Question

The solubility of sapringly soluble salt \(\text{AB}_2\) is \(18\cdot 78\times 10^{-4}\text{ g/dm}^3\) What is its solubility product ? (Molar mass of \(\text{AB}_2 = 187\cdot 8\text{ g mol}^{-1}\))

• A. \(2\times 10^{-15}\)
• B. \(4\times 10^{-15}\)
• C. \(6\times 10^{-15}\)
• D. \(8\times 10^{-15}\)

Hint:

Convert g per dm3 to mol per dm3 and use Ksp = 4S cubed.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
\(\text{AB}_2\) dissociates as \(\text{AB}_2 \rightleftharpoons \text{A}^{2+} + 2\text{B}^-\). If the solubility is \(S\) mol dm\(^{-3}\), then \([\text{A}^{2+}] = S\) and \([\text{B}^-] = 2S\).

Step 2: Convert solubility to molar units:
\[ S = \frac{18.78\times 10^{-4}}{187.8} = 1\times 10^{-5}\text{ mol dm}^{-3} \]

Step 3: Find the solubility product:
\[ K_{sp} = [\text{A}^{2+}][\text{B}^-]^2 = S\cdot(2S)^2 = 4S^3 \]
\[ K_{sp} = 4\times(10^{-5})^3 = 4\times 10^{-15} \]
Forgetting the factor 4 gives \(1\times10^{-15}\), which is not an option, so the factor 4 from \((2S)^2\) matters.

Final Answer:
The solubility product is \(4\times 10^{-15}\), option (B). \[ \boxed{4\times 10^{-15}} \]