Question

If 'S' is the solubility of $X_{3}Y_{2}$ in pure water, the solubility product ($K_{sp}$) is ________.

• A. $27~S^{4}$
• B. $108~S^{5}$
• C. $108~S^{2}$
• D. $27~S^{6}$
• E. $27~S^{2}$

Hint:

For $A_xB_y$, $K_{sp} = x^x y^y S^{(x+y)}$.

Answer 1

The Correct Option is B

Step 1: Concept
Write the dissociation equation for the salt.

Step 2: Meaning
$X_3Y_2(s) \rightleftharpoons 3X^{2+} + 2Y^{3-}$. Concentrations: $[X] = 3S$, $[Y] = 2S$.

Step 3: Analysis
$K_{sp} = [X]^3 [Y]^2 = (3S)^3 (2S)^2$. $K_{sp} = 27S^3 \times 4S^2 = 108S^5$.

Step 4: Conclusion
$K_{sp} = 108S^5$. Final Answer: (B)