A chemist plans to mix 100 mL of 0.050 M Pb(NO3)2 with a KCl(aq) solution so that PbCl2(s) begins to precipitate exactly at the moment the two solutions are combined and thoroughly mixed. The KCl solution available has a concentration of 0.10 M. Take Ksp=1.7×10−5 for PbCl2. Assume volumes are additive and temperature remains constant.
(a) Write the expression for the solubility–product constant of PbCl2 and identify the ionic species involved.
(b) Derive an algebraic relationship that links the volume of 0.10 M KCl added (in mL) to the ionic concentrations present immediately after mixing.
(c) Determine the minimum volume (in mL) of the 0.10 M KCl solution that must be added to 100 mL of 0.050 M Pb(NO3)2 so that PbCl2(s) just begins to form.
(d) Explain how your answer would change, if at all, if the initial Pb(NO3)2 solution were 0.025 M instead of 0.050 M. Justify your reasoning with appropriate quantitative support.