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# $M_2SO_4$ ($M^+$ is monovalent metal ion) has a $K_{sp}$ of $3.2 \times 10^{-5}$ at 298 K. The maximum concentration of $SO^{2-}_4$ ion that could be attained in a saturated solution of this solid at 289 K is

(a) $3 \times 10^{-3}$ M

(a) $7 \times 10^{-2}$ M

(b) $2.89 \times 10^{-4}$ M

(c) $2 \times 10^{-2}$ M

Answer: $2 \times 10^{-2}$ mol $L^{-1}$

The maximum concentration of $SO^{2-}_4$ will be same as solubility of $M_2SO_4$.

If solubility is x mol $L^{-1}$

$M_2SO_4 \rightleftharpoons 2M^+ + SO^{2-}_4$

$K^{sp} = [M^+]^2 [SO^{2-}_4] = 4x^3$
$x = (K_{sp} / 4)^{\frac{1}{3}}$

$[SO^{2-}_4] = x = (K_{sp} / 4)^{\frac{1}{3}} = (\frac{3.2 \times 10^{-5}}{4})^{\frac{1}{3}} = 2 \times 10^{-2} M$