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Chapter 17: Problem 106

The solubility product for \(\mathrm{Zn}(\mathrm{OH})_{2}\) is \(3.0 \times 10^{-16} .\) The formation constant for the hydroxo complex, \(\mathrm{Zn}(\mathrm{OH})_{4}^{2-},\) is \(4.6 \times 10^{17}\). What concentration of \(\mathrm{OH}^{-}\) is required to dissolve 0.015 mol of \(\mathrm{Zn}(\mathrm{OH})_{2}\) in a liter of solution?

Short Answer

Expert verified
The concentration of \(\mathrm{OH}^-\) required to dissolve 0.015 mol of \(\mathrm{Zn}(\mathrm{OH})_{2}\) in a liter of solution is approximately \(4.81 \times 10^{-3} \ \text{M}\).

Step by step solution

01

Write the solubility product expression for \(\mathrm{Zn}(\mathrm{OH})_{2}\)

The solubility product expression for \(\mathrm{Zn}(\mathrm{OH})_{2}\) is given by: \[K_{s} = [\mathrm{Zn^{2+}}][\mathrm{OH}^-]^2\] where \(K_s = 3.0 \times 10^{-16}\).
02

Write the formation constant expression for the hydroxo complex \(\mathrm{Zn}(\mathrm{OH})_{4}^{2-}\)

The formation constant expression for the hydroxo complex \(\mathrm{Zn}(\mathrm{OH})_{4}^{2-}\) is given by: \[K_f = \frac{[\mathrm{Zn}(\mathrm{OH})_{4}^{2-}]}{[\mathrm{Zn^{2+}}][\mathrm{OH}^-]^4}\] where \(K_f = 4.6 \times 10^{17}\).
03

Relate the solubility product and formation constant expressions

From the solubility product expression, we can write the concentration of \(\mathrm{Zn^{2+}}\) as: \[[\mathrm{Zn^{2+}}] = \frac{K_s}{[\mathrm{OH}^-]^2}\] Substitute this expression for the concentration of \(\mathrm{Zn^{2+}}\) into the formation constant expression and solve for the concentration of \(\mathrm{Zn}(\mathrm{OH})_{4}^{2-}\): \[[\mathrm{Zn}(\mathrm{OH})_{4}^{2-}] = K_f [\mathrm{Zn^{2+}}][\mathrm{OH}^-]^4 = K_f \frac{K_s}{[\mathrm{OH}^-]^2}[\mathrm{OH}^-]^4\]
04

Calculate the concentration of \(\mathrm{Zn}(\mathrm{OH})_{4}^{2-}\) required to dissolve 0.015 mol of \(\mathrm{Zn}(\mathrm{OH})_{2}\) in a liter of solution

To dissolve 0.015 mol of \(\mathrm{Zn}(\mathrm{OH})_{2}\) in a liter of solution, the moles of \(\mathrm{Zn^{2+}}\) will be equal to the moles of \(\mathrm{Zn}(\mathrm{OH})_{4}^{2-}\), so: \[0.015 = [\mathrm{Zn}(\mathrm{OH})_{4}^{2-}] = K_f \frac{K_s}{[\mathrm{OH}^-]^2}[\mathrm{OH}^-]^4\]
05

Solve for the concentration of \(\mathrm{OH}^-\)

Now, we will solve for the concentration of \(\mathrm{OH}^-\): \[[\mathrm{OH}^-]^6 = \frac{K_s K_f}{0.015}\] \[[\mathrm{OH}^-] = \sqrt[6]{\frac{K_s K_f}{0.015}}\] \[[\mathrm{OH}^-] = \sqrt[6]{\frac{(3.0 \times 10^{-16})(4.6 \times 10^{17})}{0.015}}\] \[[\mathrm{OH}^-] \approx 4.81 \times 10^{-3} \ \text{M}\] Therefore, the concentration of \(\mathrm{OH}^-\) required to dissolve 0.015 mol of \(\mathrm{Zn}(\mathrm{OH})_{\text{2}}\) in a liter of solution is approximately \(4.81 \times 10^{-3} \ \text{M}\).

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Most popular questions from this chapter

A solution of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is added dropwise to a solution that is \(0.010 \mathrm{M}\) in \(\mathrm{Ba}^{2+}\) and \(0.010 \mathrm{M}\) in \(\mathrm{Sr}^{2+}\). (a) What con- centration of \(\mathrm{SO}_{4}^{2-}\) is necessary to begin precipitation? (Neglect volume changes. \(\mathrm{BaSO}_{4}: K_{s p}=1.1 \times 10^{-10} ; \mathrm{SrSO}_{4}:\) \(\left.K_{s p}=3.2 \times 10^{-7} .\right)\) (b) Which cation precipitates first? (c) What is the concentration of \(\mathrm{SO}_{4}^{2-}\) when the second cation begins to precipitate?

You have to prepare a pH 5.00 buffer, and you have the following \(0.10 \mathrm{M}\) solutions available: \(\mathrm{HCOOH}, \mathrm{HCOONa}, \mathrm{CH}_{3} \mathrm{COOH},\) \(\mathrm{CH}_{3} \mathrm{COONa}, \mathrm{HCN},\) and \(\mathrm{NaCN}\). Which solutions would you use? How many milliliters of each solution would you use to make approximately a liter of the buffer?

A solution contains \(2.0 \times 10^{-4} \mathrm{MAg}^{+}\) and \(1.5 \times 10^{-3} \mathrm{M}\) \(\mathrm{Pb}^{2+}\). If NaI is added, will AgI \(\left(K_{s p}=8.3 \times 10^{-17}\right)\) or \(\mathrm{PbI}_{2}\) \(\left(K_{s p}=7.9 \times 10^{-9}\right)\) precipitate first? Specify the concentration of \(1^{-}\) needed to begin precipitation.

Benzenesulfonic acid is a monoprotic acid with \(\mathrm{p} K_{a}=2.25\). Calculate the \(\mathrm{pH}\) of a buffer composed of \(0.150 \mathrm{M}\) benzenesulfonic acid and \(0.125 M\) sodium benzenesulfonate.

Assume that \(30.0 \mathrm{~mL}\) of a \(0.10 \mathrm{M}\) solution of a weak base \(\mathrm{B}\) that accepts one proton is titrated with a \(0.10 \mathrm{M}\) solution of the monoprotic strong acid HX. (a) How many moles of \(\mathrm{HX}\) have been added at the equivalence point? (b) What is the predominant form of \(\mathrm{B}\) at the equivalence point? (c) What factor determines the \(\mathrm{pH}\) at the equivalence point? (d) Which indicator, phenolphthalein or methyl red, is likely to be the better choice for this titration?
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