SOLUBILITY AND PRECIPITATION EQUILIBRIA

16 CHAPTER SOLUBILITY AND PRECIPITATION EQUILIBRIA 16.1 The Nature of Solubility Equilibria 16.2 Ionic Equilibria between Solids and Solutions 16.3 Precipitation and the Solubility Product 16.4 The Effects of ph on Solubility 16.5 Complex Ions and Solubility 16.6 Selective Precipitation of Ions 733

734 16.1 THE NATURE OF SOLUBILITY EQUILIBRIA General Features of Solubility Equilibria Saturation ~ Dissolution-precipitation equilibrium Recrystallization ~ Purification of solids Solvent of crystallization 2 Li + (aq) + SO 4 2- (aq) + H 2 O(l) Li 2 SO 4 H 2 O(s) ~ different chemical formula & mass Supersaturation ~ Slow equilibrium Fig. 16.1 Deposit of K 2 PtCl 4 from the saturated aqueous solution as the water evaporates. The solubility of Ionic Solids 735 Solubility at 25C, AgClO 4 ; 5570 g/l, AgCl; 0.0018 g/l Temperature dependence - Mostly endothermic Solubility increases with T -CaSO 4 exothermic Solubility decreases with T Classification (at 25 C) Soluble > 10 g/l, Slightly soluble 0.1~10 g/l, Insoluble < 0.1 g/l General Fig. 16.3 Chemistry Temperature II dependence of solubility.

737 737 16.2 IONIC EQUILIBRIA BETWEEN SOLIDS AND SOLUTIONS Highly soluble salt: Nonideal solution, CsCl(s) Cs + (aq) + Cl - (aq) Fig. 16.5 The dissolution of the ionic solid CsCl in water

738 Solubility and K sp AgCl(s) Ag + (aq) + Cl - (aq) Solubility product: K sp = [Ag + ][Cl - ]=1.610-10 at 25 C Solubility (S) of AgCl at 25C calculated from K sp K sp = [Ag + ][Cl - ] = S 2 = 1.610-10 S = 1.2610-5 M Gram solubility = (1.2610-5 mol/l) (143.3 g/mol) = 1.810-3 g/l 738

739 EXAMPLE 16.1 Calculation of [Ca 2+ ] and [F - ] in a saturated solution of CaF 2 at 25C: K sp Solubility CaF 2 (s) Ca 2+ (aq) + 2 F - (aq) K sp = [Ca 2+ ][F - ] 2 =3.910-11 at 25C [Ca 2+ ] = S, [F - ]=2S K sp = [Ca 2+ ][F - ] 2 = S (2S) 2 = 4S 3 S = 2.1 10-4 M Gram solubility = (2.110-4 mol/l) (78.1 g/mol) = 0.017 g/l 740 EXAMPLE 16.2 Solubility (0.029 g/l) K sp Ag 2 CrO 4 (s) 2 Ag + (aq) + CrO 4 2- (aq) K sp = [Ag + ] 2 [CrO 4 2- ] = 2.7 10-12 Gram solubility: 0.029 g/l Molar solubility: 0.029 g/l = 8.74 10-5 mol/l = S [Ag + ]= 2S, [CrO 4 2- ]=S K sp = [Ag + ] 2 [CrO 4 2- ]=4S 3 = 2.7 10-12 42 % greater than the tabulated value, 1.9 10-12

16.3 PRECIPITATION AND THE SOLUBILITY PRODUCT Precipitation from Solution 740 K sp = [Ag + ][Cl - ] Q 0 = [Ag + ] 0 [Cl - ] 0 ~ initial reaction quotient Q 0 >K sp Q 0 <K sp precipitation dissolution Fig. 16.6 A plot of precipitation and dissolution equilibrium for AgCl in water. The slope of the path toward equilibrium represented by red or blue arrow is 1. 742 EXAMPLE 16.4 [Ag + ] 0 = 0.0015 M, [Cl - ] 0 = 5.010-6 M Equilibrium concentrations? Cl - is the limiting reactant complete precipitation first Remaining [Ag + ] = 0.0015-5.0 10-6 0.0015 M AgCl(s) Ag + (aq) + Cl - (aq) ---------------------------------------------------------------------- Initial 0.0015 0 Change + y + y --------------- ------ Equilibrium 0.0015 + y y ---------------------------------------------------------------------- K sp = 1.60 10-10 = (0.0015 + y) y 0.0015 y y= [Cl - ]= 1.1 10-7 M, [Ag + ] = 0.0015 M

742 The Common-Ion Effect ~ Solubility decreases in the presence of a common ion AgCl NaCl or AgNO 3 EX. Solubility of AgCl(s) in 1.00 L of 0.100 M NaCl solution [Ag + ] NaCl = S, [Cl - ] NaCl = 0.100 + S K sp = 1.60 10-10 = [Ag + ] NaCl [Cl - ] NaCl = S (0.100 + S) 0.100 S (S < S water =1.3 10-5 << 0.100) 742 [Ag + ] NaCl = S = 1.60 10-9 M [Cl - ] NaCl = 0.100 M [Ag ] 1.3 10 [Ag ] 1.6 10 5 HO 2 3 8.110 9 0.1M NaCl 5 [Ag ] HO1.310 M 2 Fig. 16.7 Common-ion effect for the solubility of AgCl in AgNO 3 solution and in NaCl solution.

