Handbook of Solvents - George Wypych - ChemTech - Ventech!

292 Kenneth A. Connors
Figure 5.5.5. Dependence of E T on composition for the
methanol-water system. The smooth line was drawn
with eq. 5.5.35. (Reproduced with permission from the
Journal of the Chemical Society. Perkin Transactions
2, reference 17.)
Figure 5.5.7. A plot of log K 1 from the E T data against
log P M; the circles represent 1-step solvents (eq. 5.5.35)
and the squares, 2-step solvents (eq. 5.5.34). (Reproduced
with permission from the Journal of the Chemical
Society, Perkin Transactions 2, reference 17.)
It is at once evident that this constitutes
a more complicated problem than those we
have already considered inasmuch as here
we have three solutes. We begin with the
thermodynamic cycles shown as Figure
5.5.8; these cycles describe complex formation
in the solid, solution, and gas phases
horizontally, and the energy changes associated
with the indicated processes. ΔG latt corresponds
to the crystal lattice energy
(solute-solute interactions), ΔG cav represents
the energy of cavity formation (identical
with the general medium effect of Section
5.5.2). ΔG comp is the free energy of complex
formation, which in the solution phase is
given by eq. [5.5.37].
ΔG () l kTlnK comp
=− 11 [5.5.37]
Eq. [5.5.37] gives the free energy with
respect to a 1M standard state, because the unit of K 11 is M -1 . To calculate the unitary (mole
fraction) free energy change we write, instead of eq. [5.5.37], eq. [5.5.38]:
*
() ( )
Figure 5.5.6. Dependence of E T on composition for the
acetone-water system. The smooth line was drawn
with eq. 5.5.34. (Reproduced with permission from the
Journal of the Chemical Society. Perkin Transactions
2,. reference 17.)
ΔGcomp l =−kTln K11M ρ [5.5.38]
where M* is the number of moles of solvent per kg of solvent and ρ is the solution density.
The unitary free energy does not include the entropy of mixing.
From cycle gl in Figure 5.5.8 we obtain eq. [5.5.39].