Multiple Choice
Liquid carbon dioxide is considered a good green alternative solvent because:
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6. Chemical Quantities & Aqueous Reactions
Solubility Rules
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Given the solubility product constant K_sp for Mg(OH)_2 is 1.8 × 10^{-11}, what is the molar solubility of Mg(OH)_2 in a 0.202 M solution of Mg(NO_3)_2?
A
8.9 × 10^{-4} M
B
0.202 M
C
2.1 × 10^{-6} M
D
1.8 × 10^{-11} M
Verified step by step guidance1
Write the dissociation equation for magnesium hydroxide: $\mathrm{Mg(OH)_2 (s) \rightleftharpoons Mg^{2+} (aq) + 2 OH^- (aq)}$.
Express the solubility product constant $K_{sp}$ in terms of the ion concentrations: $K_{sp} = [Mg^{2+}][OH^-]^2$.
Identify the initial concentration of $Mg^{2+}$ from the $Mg(NO_3)_2$ solution, which is 0.202 M, and let the molar solubility of $Mg(OH)_2$ be $s$. Then, $[Mg^{2+}] = 0.202 + s \approx 0.202$ (since $s$ is very small) and $[OH^-] = 2s$.
Substitute these concentrations into the $K_{sp}$ expression: $1.8 \times 10^{-11} = (0.202)(2s)^2$.
Solve the equation for $s$ (the molar solubility) by isolating $s$ and calculating its value without performing the final arithmetic.
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