16.4 THE EFFECTS OF ph ON SOLUBILITY 744 CaCO 3 (s) + H 3 O + (aq) Ca 2+ (aq) + HCO 3- (aq) + H 2 O(l) Fig. 16.8 Damage due to increased acidity from air pollution. On the east pier of Stanford White's Washington Square Arch is Herma A. MacNeil's Washington in War (1916) (Washington Square Park in the Greenwich Village neighborhood of Lower Manhattan in New York City) Solubility of Hydroxides 744 Zn(OH) 2 (s) Zn 2+ (aq) + 2 OH - (aq) K sp = [Zn 2+ ][OH - ] 2 = 4.5 10-17 In acidic solution, [OH - ] decreases. reaction goes to the right EXAMPLE 16.6 Comparison of solubilities of Zn(OH) 2 (s) in pure water and in a buffer with ph 6.00. In pure water, [Zn 2+ ] = S, [OH - ] = 2S K sp = S(2S) 2 S = [Zn 2+ ] = 2.2 10-6 M, [OH - ] = 2S = 4.5 10-6 M, ph = 8.65 In a ph = 6.00 buffer, [OH - ] = 1.0 10-8 M (fixed). [Zn 2+ ] = K sp / [OH - ] 2 = 0.45 M Metal hydroxides are basic more soluble in acidic solution

746 Solubility of Salts of Bases CaF 2 (s) Ca 2+ (aq) + 2 F - (aq), K sp = 3.9 10-11 - Solubility of CaF 2 (s) at low ph : F - (aq) + H 3 O + (aq) HF(aq) + H 2 O(l), K = 2.9 10 3 more soluble in acidic solution (large K) [H 3 O + ] [F - ] more CaF 2 (s) dissolves (Le Chatelier) - Solubility of AgCl(s) at low ph : AgCl(s) Ag + (aq) + Cl - (aq) - Even in acidic solution, Cl - (aq) + H 3 O + (aq) HCl(aq) + H 2 O(l) negligible effect of ph on the solubility of AgCl 16.5 COMPLEX IONS AND SOLUBILITY 746 Complex-Ion Equilibria Ag + (aq) + NH 3 (aq) Ag(NH 3 ) + (aq) K 1 = [Ag(NH 3 ) + ] / ([Ag + ][NH 3 ]) = 2.1 10 3 Ag(NH 3 ) + (aq) + NH 3 (aq) Ag(NH 3 ) 2+ (aq) K 2 = [Ag(NH 3 ) 2+ ] / ([Ag(NH 3 ) + ][NH 3 ]) = 8.2 10 3 Ag + (aq) + 2 NH 3 (aq) Ag(NH 3 ) 2+ (aq) K f = K 1 K 2 = [Ag(NH 3 ) 2+ ] / ([Ag + ][NH 3 ] 2 ) = 1.7 10 7 K f : Formation constant

747 747 EXAMPLE 16.7 0.100 mol of AgNO 3 dissolved in 1.00 L of 1.00 M NH 3 [Ag + ] and [Ag(NH 3 ) + ] at equilibrium? Assume that Ag + is present as Ag(NH 3 ) 2+. [Ag(NH 3 ) 2+ ] 0 = 0.100 M; [NH 3 ] 0 = 1.00 M (2 0.100) M = 0.80 M Ag(NH 3 ) 2+ (aq) Ag(NH 3 ) + (aq) + NH 3 (aq), K 2 = K 1 2 Ag(NH 3 ) + (aq) Ag + (aq) + NH 3 (aq), K 1 = K 1 1

747 Ag(NH 3 ) 2+ (aq) Ag(NH 3 ) + (aq) + NH 3 (aq) ------------------------------------------------------------------------------------------ Initial 0.100 0 0.80 Change y + y + y -------------- ------ ----------- Equilibrium 0.100 y y 0.80 + y ------------------------------------------------------------------------------------------ K K + 1 [Ag NH 3 ][NH 3] y 0.80 + y 1 2 = = = = + 3 K2 [AgNH ] 0.10 y 8.210 3 2 + + 1 [Ag ][NH 3] 1 1 = = = = + 5 3 K1 [AgNH ] 1.510 2.110 3 [Ag ] 0.80 y = [Ag(NH 3 ) + ] =1.5 10 5 M [Ag + ] = 9 10 9 M << [Ag(NH 3 ) 2+ ] 0.100 M Formation of coordination of complexes increases solubilities AgBr(s) Ag + (aq) + Br (aq) 749 K sp = 7.7 10 13 AgBr(s) + 2 S 2 O 3 2 (aq) Ag(S 2 O 3 ) 2 3 (aq) + Br (aq) thiosulfate ion, S 2 O 3 2 sulfate ion, SO 4 2 Fig. 16.12 Effect of complex ion formation on solubility. AgBr in thiosulfate solution and in pure water.

