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Section 11.4
mol/kg. Note the 29% increase in solubility compared with that in pure water. Reaction Equilibria Involving
The added KNO reduces g and increases the solubility, a phenomenon called Pure Solids or Pure Liquids
3

the salt effect.
(c) In 0.100 mol/kg KCl, the ionic strength is 0.100 mol/kg and the Davies

equation gives g 0.78. The Cl from AgCl is negligible compared with that

from the KCl. Setting m(Cl ) 0.100 mol/kg, we have

2
2
2
1.78 10 10 mol >kg 10.782 m1Ag 210.100 mol>kg2

Therefore m(Ag ) 2.9 10 9 mol/kg. Note the sharp decrease in solubility
compared with either pure water or the KNO solution (common-ion effect).
3
Exercise
Find the solubility of AgCl in 0.0200 mol/kg Ag SO (aq) at 25°C. Neglect ion
2
4
pairing. (Answer: 6.77 10 9 mol/kg.)
In Example 11.4, we ignored the possibility of ion-pair formation and assumed

that all the silver chloride in solution existed as Ag and Cl ions. This is a good as-
sumption for dilute solutions of a 1:1 electrolyte. However, in working with K for
sp
other than 1:1 electrolytes, substantial error can frequently result if ion-pair formation
is not taken into account; see Prob. 11.28 and L. Meites, J. S. F. Pode, and H. C.
Thomas, J. Chem. Educ., 43, 667 (1966).
Although ion-pair formation can be neglected in Example 11.4, complex-ion

formation often cannot be neglected in AgCl solutions. The ions Ag and Cl react in

aqueous solution to form a series of four complex ions: Ag Cl ∆ AgCl(aq),

3
AgCl(aq) Cl ∆ AgCl , AgCl Cl ∆ AgCl 2 , AgCl 2 Cl ∆ AgCl .
4
2
3
2
3
Inclusion of complex-ion formation shows that, although the results for (a) and (b) in
the above example are correct, the result for (c) is in error.
Fora homogeneous reaction such as N (g) 3H (g) ∆ 2NH (g)or HCN(aq)
2
2
3

H O ∆ H O (aq) CN (aq), there will always be some of each species present at
3
2
equilibrium. In contrast, reactions involving pure solids have the possibility of going to
completion. For example, for CaCO (s) ∆ CaO(s) CO (g), K° P(CO )/P°
2
3
2
[Eq. (11.25)]. At 800°C, K° 0.24 for this reaction. If we place CaCO (s) into an evac-
3
uated container at 800°C, the CaCO will decompose until P(CO ) reaches 0.24 bar. If
2
3
the container volume is large enough, all the CaCO may decompose before this equi-
3
librium pressure can be attained. Similarly, if a crystal of AgCl is added to a large enough

2
volume of water, all the AgCl can dissolve without having g m(Ag )m(Cl ) reach K .
sp

EXAMPLE 11.5 Calculation of K sp

The G° values for Ag SO (s), Ag (aq), and SO 2 (aq) are 618.41, 77.11,
4
2
298
f
4
and 744.53 kJ/mol, respectively. Find K for Ag SO in water at 25°C.
4
sp
2

The reaction is Ag SO (s) ∆ 2Ag (aq) SO (aq). We calculate G°
2
298
4
4
2
28.10 kJ/mol. Use of G° RT ln K° gives
5
3
5
K° 1.2 10 and K 1.2 10 mol >kg 3
sp
sp
Exercise

G° values for K (aq), Cl (aq), and KCl(s) are 283.27, 131.228, and
298
f
409.14 kJ/mol, respectively. Find K for KCl in water at 25°C. (Answer: 8.68
sp
2
2
mol /kg .)