 # Solubility Products Consider the equilibrium that exists in a saturated solution of BaSO 4 in water: BaSO 4 (s) Ba 2+ (aq) + SO 4 2− (aq)

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Solubility Products Consider the equilibrium that exists in a saturated solution of BaSO 4 in water: BaSO 4 (s) Ba 2+ (aq) + SO 4 2− (aq)

Solubility Products The equilibrium constant expression for this equilibrium is K sp = [Ba 2+ ] [SO 4 2− ] where the equilibrium constant, K sp, is called the solubility product.

Solubility Products  K sp is not the same as solubility.  Solubility is generally expressed as the mass of solute dissolved in 1 L (g/L) or 100 mL (g/mL) of solution, or in mol/L (M).

Factors Affecting Solubility  The Common-Ion Effect  If one of the ions in a solution equilibrium is already dissolved in the solution, the equilibrium will shift to the left and the solubility of the salt will decrease. BaSO 4 (s) Ba 2+ (aq) + SO 4 2− (aq)

Practice Calculate the molar solubility of CaF 2 at 25 o C in a solution that is a) 0.010 M Ca(NO 3 ) 2, b) 0.010 M NaF K sp = 3.9x 10 -11 (from Appendix D)

PRACTICE EXERCISE The value for K sp for manganese(II) hydroxide, Mn(OH) 2, is 1.6  10 –13. Calculate the molar solubility of Mn(OH) 2 in a solution that contains 0.020 M NaOH. Answer: 4.0  10 –10 M

Factors Affecting Solubility  pH  If a substance has a basic anion (CO 3 2- ), PO 4 3-, CN -, S 2- ), it will be more soluble in an acidic solution.  Substances with acidic cations (like metal hydroxides) are more soluble in basic solutions.

Mg(OH) 2(s) Mg 2+ (aq) + 2OH - (aq) K sp = 1.8 x 10 -11 ; sat soltn; pH 10.52; [Mg 2+ ] = 1.7 x 10 -4 M Suppose solid Mg(OH) 2 is equilibriated with a solution buffered at pH 9.0 The pOH is 5.0,so [OH-] = 1.0 x 10 -5 Factors Affecting Solubility

Mg(OH) 2(s) Mg 2+ (aq) + 2OH - (aq) [OH-] = 1.0 x 10 -5 Insert [OH-] into the solubility product Ksp = [Mg 2+ ][OH-] 2 = 1.8 x 10 -11 = [Mg 2+ ](1.0 x 10 -5 ) 2 = 1.8 x 10 -11 [Mg 2+ ] = 0.18 M Mg(OH) 2 will dissolve until [Mg 2+ ] = 0.18M Factors Affecting Solubility

 The solubility of almost any ionic compound is affected by a sufficiently acidic or basic solution  The affects are very noticeable when one or both of the ions are at least moderately acidic or basic  Metal hydroxides, like Mg(OH) 2, are prime examples

Factors Affecting Solubility  Other salts with basic anions, such as CO 3 2-, PO 4 3-, CN -, and S 2- behave similarly  The solubulity of slightly soluble salts containing basic ions increases as [H + ] increases and pH is lowered.  Salts with anions negligible basicity (anions of strong acids) are unaffected by pH

SAMPLE EXERCISE Predicting the Effect of Acid on Solubility Which of the following substances will be more soluble in acidic solution than in basic solution: (a) Ni(OH) 2 (s), (b) CaCO 3 (s), (c) BaF 2 (s), (d) AgCl(s)?

SAMPLE EXERCISE Predicting the Effect of Acid on Solubility Solve: (a) Ni(OH) 2 (s) will be more soluble in acidic solution because of the basicity of OH – ; the H + ion reacts with the OH – ion, forming water.

SAMPLE EXERCISE Predicting the Effect of Acid on Solubility (b) Similarly, CaCO 3 (s) dissolves in acid solutions because CO 3 2– is a basic anion. The reaction between CO 3 2– and H + occurs in a stepwise fashion, first forming HCO 3 –. H 2 CO 3 forms in appreciable amounts only when the concentration of H + is sufficiently high.

(d) The solubility of AgCl is unaffected by changes in pH because Cl – is the anion of a strong acid and therefore has negligible basicity. SAMPLE EXERCISE continued (c) The solubility of BaF 2 is also enhanced by lowering the pH, because F – is a basic anion.

Factors Affecting Solubility Complex Ions  Metal ions can act as Lewis acids (e- pair acceptors) and form complex ions with Lewis bases (e- pair donors) in the solvent.

Factors Affecting Solubility  Lewis bases, other than water, can also interact with metal ions, particularly transition metals.  The formation of complex ions can affect the solubility of a metal salt

Factors Affecting Solubility AgCl K sp = 1.8 x 10 -10 will dissolve in NH 3, a Lewis base

Factors Affecting Solubility AgCl (s) Ag + (aq) + Cl- (aq) Ag + (aq) + 2NH 3(aq) Ag(NH 3 ) 2 + (aq) AgCl (s) + 2NH 3(aq) Ag(NH 3 ) 2 + (aq) + Cl- (aq) NH 3 causes AgCl(s) to dissolve, moving the rxn to the right

Factors Affecting Solubility  For a Lewis base, like NH 3, to increase solubility of a metal salt, it must interact greater with the metal ion than water does  Assembly of a metal-ion & Lewis base is called a complex ion

Factors Affecting Solubility  The stability of a complex ion in an aqueous solution is determined by the size of the equilibrium constant for its formation from the hydrated metal ion K f = [Ag(NH 3 ) 2 + ] [Ag + ][NH 3 ] 2 = 1.7 x 10 7

Factors Affecting Solubility  Amphoterism  Amphoteric metal oxides and hydroxides are soluble in strong acid or base, because they can act either as acids or bases.  Examples of such cations are Al 3+, Zn 2+, and Sn 2+.

Will a Precipitate Form?  In a solution,  If Q = K sp the system is at equilibrium and the solution is saturated.  If Q < K sp more solid will dissolve until Q = K sp  If Q > K sp the salt will precipitate until Q = K sp

SAMPLE EXERCISE 17.15 Predicting whether a Precipitate will Form Will a precipitate form when 0.10 L of 8.0 x 10 -3 M Pb(NO 3 ) 2 is added to 0.40 L of 5.0 x 10 -3 M Na 2 SO 4 ? The K sp for PbSO 4 = 6.3 x 10 -7 Q = 6.4 x 10 -6 ; it will precipitate

PRACTICE EXERCISE Will a precipitate form when 0.050 L of 2.0 x10 -2 M NaF is mixed with 0.010 L of 1.0 x 10 -2 M Ca(NO 3 ) 2 ? The K sp of CaF 2 is 3.9 x 10 -11 Q = 4.6 x 10 -7 it will precipitate

Selective Precipitation of Ions One can use differences in solubilities of salts to separate ions in a mixture.

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