Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.7 ACTIVITY OF ANUNCHARGEDSPECIES 272

Table 9.5 Expressions for activities of nonelectrolytes. For a con-

stituent of a condensed-phase mixture,fi,fA, andfBrefer to the

fugacity in a gas phase equilibrated with the condensed phase.

Substance Activity

Pure gas a(g)D(g)D

f

p

Pure liquid or solid aD

Substanceiin a gas mix-

ture

ai(g)Di(g)i

pi

p

D

fi

p

Substanceiin a liquid or

solid mixture

aiDi (^) ixiDi
fi
fi
Solvent A of a solution aADA (^) AxADA
fA
fA
Solute B, mole fraction
basis
ax;BDx;B (^) x;BxBDx;B
fB
kH,B
Solute B, concentration
basis
ac;BDc;B (^) c;B
cB
c
Dc;B
fB
kc;Bc
Solute B, molality basis am;BDm;B (^) m;B
mB
m
Dm;B
fB
km;Bm

9.7.3 Pressure factors and pressure

At a given temperature, the pressure factoriof componentiof a mixture is a function
only of pressure. To derive the pressure dependence ofifor various kinds of mixture
components, we need expressions for.refi i/as functions of pressure to substitute in
the defining equationiDexpå .refi i/=RT ç.
For componentiof agas mixture, the reference state is pure gasiat the pressure of
the mixture, behaving as an ideal gas. The chemical potential of a pure ideal gas depends
on its pressure according to Eq.7.8.6:D(g)CRTln.p=p/. Thus the chemical
potential of the reference state of gas componentiisrefi (g)Di(g)CRTln.p=p/,
andrefi (g)i(g) is equal toRTln.p=p/. This gives us the following expression for the
pressure dependence of the pressure factor:

i(g)D

p

p

(9.7.13)

For a mixture in acondensed phase, we will make use of.@i=@p/T;fnigDVi(Eq.
9.2.49). The relation between changes ofiandpat constant temperature and composi-
tion is therefore diDVidp. Recall (Sec.9.1.5) that “constant composition” means that
the mole fraction or molality of each component, but not necessarily the concentration, is
constant.
Consider a process in which the system initially consists of a phase with componenti
in its standard state. We change the pressure isothermally frompto the pressurep^0 of
the mixture of interest. For a pure-liquid, pure-solid, or solvent reference state, or a solute