Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.4 LIQUID ANDSOLIDMIXTURES OFNONELECTROLYTES 255

Raoult’s law

Henry’s law

0 0:2 0:4 0:6 0:8 1:0

0

2

4

6

8

bc

bc

bcbc

bc

bc bc

bc

bc

bc

bc

xA

fA

=kPa

Figure 9.8 Fugacity of ethanol in a gas phase equilibrated with a binary liquid mix-

ture of ethanol (A) and H 2 O at 25 C and 1 bar. Open circles: experimental measure-

ments.aThe dashed lines show Henry’s law behavior and Raoult’s law behavior.

aRef. [ 45 ].

Comparison with Eq.9.4.5on page 247 shows that Eq.9.4.35is equivalent to Raoult’s law
for fugacity.
Thus, in an ideal-dilute solution of nonelectrolyteseach solute obeys Henry’s law and
the solvent obeys Raoult’s law.
An equivalent statement is that a nonelectrolyte constituent of a liquid mixture ap-
proaches Henry’s law behavior as its mole fraction approaches zero, and approaches Raoult’s
law behavior as its mole fraction approaches unity. This is illustrated in Fig.9.8, which
shows the behavior of ethanol in ethanol-water mixtures. The ethanol exhibits positive
deviations from Raoult’s law and negative deviations from Henry’s law.

9.4.7 Partial molar quantities in an ideal-dilute solution

Consider thesolvent, A, of a solution that is dilute enough to be in the ideal-dilute range.
In this range, the solvent fugacity obeys Raoult’s law, and the partial molar quantities of the
solvent are the same as those in an ideal mixture. Formulas for these quantities were given
in Eqs.9.4.8–9.4.13and are collected in the first column of Table9.2on the next page.
The formulas show that the chemical potential and partial molar entropy of the solvent, at
constantTandp, vary with the solution composition and, in the limit of infinite dilution
(xA! 1 ), approach the values for the pure solvent. The partial molar enthalpy, volume,
internal energy, and heat capacity, on the other hand, are independent of composition in the
ideal-dilute region and are equal to the corresponding molar quantities for the pure solvent.
Next consider asolute, B, of a binary ideal-dilute solution. The solute obeys Henry’s
law, and its chemical potential is given byBDrefx;BCRTlnxB(Eq.9.4.24) whererefx;B
is a function ofTandp, but not of composition.Bvaries with the composition and goes
to1as the solution becomes infinitely dilute (xA! 1 andxB! 0 ).