Chapter 9 Chemical Equilibrium 9.6 Equilibrium in Saturated Solutions

Saturated Solution A saturated solution contains the maximum amount of dissolved solute contains solid solute is an equilibrium system: rate of dissolving = rate of recrystallization solid ions in solution

Solubility Product Constant The solubility product constant for a saturated solution gives the ion concentrations at constant temperature is expressed as Ksp does not include the solid, which is constant Fe(OH)2(s) Fe2+(aq) + 2OH−(aq) Ksp = [Fe2+] [OH−]2

Learning Check Write the Ksp expression for each of the following: A. FeS(s) B. Ag2CO3(s) C. Ca(IO3)2(s)

Solution Write the Ksp expression for each of the following: A. FeS(s) Fe2+(aq) + S2−(aq) Ksp = [Fe2+][S2−] B. Ag2CO3(s) 2Ag+(aq) + CO32− (aq) Ksp = [Ag+]2 [CO32−] C. Ca(IO3)2(s) Ca2+(aq) + 2IO3−(aq) Ksp = [Ca2+][IO3−]2

Guide to Calculating Ksp

Example of Calculating Solubility Product Constant Calculate the Ksp of PbSO4 (solubility 1.4 x 10–4 M). STEP 1 Write the equilibrium equation for dissociation: PbSO4(s) Pb2+(aq) + SO42−(aq) STEP 2 Write the Ksp expression: Ksp = [Pb2+][SO42−] STEP 3 Substitue molarity values and calculate: Ksp = (1.4 x 10–4) x (1.4 x 10–4) = 2.0 x 10–8

Examples of Solubility Product Constants

Learning Check What is the Ksp value of PbF2 if the solubility at 25 C is 2.6 x 10–3 M? 1) 1.4 x 10–5 2) 6.8 x 10–6 3) 7.0 x 10–8

Solution 3) 7.0 x 10-8 STEP 1 Write the equilibrium equation for dissociation: PbF2(s) Pb2+(aq) + 2F−(aq) STEP 2 Write the Ksp expression: Ksp = [Pb2+][F−]2 STEP 3 Substitute molarity values and calculate: [Pb2+] = 2.6 x 10–3 M [F−] = 2 x [Pb2+] = 5.2 x 10–3 M Ksp = (2.6 x 10–3) x (5.2 x 10–3)2 = 7.0 x 10–8

Molar Solubility (S) The molar solubility (S) is the number of moles of solute that dissolve in 1 L of solution determined from the formula of the salt calculated from the Ksp

Calculating Molar Solubility (S)

Solubility Calculation Determine the solubility (S)2 of SrCO3 (Ksp = 5.4 x 10–10). STEP 1 Write the equilibrium equation for dissociation: SrCO3(s) Sr2+(aq) + CO32−(aq) STEP 2 Write the Ksp expression: Ksp = [Sr2+][CO32−] STEP 3 Substitute S for the molarity of each ion into Ksp: Ksp = [Sr2+][CO32−] = [S][S] = S2 = 5.4 x 10−10 STEP 4 Calculate the solubility, S: S = = 2.3 x 10−5 M

Learning Check Calculate the solubility (S) of PbSO4 , if the Ksp = 1.6 x 10–8. 1) 1.3 x 10–4 M 2) 4.0 x 10–4 M 3) 2.6 x 10–16 M

Solution 1) 1.3 x 10–4 M STEP 1 Write the equilibrium equation for dissociation: PbSO4(s) Pb2+(aq) + SO42−(aq) STEP 2 Write the Ksp expression: Ksp = [Pb2+][SO42−] STEP 3 Substitute S for the molarity of each ion into Ksp: Ksp = [Pb2+][SO42−] = [S][S] = S2 = 1.6 x 10–8 STEP 4 Calculate the solubility, S: S = = 1.3 x 10–4 M