Page 351 - Physical Chemistry

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Chapter 11 Note that m° of the solvent cannot be omitted from G° (unless n 0) even if the
A
m
Reaction Equilibrium solution is very dilute.
in Nonideal Systems
The molar concentration scale is occasionally used for solute activities. Here,
a c,i g c /c° [Eq. (10.32)]. The equations for K° and G° are the same as (11.7)
c,i i
c
c
to (11.9) except that the letter m is replaced by c everywhere.
K , K°, and K° have different values for the same reaction. Likewise, G°, G°,
c
x
m
x
c
and G° differ for the same reaction, since the value of the standard-state quantity m° i
m
depends on the choice of standard state for species i. Thus, in using Gibbs free-energy
data to calculate equilibrium compositions, one must be clear what the choice of stan-
dard state is for the tabulated data.
To apply these expressions to calculate equilibrium compositions, we use the
procedures discussed in Chapter 10 to determine activity coefficients. If the nonelec-
trolyte solution is dilute, we can approximate each activity coefficient as 1. The equi-
n
librium constant K then reduces to the expression K ß (x ) i for ideally dilute
i,eq
x
x
i
solutions (Sec. 9.8).
Since m° for solute i depends on what the solvent is, the equilibrium constant K° m
m,i
for a given reaction is different in different solvents. Also, the activity coefficients are
different in different solvents because of different intermolecular interactions. Thus
the equilibrium amounts differ in different solvents.
11.3 REACTION EQUILIBRIUM IN ELECTROLYTE SOLUTIONS
The most commonly studied solution equilibria are ionic equilibria in aqueous solu-
tions. As well as being important in inorganic chemistry, ionic equilibria are signifi-
cant in biochemistry. For the majority of biologically important reactions, at least
some of the species involved are ions. Examples include the organic phosphates (such
as adenosine triphosphate, ATP) and the anions of certain acids (such as citric acid)

involved in metabolic energy transformations; inorganic ions such as H O and Mg 2
3
participate in many biochemical reactions.
Since thermodynamic data for ionic species are usually tabulated for the molality-
scale standard state, we shall use the molality-scale equilibrium constant K° of
m
Eq. (11.7) for electrolytes.
Many ionic reactions in solution are acid–base reactions. We adopt the Brønsted
definition of an acid as a proton donor and a base as a proton acceptor.
The water molecule is amphoteric, meaning that water can act as either an acid or
a base. In pure liquid water and in aqueous solutions, the following ionization reaction
occurs to a slight extent:

H O H O ∆ H O OH (11.10)
2
2
3
For (11.10), the activity equilibrium constant (11.6) is

a1H O 2a1OH 2
3
K° (11.11)
w 2
3a1H O24
2
where the subscript w (for water) is traditional. The standard state of the solvent H O
2
is pure H O, so a(H O) 1 for pure H O [Eq. (11.1)]. In aqueous solutions, a(H O)
2
2
2
2
g (H O)x(H O). For dilute aqueous solutions, the mole fraction x(H O) is close to
2
2
2
x
1, and (since H O is uncharged) g (H O) is close to 1. Therefore, we usually approx-
2
2
x
imate a(H O) as 1 in dilute aqueous solutions. Use of a(H O) 1, and a g m /m°
i
i
2
i
2
[Eq. (10.32)] for each ion gives

K° a1H O 2a1OH 2 3g1H O 2m1H O 2>m°43g1OH 2m1OH 2>m°4
w
3
3
3
where m° 1 mol/kg and where the subscript m was omitted from g. All unsub-
scripted activity coefficients in this section are on the molality scale. This expression