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Concept 08 / 08Equilibrium
Solubility Product, Common Ion Effect and Precipitation
Solubility equilibria of sparingly soluble salts, the solubility product Ksp and its relation to molar solubility for different stoichiometries, comparing solubilities, the common ion effect, the ionic product condition for precipitation, and selective precipitation in qualitative analysis.
Figure 1
Solubility equilibrium. A saturated solution of a sparingly soluble ionic salt is in equilibrium with the undissolved solid:
AxBy(s)⇌xAy+(aq)+yBx−(aq).
Since the solid is omitted, the equilibrium constant is the solubility product
Ksp=[Ay+]x[Bx−]y,
which depends only on temperature.
Relation to molar solubility s (in molL−1, in pure water):
AB (AgCl, BaSO4): Ksp=s2.
AB2 or A2B (CaF2, Ag2CrO4): Ksp=4s3.
AB3 (Fe(OH)3): Ksp=27s4.
A3B2 (Ca3(PO4)2): Ksp=108s5.
In general, Ksp=xxyysx+y.
Solubilities can be compared directly from Ksp only for salts of the same type.
Common ion effect. Solubility decreases in a solution that already contains one of the ions. For AgCl in cM NaCl: s(s+c)=Ksp, so s≈cKsp when c≫s (see figure). This is why excess precipitating reagent is used in gravimetric analysis and why NaCl is purified by passing HCl gas into its saturated solution. (Very high concentrations can raise solubility again through complex formation, such as AgCl2−.)
Precipitation condition. Compare the ionic product Qsp (same expression as Ksp with actual concentrations after mixing) with Ksp:
Qsp>Ksp: supersaturated, precipitation occurs.
Qsp=Ksp: saturated.
Qsp<Ksp: unsaturated, no precipitate; more solid can dissolve.
Remember that mixing dilutes each solution.
Selective precipitation. In qualitative analysis, group II sulfides (CuS, PbS, CdS; tiny Ksp) are precipitated with H2S in acidic medium, where H+ suppresses [S2−] (common ion effect), so only they exceed their Ksp. Group IV sulfides (ZnS, NiS, CoS, MnS; larger Ksp) need the higher [S2−] of ammoniacal medium. Similarly, group III hydroxides (Fe(OH)3, Al(OH)3) are precipitated by NH4OH in the presence of NH4Cl, which lowers [OH−] enough to keep Mg(OH)2 and group IV hydroxides in solution.
Key Takeaways:
- Ksp=xxyysx+y; s2, 4s3, 27s4, 108s5.
- Common ion: s≈cKsp for a 1:1 salt.
- Precipitation when Qsp>Ksp.
- Compare solubilities through s, not Ksp, for salts of different types.
- Pitfall: after mixing equal volumes, each concentration halves.
Brain-Teaser 1: Ksp of AgCl is 1.8×10−10 and of Ag2CrO4 is 1.1×10−12. Which is more soluble in water?
Solution: AgCl: s=1.8×10−10=1.34×10−5M. Ag2CrO4: s=(41.1×10−12)1/3=6.5×10−5M. Silver chromate is about five times more soluble, despite its smaller Ksp. (This is why, in Mohr's titration, AgCl precipitates before red Ag2CrO4 appears at the end point.)
Brain-Teaser 2: Equal volumes of 2×10−4MAgNO3 and 2×10−4M NaCl are mixed. Will AgCl precipitate?
Solution: After mixing, [Ag+]=[Cl−]=10−4M. Qsp=10−8>1.8×10−10, so a precipitate forms.
Brain-Teaser 3: The solubility of Mg(OH)2 in water is 1.4×10−4M. Find its Ksp and its solubility in a solution of pH 12.
Solution: Ksp=4s3=4×(1.4×10−4)3=1.1×10−11. At pH 12, [OH−]=10−2, so s=[OH−]2Ksp=10−41.1×10−11=1.1×10−7M, over a thousand times less.
