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Multiple Choice
Given that the solubility product constant (K_sp) for Ca(OH)_2 at 25°C is 5.5 × 10^{-6}, what is the molar solubility of Ca(OH)_2 in pure water?
A
1.2 × 10^{-2} mol/L
B
1.2 × 10^{-2} mol/L
C
1.1 × 10^{-2} mol/L
D
1.1 × 10^{-2} mol/L
Verified step by step guidance
1
Write the dissociation equation for calcium hydroxide: $\mathrm{Ca(OH)_2 (s) \rightleftharpoons Ca^{2+} (aq) + 2 OH^- (aq)}$.
Define the molar solubility of $\mathrm{Ca(OH)_2}$ as $s$, which means the concentration of $\mathrm{Ca^{2+}}$ ions is $s$ and the concentration of $\mathrm{OH^-}$ ions is $2s$ because each formula unit produces two hydroxide ions.
Write the expression for the solubility product constant $K_{sp}$ in terms of $s$: $K_{sp} = [Ca^{2+}][OH^-]^2 = s \times (2s)^2 = 4s^3$.
Set the expression equal to the given $K_{sp}$ value and solve for $s$: $4s^3 = 5.5 \times 10^{-6}$.
Rearrange to isolate $s$: $s^3 = \frac{5.5 \times 10^{-6}}{4}$, then take the cube root of both sides to find the molar solubility $s$.