Handbook of Solvents - George Wypych - ChemTech - Ventech!

290 Kenneth A. Connors
( K1 / 2)
x2
+ ( / 2)
⎡
γ = γ + γ′
1 ⎢
⎣x
K x
1 1 2
⎤
⎥
⎦
[5.5.29]
Eq. [5.5.29] will be recognized as equivalent to eq. [5.5.27] for the 1-step model. The
interpretation is as follows: the 2-step model, eq. [5.5.26], can always be applied, but if the
result is that K 1 ≈ 4K 2 the 1-step model will suffice to describe the data. Moreover, if K 1 ≈
4K 2 from the 2-step treatment, no physical significance is to be assigned to the second parameter.
These considerations are pertinent to real systems. Table 5.5.4 lists K 1 and K 2 values
obtained by applying eq. [5.5.26] to literature data. 15 Several systems conform reasonably to
the K 1 ≈4K 2 condition. Recall that ideal behavior requires the special case K 1 =2,K 2= 1/2.
The less restrictive condition K 1 ≈ 4K 2 we call “well-behaved.” Figure 5.5.3 shows a
well-behaved system; Figure 5.5.4 shows one that is not well-behaved. The distinction is
between a hyperbolic dependence on x 2 (well-behaved) and a non-hyperbolic dependence.
Table 5.5.4. Solvation parameter estimates for surface tension data according to eq.
[5.5.26]
Cosolvent K1 K2 K1/K2
Methanol 19.8 2.9 6.8
2-Propanol 130 29.4 4.4
1-Propanol 232 50 4.6
t-Butanol 233 65 3.6
Acetic acid 115 2.7 42.6
Acetone 138 7.1 19.4
Acetonitrile 33.4 14.5 2.3
Dioxane 62.1 7.4 8.4
THF 136 25.9 5.3
Glycerol 22.7 0.80 28.4
DMSO 12.3 1.43 8.6
Formamide 5.52 2.57 2.1
Ethylene glycol 9.4 2.62 3.6
A further observation from these results is that some of the K1 values are much larger
than those encountered in solubility studies. Correlations with log PM have been shown. 14
5.5.3.3 Electronic absorption spectra
The energy of an electronic transition is calculated from the familiar equation
E hv hc
T = = λ
[5.5.30]