Handbook of Solvents - George Wypych - ChemTech - Ventech!

560 Y. Y. Fialkov, V. L. Chumak
( 2 / / ε) ( / / ε)
ΔH =− R a + a T + a ΔS
= R a − a T + a
T 01 02 11 T
00 02 10
Comparison of ΔH i with ΔH T and ΔS i with ΔS T shows that integral values of thermodynamic
characteristics of the ionic association process for HCOOH are not only less informative
than van’t Hoff’s characteristics, but they contradict the physical model of the process
in this case. Indeed, corresponding dependencies of compensative effect are described by
equations:
ΔH i = -0.704ΔS i + 22.87 kJ/mol
ΔH T = 0.592ΔS T - 22.22 kJ/mol
Thus, if the compensative effect for integral thermodynamic functions is interpreted,
one should conclude that characteristic temperature (this is tanα = ΔH/ΔS) is a negative
value, but that is, of course, devoid of physical sense.
In common cases, when the dependence [9.125] is approximated using equation
[9.56], “van’t Hoff’s” (original) thermodynamic constituents of equilibrium process are
equal to:
( )
ΔH =− R a + a
T
01 11
( )
ΔS = R a + a
T
00 10
/ ε [9.130]
/ ε [9.131]
As it is evident from [9.130] and [9.131], the original thermodynamic characteristics
of the process are summarized by the terms where the first of them does not depend, and the
second one depends, on permittivity. These terms accordingly are called covalent and electrostatic
constituents of the process in solution, i.e.,
cov
el
ΔH=− Ra01 and ΔH=−Ra11
/ ε [9.132]
cov
el
ΔS= Ra00 and ΔS=
Ra10
/ ε [9.133]
It should be emphasized that ΔG T values are substantially more informative than integral
thermodynamic values for thermodynamic analysis of chemical equilibrium in solutions
of mixed solvents. Indeed, in frequent cases of equilibrium constant polytherm
characterized by an extreme (i.e., sign of ΔH i changes), one may arrive at the wrong conclusion
that the process nature changes greatly at temperature of extreme value. As has been
shown, 71 appearance of extreme value of equilibrium constant polytherms is caused in the
majority of cases by temperature change of solvent permittivity. The condition of extreme
appearance for the process described by equation [9.55] is:
where:
( ) ( )
a exp αT + γ + αa
T a T + a = [9.134]
01 extr 11 extr 10 extr 11 0
αγ , the coefficients of lnε = αT +γequation
γ activity coefficient
Textr temperature corresponding to extremum of isotherm of equilibrium constant