Page 356 - Physical Chemistry

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Other types of aqueous ionic equilibria include reactions of cationic and anionic Section 11.4

2

acids and bases (for example, NH , C H O , CO ) with water (Prob. 11.13); solubil- Reaction Equilibria Involving
4
3
2
3
2
Pure Solids or Pure Liquids
ity equilibria (Sec. 11.4); association equilibria involving complex ions [the equilib-

rium constants for the reactions Ag NH ∆ Ag(NH ) and Ag(NH ) NH ∆
3
3
3
3

Ag(NH ) are called association or stability constants, and those for the reverse reac-
3 2
tions are called dissociation constants]; association equilibria to form ion pairs (Sec.
10.8). See Fig. 11.4. Instead of listing the equilibrium constant K, tables often give pK,
where pK log K.
10
In first-year-chemistry equilibrium calculations, molar concentrations (and not
molalities) are used. It turns out (Prob. 11.21) that, in dilute aqueous solutions, the
molality-scale and the concentration-scale equilibrium constants are nearly equal nu-
merically, and the equilibrium molar concentrations and molalities are nearly equal
numerically. It therefore makes little difference whether the molar-concentration scale
or the molality scale is used for dilute aqueous solutions.
11.4 REACTION EQUILIBRIA INVOLVING PURE SOLIDS
OR PURE LIQUIDS
So far in this chapter, we have considered only reactions that occur in a single phase.
However, many reactions involve one or more pure solids or pure liquids. An exam-
ple is CaCO (s) ∆ CaO(s) CO (g). The equilibrium condition n m i,eq 0 applies
i
3
i
2
whether or not all species are in the same phase. To apply the equilibrium relation
n
K° ß (a ) i , we want an expression for the activity of a pure solid or liquid. The
i,eq
i
activity a satisfies m m° RT ln a [Eq. (11.2)], so Figure 11.4
i
i
i
i
RT ln a m m° pure sol. or liq. (11.20) Equilibrium constants for
i
i
i
As in Sec. 5.1, we choose the standard state of a pure solid or liquid to be the state association of ions to form ion
with P 1 bar P° and T equal to the temperature of the reaction mixture. Therefore pairs in water at 25°C and 1 atm.
The scale is logarithmic.
m° is a function of T only. To find ln a in (11.20), we need m m°. For a pure sub-
i
i
i
i
stance, m m° m*(T, P) m*(T, P°), since the standard state is at the same
i
i
i
i
temperature as the system. The pressure dependence of m for a pure substance is found
from dm dG S dT V dP as dm V m,i dP at constant T. Integration from
m
i
m
m
the standard pressure P° to an arbitrary pressure P gives
m 1T, P2 m°1T2 P V dP¿ const. T, pure sol. or liq. (11.21)
m,i
i
i
P°
where the prime was added to the dummy integration variable to avoid the use of P with
two different meanings in the same equation. Substitution of (11.21) into (11.20) gives
1 P
ln a V dP¿ pure sol. or liq., T const. (11.22)
i
m,i
RT
P°
where V m,i is the molar volume of pure i. Since solids and liquids are rather incom-
pressible, it is a good approximation to take V m,i as independent of P and remove it
from the integral to give
ln a 1P P°2V >RT pure sol. or liq. (11.23)
i
m,i
At the standard pressure of 1 bar, the activity of a pure solid or liquid is 1 (since
the substance is in its standard state). G is relatively insensitive to pressure for con-
densed phases (Sec. 4.4). Hence we expect a to be rather insensitive to pressure for
i
solids and liquids. For example, a solid with molecular weight 200 and density 2.00
3
3
g/cm has V 100 cm /mol. From (11.23), we find at P 20 bar and T 300 K
m,i
that a 1.08, which is pretty close to 1. Provided P remains below, say, 20 bar,
i