QuestionJune 20, 2025

C_(2)D_(3) has a solubility product constant of 9.14times 10^-9 What is the mola solubility C_(2)D_(3) Express your answer with the appropriate units.

C_(2)D_(3) has a solubility product constant of 9.14times 10^-9 What is the mola solubility C_(2)D_(3) Express your answer with the appropriate units.
C_(2)D_(3) has a solubility product constant of 9.14times 10^-9 What is the mola solubility C_(2)D_(3) Express your answer with the appropriate units.

Solution
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Answer

0.00032 \, \text{M} Explanation 1. Write the Dissolution Equation C_{2}D_{3}(s) \rightleftharpoons 2C^{2+}(aq) + 3D^{3-}(aq) 2. Express Solubility Product Expression K_{sp} = [C^{2+}]^2[D^{3-}]^3 3. Define Molar Solubility Let s be the molar solubility of C_{2}D_{3}. Then, [C^{2+}] = 2s and [D^{3-}] = 3s. 4. Substitute into K_{sp} Expression K_{sp} = (2s)^2(3s)^3 = 4s^2 \cdot 27s^3 = 108s^5 5. Solve for s 9.14 \times 10^{-9} = 108s^5 \implies s^5 = \frac{9.14 \times 10^{-9}}{108} \implies s = \left(\frac{9.14 \times 10^{-9}}{108}\right)^{1/5} 6. Calculate s s \approx 0.00032 \, \text{M}

Explanation

1. Write the Dissolution Equation<br /> $C_{2}D_{3}(s) \rightleftharpoons 2C^{2+}(aq) + 3D^{3-}(aq)$<br /><br />2. Express Solubility Product Expression<br /> $K_{sp} = [C^{2+}]^2[D^{3-}]^3$<br /><br />3. Define Molar Solubility<br /> Let $s$ be the molar solubility of $C_{2}D_{3}$. Then, $[C^{2+}] = 2s$ and $[D^{3-}] = 3s$.<br /><br />4. Substitute into $K_{sp}$ Expression<br /> $K_{sp} = (2s)^2(3s)^3 = 4s^2 \cdot 27s^3 = 108s^5$<br /><br />5. Solve for $s$<br /> $9.14 \times 10^{-9} = 108s^5 \implies s^5 = \frac{9.14 \times 10^{-9}}{108} \implies s = \left(\frac{9.14 \times 10^{-9}}{108}\right)^{1/5}$<br /><br />6. Calculate $s$<br /> $s \approx 0.00032 \, \text{M}$
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