Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.5 ACTIVITYCOEFFICIENTS INMIXTURES OFNONELECTROLYTES 258

9.5.2 Ideal mixtures

Since the activity coefficient of a species relates its actual behavior to its ideal behavior at
the sameTandp, let us begin by examining behavior in ideal mixtures.
Consider first an ideal gas mixture at pressurep. The chemical potential of substancei
in this ideal gas mixture is given by Eq.9.3.5(the superscript “id” stands for ideal):

idi(g)Di(g)CRTln

pi

p

(9.5.1)

The reference state of gaseous substanceiis pureiacting as an ideal gas at pressurep. Its
chemical potential is given by

refi (g)Di(g)CRTln

p

p

(9.5.2)

Subtracting Eq.9.5.2from Eq.9.5.1, we obtain

idi(g)refi (g)DRTln

pi

p

(9.5.3)

Consider the following expressions for chemical potentials in ideal mixtures and ideal-
dilute solutions of nonelectrolytes. The first equation is a rearrangement of Eq.9.5.3, and
the others are from earlier sections of this chapter.^7

Constituent of an ideal gas mixture idi(g)Drefi (g)CRTln

pi

p

(9.5.4)

Constituent of an ideal liquid or solid mixture idi DiCRTlnxi (9.5.5)

Solvent of an ideal-dilute solution idADACRTlnxA (9.5.6)

Solute, ideal-dilute solution, mole fraction basis idBDrefx;BCRTlnxB (9.5.7)

Solute, ideal-dilute solution, concentration basis idBDrefc;BCRTln

cB

c

(9.5.8)

Solute, ideal-dilute solution, molality basis idBDrefm;BCRTln

mB

m

(9.5.9)

Note that the equations for the condensed phases have the general form

idi Drefi CRTln



composition variable

standard composition



(9.5.10)

whererefi is the chemical potential of componentiin an appropriate reference state. (The
standard composition on a mole fraction basis isxD 1 .)

9.5.3 Real mixtures

If a mixture isnotideal, we can write an expression for the chemical potential of each
component that includes anactivity coefficient. The expression is like one of those for the
ideal case (Eqs.9.5.4–9.5.9) with the activity coefficient multiplying the quantity within the
logarithm.

(^7) In order of occurrence, Eqs.9.4.8,9.4.35,9.4.24,9.4.27, and9.4.28.