749 EXAMPLE 16.8 Solubility of AgBr in 1.00 M aqueous solution of NH 3? AgBr(s) + 2 NH 3 (aq) Ag(NH 3 ) 2+ (aq) + Br (aq), K AgBr(s) Ag + (aq) + Br (aq), K sp = 7.7 10 13 Ag + (aq) + 2 NH 3 (aq) Ag(NH 3 ) 2+ (aq), K f = 1.7 10 7 K = K sp K f = 1.3 10 5 Solubility of AgBr: S S = [Br ] [Ag(NH 3 ) 2+ ] [NH 3 ] = 1.00 2S + 2 [Ag(NH 3) 2][Br ] S K = 1.310 2 2 [NH ] 1.00-2S 3 S = 3.6 10 3 = [Br ] [Ag(NH 3 ) 2+ ] [Ag + ] = K sp / [Br ] = K sp / S = 2.1 10 10 << [Ag(NH 3 ) 2+ ] 5 749 Re-dissolving by forming complex ions The opposite of common ion effects Hg 2+ (aq) + 2I (aq) HgI 2 (s) HgI 2 (s) + I (aq) HgI 3 (aq) HgI 3 (aq) + I (aq) HgI 2 4 (aq) Fig. 16.13 "Orange Tornado"

Separation of cations In a strongly basic solution of Mg 2+ and Zn 2+ Mg(OH) 2 (s) Zn(OH) 2 4 (aq) 750 In a strongly basic solution of Al 3+ and Fe 3+ Fe(OH) 3 (s) Al(OH) 4 2 (aq) Fig.16.14 AlCl 3 (s) + H 2 O(l) Fig. 16.15 Solubility of Zn(OH) 2 General Chemistry Al(OH) 4 (aq) II + HCl(aq) in acid, water, base. Selective Precipitation of Ions 751 Example: Separating Ag + (0.1 M) from Pb 2+ (0.1 M) Search for a common anion having widely different solubilities AgCl(s) Ag + (aq) + Cl - (aq), K sp = 1.6 10-10 PbCl 2 (s) Pb 2+ (aq) + 2 Cl - (aq), K sp = 2.4 10-4 Goal: ~ Precipitate almost all Ag + leaving all Pb 2+ in solution by adding Cl - Q 0 (PbCl 2 ) = [Pb 2+ ] 0 [Cl - ] 02 < K sp (PbCl 2 ) Pb 2+ remains in solution Q 0 (AgCl) = [Ag + ] 0 [Cl - ] 0 > K sp (AgCl) AgCl precipitates [Cl - ] 2 < K sp (PbCl 2 )/ [Pb 2+ ] = 2.4 10-4 / 0.10 = 2.4 10-3 [Cl - ] max = 4.9 10-2 M [Ag + ] < K sp (AgCl)/ [Cl - ] = 1.6 10-10 / 0.049 = 3.3 10-9 << 0.1 M

Graphic method 752 Q = K sp for PbCl 2 [Pb 2+ ] = K sp /[Cl ] 2 log [Pb 2+ ] = 2 log [Cl ] + log K sp y = 2x + b (cf. Equil. curve for PbCl 2 ) PbCl 2 (s) dissolves below the blue line. Q = K sp for AgCl [Ag + ] = K sp /[Cl ] log [Ag + ] = log [Cl ] + log K sp y = x + b (cf. Equil. curve for AgCl) AgCl(s) dissolves below the red line. Fig. 16.16 Separation of a mixture of Ag + and Pb 2+ ions by selecting a [Cl ] Metal Sulfides 753 EXAMPLE 16.10 Solubility of FeS(s) in a ph 3.0 buffer saturated with H 2 S, [H 2 S] = 0.1 M. K a = 9.1 10-8, K sp =510-19 [H 3 O + ] = 1 10-3 M, [OH - ] = 1 10-11 M (fixed) Ionization of H 2 S: H 2 S(aq) + H 2 O(l) H 3 O + (aq) + HS - (aq) K a = [H 3 O + ][HS - ] /[H 2 S] = (1 10-3 )[HS - ] /(0.1) = 9.1 10-8 [HS - ] = 9 10-6 M FeS(s) + H 2 O(l) Fe 2+ (aq) + HS - (aq) + OH - (aq) K =[Fe 2+ ][HS - ][OH - ] = 5 10-19 [Fe 2+ ] = K / ([OH - ][HS - ]) = (5 10-19 )/[(1 10-11 )(9 10-6 )] = 6 10-3 M

754 PbS, Bi 2 S 3, CuS, CdS, Sb 2 S 3, SnS 2, As 2 S 3, HgS Fig. 16.17 Insoluble sulfides at ph 1. 12.14 Qualitative Analysis A507 HCl(aq) H 2 S(g) NH 3 (aq)

In the mixture of Hg 2 Cl 2, PbCl 2, and AgCl, A507 A508 AgCl AgCl Hg 2 Cl Hg 2 Cl 2 2 + NH 3 + NH 3 Hg(0)

10 Problem Sets For Chapter 16, 14, 22, 30, 34, 44, 48, 66, 74, 76, 82