Find the solubility of Mg(OH)2 in 0.50 M NH4Cl solution, from Mg(OH)2(s) + 2NH4+ leftharpoons Mg^2+ + 2NH3 + 2H2O. Given K_sp(Mg(OH)2) = 1.2 x 10^-11 and K_b(NH3) = 1.8 x 10^-5. Treat NH4+ and NH3 as the only nitrogen species.

JEE Advanced levelSingle correct optionDifficulty 3 of 3ia086

Find the solubility of $Mg (OH) X_{2}$ in $0.50 M$ $NH X_{4} Cl$ solution, from $Mg (OH) X_{2} (s) + 2 NH X_{4} X^{+} ⇌ Mg X^{2 +} + 2 NH X_{3} + 2 H X_{2} O$ . Given $K_{s p} (Mg (OH) X_{2}) = 1.2 \times 1 0^{- 11}$ and $K_{b} (NH X_{3}) = 1.8 \times 1 0^{- 5}$ . Treat $NH X_{4} X^{+}$ and $NH X_{3}$ as the only nitrogen species.

K = K_{s p} / K_{b}^{2} = 0.0370

. With

[Mg X^{2 +}] = s

[NH X_{3}] = 2 s

[NH X_{4} X^{+}] = 0.50 - 2 s

4 s^{3} / (0.50 - 2 s)^{2} = 0.0370

. Solving numerically gives

s = 9.6 \times 1 0^{- 2} M