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Defining K° to be the product in this last equation, we have Section 11.2
Reaction Equilibrium
¢G° RT ln K° (11.4)* in Nonelectrolyte Solutions
¢G° a n m° i (11.5)*
i
i
K° q 1a i,eq 2 n i (11.6)*
i
(Perhaps a better symbol for © n m° i would be m°, but G° is the commonly used
i
i
symbol.)
K° is called the standard equilibrium constant, the activity equilibrium con-
stant, or simply the equilibrium constant. We always choose the standard states so
that m° depends at most on T and P. (For gases, m° depends on T only.) Hence G°
i
i
depends at most on T and P, and K°, which equals exp( G°/RT), depends at most
on T and P, and not on the mole fractions. We have thus “solved” the problem of
chemical equilibrium in an arbitrary system. The equilibrium position occurs when the
n
activities are such that ß (a ) i equals the equilibrium constant K°, where K° is found
i
i
from (11.4) as exp( G°/RT). To solve the problem in a practical sense, we must
express the activities in terms of experimentally observable quantities.
11.2 REACTION EQUILIBRIUM IN
NONELECTROLYTE SOLUTIONS

To apply the results of the last section to solutions of nonelectrolytes, we choose one
of the conventions of Chapter 10 and introduce the appropriate expressions for the ac-
tivities a into the equilibrium constant K° of (11.6).
i
Most commonly, one component of the solution is designated the solvent. For the
solvent, we use the mole-fraction scale [Eq. (10.30)]. For the solutes, one can use the
mole-fraction scale, the molality scale, or the molar concentration scale.
If the mole-fraction scale is used for the solutes, the activity a x,i of species i is
a x,i g x [Eq. (10.5)], where g denotes the Convention II activity coefficient
II
II,i i
(Sec. 10.1), which goes to 1 at infinite dilution. The subscript x on a reminds us that
the activity depends on which scale is used. The equilibrium constant K° in Eq. (11.6)
n
then becomes K ß (g x ) i , where the subscript on K denotes use of the mole-
i
II,i i
x
fraction scale and where the eq subscript has been omitted for simplicity. Equa-
tions (11.4) and (11.5) become G° n m° RT ln K .
x
i
x
i
II,i
Thermodynamic data for species in aqueous solutions are usually tabulated for the
molality-scale standard state. Therefore, one most commonly uses the molality scale
for solutes. From (10.32), the activity a m,i of solute i on the molality scale is a m,i
g m /m°(i A, where A is the solvent), where the standard molality m° equals
i
m,i
1 mol/kg. The equilibrium constant (11.6) becomes
x 2
K° 1g x,A A n A q 1g m,i m >m°2 n i (11.7)
m
i
i A
The degree superscript on K indicates a dimensionless equilibrium constant. The
mole-fraction scale is retained for the solvent A, so the solvent activity in (11.7) is dif-
ferent in form from the solute activities. The solvent stoichiometric number n is zero
A
if the solvent does not appear in the chemical reaction. If the solution is dilute, both
n
x and g are close to 1 and it is a good approximation to omit the factor (g x ) A
A x,A x,A A
from K°. For the molality scale, (11.4) and (11.5) become
m
¢G° RT ln K° (11.8)
m m
¢G° n m° a n m° (11.9)
m A x,A i m,i
i A