Question

Two salts A\(_2\)X and MX have the same value of solubility product of 4.0 \(\times\) 10\(^{-12}\). The ratio of their molar solubilities i.e. \(\frac{S(A_2X)}{S(MX)}\) = __________. (Round off to the Nearest Integer)

Hint:

For A₂X, K_sp = 4S³; for MX, K_sp = S².

Answer 1

Correct Answer: 50

For \(\mathrm{A_2X \rightleftharpoons 2A^+ + X^{2-}}\): \(K_{sp} = (2S_1)^2 (S_1) = 4S_1^3\). So \(S_1^3 = \frac{4.0 \times 10^{-12}}{4} = 1.0 \times 10^{-12}\) and \(S_1 = 1.0 \times 10^{-4}\) M.
For \(\mathrm{MX \rightleftharpoons M^+ + X^-}\): \(K_{sp} = S_2^2\), so \(S_2 = \sqrt{4.0 \times 10^{-12}} = 2.0 \times 10^{-6}\) M.
Ratio \(= \frac{S_1}{S_2} = \frac{1.0 \times 10^{-4}}{2.0 \times 10^{-6}} = 50\).
Answer: 50