Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.4 LIQUID ANDSOLIDMIXTURES OFNONELECTROLYTES 252

Note that the Henry’s law constants are not dimensionless, and are functions ofTandp.
To evaluate one of these constants, we can plotfBdivided by the appropriate composition
variable as a function of the composition variable and extrapolate to infinite dilution. The
evaluation ofkH,Bby this procedure is illustrated in Fig.9.7(b).
Relations between these Henry’s law constants can be found with the use of Eqs.9.1.14
and9.4.16–9.4.18:
kc;BDVAkH,B km;BDMAkH,B (9.4.22)

9.4.5 The ideal-dilute solution

Anideal-dilute solutionis a real solution that is dilute enough for each solute to obey
Henry’s law. On the microscopic level, the requirement is that solute molecules be suffi-
ciently separated to make solute–solute interactions negligible.
Note that an ideal-dilute solution is not necessarily an ideal mixture. Few liquid mix-
tures behave as ideal mixtures, but a solution of any nonelectrolyte solute becomes an ideal-
dilute solution when sufficiently dilute.
Within the composition range that a solution effectively behaves as an ideal-dilute
solution, then, the fugacity of solute B in a gas phase equilibrated with the solution is
proportional to its mole fractionxBin the solution. The chemical potential of B in the
gas phase, which is equal to that of B in the liquid, is related to the fugacity byB D
B(g)CRTln.fB=p/(Eq.9.3.12). SubstitutingfB DkH,BxB(Henry’s law) into this
equation, we obtain

BDB(g)CRTln

kH,BxB

p

D



B(g)CRTln

kH,B

p



CRTlnxB (9.4.23)

where the composition variablexBis segregated in the last term on the right side.
The expression in brackets in Eq.9.4.23is a function ofT andp, but not ofxB, and
represents the chemical potential of B in a hypothetical solute reference state. This chemical
potential will be denoted byrefx;B, where thexin the subscript reminds us that the reference
state is based on mole fraction. The equation then becomes

B.T; p/Drefx;B.T; p/CRTlnxB (9.4.24)

(ideal-dilute solution

of a nonelectrolyte)

Here the notation emphasizes the fact thatBandrefx;Bare functions ofTandp.

Equation9.4.24, derived using fugacity, is valid even if the solute has such low volatil-

ity that its fugacity in an equilibrated gas phase is too low to measure. In principle, no

solute is completely nonvolatile, and there is always a finite solute fugacity in the gas

phase even if immeasurably small.

It is worthwhile to describe in detail the reference state to whichrefx;Brefers. The

general concept is also applicable to other solute reference states and solute standard

states to be encountered presently. Imagine a hypothetical solution with the same

constituents as the real solution. This hypothetical solution has the magical property