Thermodynamics and Chemistry

CHAPTER 12 EQUILIBRIUM CONDITIONS IN MULTICOMPONENT SYSTEMS

12.6 LIQUID–LIQUIDEQUILIBRIA 393

bc

bc bc bc bc

bc bc

bc

bc

bc

bc

0 10 20 30 40 50

13:3

13:2

13:1

13:0

12:9

t=ıC

ln

xB

Figure 12.8 Aqueous solubility of liquidn-butylbenzene as a function of temperature

(Ref. [ 125 ]).

Pure-liquid reference state

The condition for transfer equilibrium of component B isíBDìB. If we use a pure-liquid
reference state for B in both phases, this condition becomes

BCRTln.

BíxíB/DBCRTln.

BìxìB/ (12.6.4)

This results in the following relation between the compositions and activity coefficients:

(^) BíxíBD (^) BìxìB (12.6.5)
As before, we assume the two components have low mutual solubilities, so that the B-
rich phase is almost pure liquid B. ThenxBìis only slightly less than 1 , (^) Bìis close to 1 , and
Eq.12.6.5becomesxBí1=
Bí. SincexBíis much less than 1 , (^) Bímust be much greater
than 1.
In environmental chemistry it is common to use a pure-liquid reference state for a non-
polar liquid solute that has very low solubility in water, so that the aqueous solution is
essentially at infinite dilution. Let the nonpolar solute be component B, and let the aqueous
phase that is equilibrated with liquid B be phaseí. The activity coefficient (^) Bíis then a
limiting activity coefficientoractivity coefficient at infinite dilution. As explained above,
the aqueous solubility of B in this case is given byxBí1=
Bí, and (^) Bíis much greater than

1. We can also relate the solubility of B to its Henry’s law constantkíH,B. Suppose the two
   liquid phases are equilibrated not only with one another but also with a gas phase. Since
   B is equilibrated between phaseíand the gas, we have (^) x;íBDfB=kH,Bí xíB(Table9.4).
   From the equilibration of B between phaseìand the gas, we also have (^) BìDfB=xìBfB.
   By eliminating the fugacityfBfrom these relations, we obtain the general relation
   xíBD
   (^) BìxìBfB
   (^) x;íBkH,Bí

(12.6.6)