Handbook of Solvents - George Wypych - ChemTech - Ventech!

9.4 Mixed solvent influence on the chemical equilibrium 539
Kus = KII / KI
[9.92]
The method of K us determination, based on the differences between free energy values
of electrolyte transfer from some standard solvent to A and B, respectively, leads to a high
error.
If the concentration ratio of different solvative forms is expressed as α, the concentrations
A and B are expressed as 1-x B and x B, respectively, (x B - molar part B), equation [9.91]
may be presented in the form:
or
( )
p
K = α x / 1 −x
[9.91a]
us B
B
q
( )
lnK = lna + plnx −qln 1 −x
[9.93]
us B B
The last equation permits to calculate value for the solvent of fixed composition and x B
determination at certain composition of the solvate complexes p and q and resolvation constant
K us.
It follows from the equations [9.91] and [9.91a]
where:
Hence
( q)
o ( q) ⎡ ( q)
( q)
[ ( E E ) ] ( B )
q
Kus = m q / m −m p x 1 −x
⎤
[9.91b]
E
0
⎣⎢
⎦⎥
o
m E
(q)
m E
a number of moles E in solution
a number of moles E solvated by the solvent A
q
[ ( B)( B)
]
p
K = x′ x / 1− x′ 1 −x
[9.91c]
us B B
where:
xB′ molar fraction of B in solvate shell
Equation [9.91c] developed for the ideal solution E-A-B permits us to establish the relationship
between the composition of mixed solvent xB and the solvate shell composition
x′ B . For the special case of equimolar solvates, the expression of resolvation constant is written
in the form:
( )
K = α x / 1 −x
[9.91d]
us B B
It follows that even in ideal solution of the simplest stoichiometry, α is not a linear
function of the mixed solvent composition xB. Dependence of isotherm α on the solvent
composition at Kus = 1 is presented in Figure 9.9a.
Analytical correlation between the composition of solvate shell x′ B and the mixed solvent
composition can be developed:
q
[ ]
p
[ / ( ) ] / ( B)
K = x′ 1− x′ x 1 −x
[9.94]
us B B B