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Q. If the salts $ M_2X $ , $ QY_2 $ and $ PZ_3 $ have the same solubilities, their $ K_{sp} $ values are related as

AMUAMU 2011Equilibrium

Solution:

For $M_2 - X $;
$M_2X \rightleftharpoons 2M^+ + X^{2-}$
$\therefore K_{sp} = (2s)^2 \times s$
$ = 4s^2$
For $QY_2$;
$QY_2 \rightleftharpoons Q^{2+} + 2Y^-$
$\therefore K_{sp} = s \times (2s)^2 = 4s^2$
For $PZ_3$;
$PZ_3 \rightleftharpoons P^3 + 3Z^-$
$\therefore K_{sp} = s \times (3s)^3 = 27 s^4$
Thus, $K_{sp}$ is in order,
$K_{sp}(M_2X) = K_{sp} (QY_2) < K_{sp}(PZ_3)$