Question

Given, $\left[Ag\right(N{H}_3{)}_2^{+}]\rightleftharpoons A{g}^{+}+2N{H}_3$,
$K_c=6.2\times {10}^{-8}$ and $K_{sp}$ of $AgCl$
$=1.8\times {10}^{-10}$ at 298 K.
If ammonia is added to a water solution containing excess of $AgCl\left(s\right)$ only. Calculate the concentration of the complex in 1.0 M aqueous ammonia.

Answer 1

$AgCl\rightleftharpoons A{g}^{+}+C{l}^{-}$

$S$ $S$

$K_{sp}=S^2=1.8\times {10}^{-10}$

$\therefore \left[A{g}^{+}\right]=S=1.34\times {10}^{-5}M$

$K_C=\frac{\left[A{g}^{+}\right][N{H}_3{]}^2}{\left[Ag\right(N{H}_3{)}_2{]}^{+}}$

$\therefore$ Concentration of the complex= $\frac{\left[A{g}^{+}\right][N{H}_3{]}^2}{K_C}=\frac{1.34\times {10}^{-5}\times (1{)}^2}{6.2\times {20}^{-8}}=216.13$