Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.4 LIQUID ANDSOLIDMIXTURES OFNONELECTROLYTES 253

that it continues to exhibit the ideal-dilute behavior described by Eq.9.4.24, even when

xBincreases beyond the ideal-dilute range of the real solution. The reference state is

the state of this hypothetical solution atxBD 1. It is a fictitious state in which the mole

fraction of B is unity and B behaves as in an ideal-dilute solution, and is sometimes

called theideal-dilute solution of unit solute mole fraction.

By settingxBequal to unity in Eq.9.4.24, so that lnxBis zero, we see thatrefx;B

is the chemical potential of B in the reference state. In a gas phase equilibrated with

the hypothetical solution, the solute fugacityfBincreases as a linear function ofxBall

the way toxBD 1 , unlike the behavior of the real solution (unless it happens to be an

ideal mixture). In the reference state,fBis equal to the Henry’s law constantkH,B; an

example is indicated by the filled circle in Fig.9.7(a).

By similar steps, combining Henry’s law based on concentration or molality (Eqs.
9.4.17and9.4.18) with the relationBDB(g)CRTln.fB=p/, we obtain for the solute
chemical potential in the ideal-dilute range the equations

BDB(g)CRTln



kc;BcB

p

c

c



D



B(g)CRTln

kc;Bc

p



CRTln

cB

c

(9.4.25)

BDB(g)CRTln



km;BmB

p

m

m



D



B(g)CRTln

km;Bm

p



CRTln

mB

m

(9.4.26)

Note how in each equation the argument of a logarithm is multiplied and divided by a
constant,corm, in order to make the arguments of the resulting logarithms dimension-
less. These constants are calledstandard compositionswith the following values:

standard concentrationcD 1 mol dm^3 (equal to one mole per liter, or one molar)

standard molalitymD 1 mol kg^1 (equal to one molal)

Again in each of these equations, we replace the expression in brackets, which depends
onTandpbut not on composition, with the chemical potential of a solute reference state:

B.T; p/Drefc;B.T; p/CRTln

cB

c

(9.4.27)

(ideal-dilute solution

of a nonelectrolyte)

B.T; p/Drefm;B.T; p/CRTln

mB

m

(9.4.28)

(ideal-dilute solution

of a nonelectrolyte)

The quantitiesrefc;Bandrefm;Bare the chemical potentials of the solute in hypothetical refer-
ence states that are solutions of standard concentration and standard molality, respectively,
in which B behaves as in an ideal-dilute solution. Section9.7.1will show that when the
pressure is the standard pressure, these reference states are solutestandardstates.