Handbook of Solvents - George Wypych - ChemTech - Ventech!

5.5 The phenomenological theory of solvent effects 291
where h is Planck’s constant, c is the velocity of light, v is frequency, and λis wavelength. If
λ is expressed in nm, eq. [5.5.31] yields E T in kcal mol -1 .
E T = 2 859× 10 4
. / λ [5.5.31]
The phenomenological theory has been applied by Skwierczynski to the E T values of
the Dimroth-Reichardt betaine, 13 a quantity sensitive to the polarity of the medium. 17 The
approach is analogous to the earlier development. We need only consider the solvation effect.
The solute is already in solution at extremely low concentration, so solute-solute interactions
need not be accounted for. The solvent cavity does not alter its size or shape during
an electronic transition (the Franck-Condon principle), so the general medium effect does
not come into play. We write E T of the mixed solvent as a weighted average of contributions
from the three states:
( ) ( ) ( ) ( )
E x = F E WW + F E WM + F E MM
[5.5.32]
T 2 WW T WM T MM T
where the symbolism is obvious. Although E T(WW) can be measured in pure water and
E T(MM) in pure cosolvent, we do not know E T(WM), so provisionally we postulate that E T
(WM) = [E T(WW) + E T(MM)]/2. Defining a quantity Γ by
( 2)
− ( )
( ) − ( )
ET x ET WW
Γ=
E MM E WW
T T
we find, by combining eqs. [5.5.9], [5.5.10], and [5.5.32],
2
Kxx 1 1 1 / 2+
KK 1 2x2 Γ=
2
x + K x x + K K x
1
1 1 2 1 2
2
2
[5.5.33]
[5.5.34]
The procedure is to fit Γ to x 2. As before, a 1-parameter version can be obtained by setting
K 2 =0:
Kx 1 2
Γ=
x + K x
1 1 2
[5.5.35]
Figure 5.5.5 shows a system that can be satisfactorily described by eq. [5.5.35],
whereas the system in Figure 5.5.6 requires eq. [5.5.34]. The K1 values are similar in magnitude
to those observed from solubility systems, with a few larger values; K2, for those systems
requiring eq. [5.5.34], is always smaller than unity. Some correlations were obtained
of K1 and K2 values with solvent properties. Figure 5.5.7 shows log K1 as a function of log
PM, where PM is the partition coefficient of the pure organic solvent.
5.5.3.4 Complex formation.
We now inquire into the nature of solvent effects on chemical equilibria, taking noncovalent
molecular complex formation as an example. Suppose species S (substrate) and L (ligand)
interact in solution to form complex C, K11 being the complex binding constant.
K 11
S L C
+
[5.5.36]