Question

Given $K_{SP}(Ag_2C_2O_4) = 32X$, $K_{SP}(AgBr) = 4Y$. Find ratio of solubility of the given salts in pure water

• A. $\frac{X^{1/3}}{\sqrt{2Y}}$
• B. $\frac{2X^{1/3}}{\sqrt{2Y}}$
• C. $\frac{2X^{1/3}}{\sqrt{Y}}$
• D. $\frac{X^{1/3}}{\sqrt{Y}}$

Answer 1

The Correct Option is D

Solubility calculation from $K_{SP}$ values for different types of salts (AB2 type vs AB type).

STEPS:
1. Salt 1 ($A_2B$ type): $K_{SP} = 4S^3$. Given $32X = 4S_1^3$. Solving for $S_1$: $S_1 = \sqrt[3]{\frac{32X}{4}} = \sqrt[3]{8X} = 2X^{1/3}$.
2. Salt 2 ($AB$ type): $K_{SP} = S^2$. Given $4Y = S_2^2$. Solving for $S_2$: $S_2 = \sqrt{4Y} = 2\sqrt{Y}$ (or $2Y^{1/2}$).
3. Ratio: $\frac{S_1}{S_2} = \frac{2X^{1/3}}{2Y^{1/2}} = \frac{X^{1/3}}{Y^{1/2}}$.
4. This corresponds to $\frac{X^{1/3}}{\sqrt{Y}}$, which is Option (4).