvation-indifferent
components (i.e., universal media), equilibrium constants of the [9.45] process are expo-