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Chapter 18: Problem 41

\(\mathrm{KI}(\mathrm{aq})\) is slowly added to a solution with \(\left[\mathrm{Pb}^{2+}\right]=\) \(\left[\mathrm{Ag}^{+}\right]=0.10 \mathrm{M} .\) For \(\mathrm{PbI}_{2}, K_{\mathrm{sp}}=7.1 \times 10^{-9} ;\) for \(\mathrm{AgI},\) \(K_{\mathrm{sp}}=8.5 \times 10^{-17}\). (a) Which precipitate should form first, \(\mathrm{PbI}_{2}\) or AgI? (b) What \(\left[\mathrm{I}^{-}\right]\) is required for the second cation to begin to precipitate? (c) What concentration of the first cation to precipitate remains in solution at the point at which the second cation begins to precipitate? (d) \(\operatorname{Can} \mathrm{Pb}^{2+}(\mathrm{aq})\) and \(\mathrm{Ag}^{+}(\) aq) be effectively separated by fractional precipitation of their iodides?

Short Answer

Expert verified
The precipitate that forms first is PbI2 as it requires a lower iodide concentration to precipitate out than AgI. The calculated iodide concentration for the second precipitate to begin to form and the concentration of the first cation at the point when the second begins to precipitate can be found by using the \(K_{sp}\) equations and the ion concentrations. The effectiveness of the fractional precipitation depends on the significant difference in the solubilities of \(Pb^{2+}\) and \(Ag^+\) under the condition.

Step by step solution

01

Determine which precipitate forms first

Use the solubility product (\(K_{sp}\)) expressions for both salts, i.e., \(AgI \rightarrow Ag^+ + I^-\) and \(PbI2 \rightarrow Pb^{2+} + 2I^-\). Plug both ion concentrations into their respective \(K_{sp}\) expression: \(K_{sp}(AgI) = [Ag^+][I^-]\) and \(K_{sp}(PbI2) = [Pb^{2+}][I^-]^{2}\). Calculate the iodide concentration necessary for each salt to precipitate out of solution by using the given \(K_{sp}\) values. The substance needing the lower iodide concentration to precipitate out will be the one that forms first.
02

Calculate the iodide concentration for the second precipitate

Using the \(K_{sp}\) expression for the precipitate that does not form first, calculate what the iodide concentration must be for the second precipitate to form. This can be done by setting up the \(K_{sp}\) equation and solving for the iodide ion concentration.
03

Determine the concentration of the first cation when the second begins to precipitate

When the second cation begins to precipitate, the concentration of the first cation will be what's left in the solution. This can be determined by using the \(K_{sp}\) equation for the first precipitate, inserting the calculated iodide concentration from Step 2, and solving for the first cation concentration.
04

Evaluate the effectiveness of fractional precipitation

Fractional precipitation of iodides will be effective in separating \(Pb^{2+}\) and \(Ag^+\) if there is a significant difference in their solubilities under the condition. If the concentrations of the remaining cations in solution after precipitation of one of the cations are significantly different, the separation can be considered effective.

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Most popular questions from this chapter

The solubility of \(\mathrm{AgCN}(\mathrm{s})\) in \(0.200 \mathrm{M} \mathrm{NH}_{3}(\mathrm{aq})\) is \(8.8 \times 10^{-6} \mathrm{mol} / \mathrm{L} .\) Calculate \(K_{\mathrm{sp}}\) for \(\mathrm{AgCN}\).

For the equilibrium \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{OH}^{-}(\mathrm{aq})\) \(K_{\mathrm{sp}}=1.3 \times 10^{-33}\) (a) What is the minimum \(p H\) at which \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) will precipitate from a solution that is \(0.075 \mathrm{M}\) in \(\mathrm{Al}^{3+} ?\) (b) A solution has \(\left[\mathrm{Al}^{3+}\right]=0.075 \mathrm{M}\) and \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]=1.00 \mathrm{M} .\) What is the maximum quantity of \(\mathrm{NaCH}_{3} \mathrm{COO}\) that can be added to \(250.0 \mathrm{mL}\) of this solution before precipitation of \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) begins?

A solution is \(0.010 \mathrm{M}\) in both \(\mathrm{CrO}_{4}^{2-}\) and \(\mathrm{SO}_{4}^{2-}\). To this solution, \(0.50 \mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\text { aq })\) is slowly added. (a) Which anion will precipitate first from solution? (b) What is \(\left[\mathrm{Pb}^{2+}\right]\) at the point at which the second anion begins to precipitate? (c) Are the two anions effectively separated by this fractional precipitation?

A 2.50 g sample of \(\mathrm{Ag}_{2} \mathrm{SO}_{4}(\mathrm{s})\) is added to a beaker containing 0.150 L of 0.025 M BaCl\(_2\) (a) Write an equation for any reaction that occurs. (b) Describe the final contents of the beaker- -that is, the masses of any precipitates present and the concentrations of the ions in solution.

Briefly describe each of the following ideas, methods, or phenomena: (a) common-ion effect in solubility equilibrium; (b) fractional precipitation; (c) ion-pair formation; (d) qualitative cation analysis.
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