Question

The solubility of salt \(\text{AX}_2\) is \(6\times 10^{-12} \text{mol dm}^{-3}\). What is solubility product of the salt ?

• A. \(2.06\times 10^{-24}\)
• B. \(2.48\times 10^{-24}\)
• C. \(4.32\times 10^{-34}\)
• D. \(8.64\times 10^{-34}\)

Hint:

For AX2, Ksp = 4 s^3, where s is the molar solubility.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
A salt of type \(\text{AX}_2\) dissolves as \(\text{AX}_2 \rightleftharpoons \text{A}^{2+} + 2\text{X}^-\). If the solubility is \(s\), then \([\text{A}^{2+}] = s\) and \([\text{X}^-] = 2s\).

Step 2: Key Formula or Approach:
\[ K_{sp} = [\text{A}^{2+}][\text{X}^-]^2 = s(2s)^2 = 4s^3 \]

Step 3: Detailed Explanation:
Here \(s = 6\times 10^{-12} \text{ mol dm}^{-3}\).
\[ s^3 = (6\times10^{-12})^3 = 216 \times 10^{-36} \]
\[ K_{sp} = 4 \times 216\times 10^{-36} = 864\times 10^{-36} = 8.64\times 10^{-34} \]
Options (A) and (B) have the exponent -24, which would arise from squaring instead of cubing. Option (C), 4.32e-34, is half of the correct value, which comes from using \(2s^3\) instead of \(4s^3\).

Final Answer:
The solubility product is \(8.64\times 10^{-34}\), option (D). \[ \boxed{8.64\times 10^{-34} \text{ (D)}} \]