Handbook of Solvents - George Wypych - ChemTech - Ventech!

296 Kenneth A. Connors
ten ΔG � rxn, is the free energy of activation in the solution phase.
ΔG � rxn(1) = ΔG � rxn(g) +(ΔG � gen med + ΔG � R
solv) − (Δ gen med Δ
Applying the δ M operation gives eq. [5.5.48]:
δ M ΔG � rxn = ΔG � rxn(x 2 ) −ΔG � rxn(x 2 =0)
R
G + G ) [5.5.47]
solv
[5.5.48]
The quantity ΔG � rxn(g), disappears in this subtraction, as do other composition-independent
quantities. We make use of eq. [5.5.13] and eq. [5.5.19] to obtain a function having
six parameters, namely K 1 R ,K2 R ,K � 1,gA R , and gA � . This function is made manageable by
adopting the full cancellation approximation, setting K 1 R =K � 1=K 1and K 2 R =K � 2=K 2.We
then obtain
δMΔG � rxn = (ΔgA � γ ′ K1x1x2 +2ΔgA � 2 2 2
γ ′ K1K2x 2)/(x1
+ K1x1x2 + K1K2x 2)
[5.5.49]
where ΔgA � =gA � -gA R ; this is the difference between the curvature-corrected molecular
surface areas of the cavities containing the transition state and the reactant. This quantity
may be positive or negative.
LePree 21 tested eq. [5.5.49] with the decarboxylative dechlorination of N-chloroamino
acids in mixed solvents
RCH(NHCl)COOH + H 2O → RCHO + NH 3 +HCl+CO 2
Figure 5.5.10. Solvent effect on the decomposition of
N-chloroaniline in acetonitrile-water mixtures. The
smooth curve is drawn with eq. 5.5.49. (Reproduced
with permission from the Journal of Pharmaceutical
Sciences, reference 21.)
[5.5.50]
Figure 5.5.11. Solvent effect on the decomposition of
N-chloroleucine in 2-propanol-water mixtures. The
smooth curve is drawn with eq. 5.5.49. (Reproduced
with permission from the Journal of Pharmaceutical
Sciences, reference 21.)