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Chapter 18: Problem 72

Calculate the molar solubility of \(\mathrm{Mg}(\mathrm{OH})_{2}\) in \(1.00 \mathrm{M}\) \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{aq})\).

Short Answer

Expert verified
The molar solubility solution involves setting up the equilibrium based on the problem, using the given \(K_{sp}\), and solving for \(s\). The exact numeric value will depend on the approximation or solution method used for the quadratic equation, but should be in the molar range.

Step by step solution

01

Write the Chemical Equation and Expressions for Molar Solubility and Solubility Product

The balance chemical equation for the dissolution of \(\mathrm{Mg}(\mathrm{OH})_{2}\) is: \(\mathrm{Mg(OH)_{2}(s)} \rightleftharpoons \mathrm{Mg^{2+}(aq)} + 2\mathrm{OH^{-}(aq)}\). Let \(s\) represent the molar solubility of \(\mathrm{Mg}(\mathrm{OH})_{2}\) in \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{aq})\). The concentration of \(\mathrm{Mg}^{+2}(aq)\) will be \(s\) and \(\mathrm{OH}^{-}\) will be \(2s\). The solubility product expression for \(\mathrm{Mg(OH)_{2}\) is: \(K_{sp} = [\mathrm{Mg^{2+}}][\mathrm{OH}^-]^{2}\)
02

Use the \(K_{sp}\) value of \(\mathrm{Mg(OH)_{2}\)

The \(K_{sp}\) value of \(\mathrm{Mg(OH)_{2}\) at room temperature is \(5.61 \times 10^{-12}\). Substitute these values into the \(K_{sp}\) equation: \(5.61 \times 10^{-12} = (s)(2s)^2\)
03

Solve for Molar Solubility

Now simplify the equation, reduce it to a quadratic form, and solve for \(s\) to find the molar solubility of \(\mathrm{Mg(OH)_{2}\) in \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{aq})\). Remember to check if the quadratic approximation is valid; if not, use the quadratic formula to solve the equation.

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Most popular questions from this chapter

Write net ionic equations for each of the following observations. (a) When concentrated \(\mathrm{CaCl}_{2}(\mathrm{aq})\) is added to \(\mathrm{Na}_{2} \mathrm{HPO}_{4}(\mathrm{aq}),\) a white precipitate forms that is \(38.7 \%\) Ca by mass. (b) When a piece of dry ice, \(\mathrm{CO}_{2}(\mathrm{s}),\) is placed in a clear dilute solution of limewater \(\left[\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})\right]\), bubbles of gas evolve. At first, a white precipitate forms, but then it redissolves.

Determine whether \(1.50 \mathrm{g} \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) (oxalic acid: \(K_{\mathrm{a}_{1}}=\) \(\left.5.2 \times 10^{-2}, K_{\mathrm{a}_{2}}=5.4 \times 10^{-5}\right)\) can be dissolved in \(0.200 \mathrm{L}\) of \(0.150 \mathrm{M} \mathrm{CaCl}_{2}\) without the formation of \(\mathrm{CaC}_{2} \mathrm{O}_{4}(\mathrm{s})\left(K_{\mathrm{sp}}=1.3 \times 10^{-9}\right)\).

Fluoridated drinking water contains about 1 part per million (ppm) of \(\mathrm{F}^{-}\). Is \(\mathrm{CaF}_{2}\) sufficiently soluble in water to be used as the source of fluoride ion for the fluoridation of drinking water? Explain. [Hint: Think of 1 ppm as signifying \(1 \mathrm{g} \mathrm{F}^{-}\) per \(10^{6} \mathrm{g}\) solution.

When \(200.0 \mathrm{mL}\) of \(0.350 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4}(\mathrm{aq})\) are added to 200.0 mL of 0.0100 M AgNO 3(aq), what percentage of the \(\mathrm{Ag}^{+}\) is left unprecipitated?

Show that in qualitative cation analysis group \(1,\) if you obtain \(1.00 \mathrm{mL}\) of saturated \(\mathrm{PbCl}_{2}(\mathrm{aq})\) at \(25^{\circ} \mathrm{C}\), sufficient \(\mathrm{Pb}^{2+}\) should be present to produce a precipitate of \(\mathrm{PbCrO}_{4}(\mathrm{s}) .\) Assume that you use \(1 \mathrm{drop}\) \((0.05 \mathrm{mL})\) of \(1.0 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4}\) for the test.
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