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Chapter 18: Problem 49

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?

Short Answer

Expert verified
The exact values will depend on the calculated results, but the solution should provide the minimum pH at which \(\mathrm{Al(OH)_{3}}\) precipitates and the maximum amount of sodium acetate that can be added before precipitation begins.

Step by step solution

01

Calculation of Concentration of OH- ions

For the reaction: \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\rightleftharpoons \mathrm{Al}^{3+}(\mathrm{aq})+3 \mathrm{OH}^{-}(\mathrm{aq})\), the dissociation can be written as: \(K_{\mathrm{sp}} = [\mathrm{Al^{3+}}][\mathrm{OH^-}]^{3}\). Given that the \(\mathrm{Al}^{3+}\) ion concentration is 0.075 M and that \(K_{\mathrm{sp}} = 1.3 \times 10^{-33}\), the hydroxide ion concentration can be determined by substituting these values into the equation to solve for \([\mathrm{OH^{-}}]\).
02

Calculation of pH

After getting the \(\mathrm{OH^{-}}\) concentration, convert this to \(\mathrm{pOH}\) using the formula: \(pOH = -log[\mathrm{OH^{-}}]\). After getting the \(\mathrm{pOH}\), you can find the pH by using the relationship: \(\mathrm{pH} = 14 - [\mathrm{pOH}]\). This will give the minimum pH at which \(\mathrm{Al(OH)_{3}}\) will precipitate from the solution.
03

Calculation of Maximum Quantity of Sodium Acetate (NaCH3COO)

First, calculate the concentration of \(\mathrm{OH^{-}}\) ions at equilibrium from Step 1. To find out the maximum quantity of sodium acetate (NaCH3COO) that can be added to the solution before precipitation of \(\mathrm{Al(OH)_{3}}\) begins, you need to find out the concentration of sodium acetate (which essentially provides \(\mathrm{OH^{-}}\) ions in the solution) that will initiate precipitation. Use M1V1 = M2V2 to calculate the new concentration of \(\mathrm{OH^{−}}\) due to NaCH3COO (where M1 and V1 are the initial molarity and volume, M2 is the final molarity, and V2 is the final volume). The number of moles of sodium acetate can then be calculated.
04

Conclusion of Results

Following these steps and using the appropriate equations will result in the solution of the two questions: the minimum pH at which \(\mathrm{Al(OH)_{3}}\) will precipitate and the maximum quantity of sodium acetate that can be added to the solution before precipitation of \(\mathrm{Al(OH)_{3}}\) begins.

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Most popular questions from this chapter

In an experiment to measure \(K_{\mathrm{sp}}\) of \(\mathrm{CaSO}_{4}\) [D. Masterman, J. Chem. Educ., 64, 409 (1987)], a saturated solution of \(\mathrm{CaSO}_{4}(\mathrm{aq})\) is poured into the ion-exchange column pictured (and described in Chapter 21 ). As the solution passes through the column, \(\mathrm{Ca}^{2+}\) is retained by the ion-exchange medium and \(\mathrm{H}_{3} \mathrm{O}^{+}\) is released; two \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions appear in the effluent solution for every \(\mathrm{Ca}^{2+}\) ion. As the drawing suggests, a \(25.00 \mathrm{mL}\) sample is added to the column, and the effluent is collected and diluted to \(100.0 \mathrm{mL}\) in a volumetric flask. A \(10.00 \mathrm{mL}\) portion of the diluted solution requires \(8.25 \mathrm{mL}\) of \(0.0105 \mathrm{M} \mathrm{NaOH}\) for its titration. Use these data to obtain a value of \(K_{\mathrm{sp}}\) for \(\mathrm{CaSO}_{4}\).

Which of the following saturated aqueous solutions would have the highest \(\left[\mathrm{Mg}^{2+}\right]\): (a) \(\mathrm{MgCO}_{3} ;\) (b) \(\mathrm{MgF}_{2};\) (c) \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2} ?\) Explain.

Both \(\mathrm{Mg}^{2+}\) and \(\mathrm{Cu}^{2+}\) are present in the same aqueous solution. Which of the following reagents would work best in separating these ions, precipitating one and leaving the other in solution: \(\mathrm{NaOH}(\mathrm{aq}), \mathrm{HCl}(\mathrm{aq})\), \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{aq}),\) or \(\mathrm{NH}_{3}(\mathrm{aq}) ?\) Explain your choice.

Will \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) precipitate from a buffer solution that is \(0.45 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) and \(0.35 \mathrm{M} \mathrm{NaCH}_{3} \mathrm{COO}\) and also \(0.275 \mathrm{M}\) in \(\mathrm{Al}^{3+}(\mathrm{aq}) ?\) For \(\mathrm{Al}(\mathrm{OH})_{3}, K_{\mathrm{sp}}=\) \(1.3 \times 10^{-33} ;\) for \(\mathrm{CH}_{3} \mathrm{COOH}, K_{\mathrm{a}}=1.8 \times 10^{-5}\).

Will precipitation of \(\mathrm{MgF}_{2}(\mathrm{s})\) occur if a \(22.5 \mathrm{mg}\) sample of \(\mathrm{MgCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) is added to \(325 \mathrm{mL}\) of \(0.035 \mathrm{M} \mathrm{KF}\) ?
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