1 mole of ${\mathrm{AgNO}}_3$ is added to 10 litre of $1 \mathrm{M} {\mathrm{NH}}_3$. What is the concentration of $\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}^{+}$ in solution? [Given: For $\left.\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2^{+}, K_{f_1}=2.0\times {10}^3; K_{f_2}={10}^4\right]$

Inn the reaction,

${\left[{\mathrm{Ag}}^{+}\right]}_0=\left[{\mathrm{Ag}}^{+}\right]+\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}^{+}\right]+\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2^{+}\right]$

$\frac{1}{10}=\frac{\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}^{+}\right]}{K_{f_1}\times \left[{\mathrm{NH}}_3\right]}+\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}^{+}\right] +K_{f_2}\left[{\mathrm{Ag}}_g{\left({\mathrm{NH}}_3\right)}^{+}\right]\left[{\mathrm{NH}}_3\right]$

$$\begin{gathered} \frac{1}{10}=\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}^{+}\right]\left\{\frac{1}{K_{f_1}\times \left[{\mathrm{NH}}_3\right]}+1+K_{f_2}\left[{\mathrm{NH}}_3\right]\right\} \\ \mathrm{negligible} \end{gathered}$$

${\left[{\mathrm{NH}}_3\right]}_{eq}\simeq 1-0.2=0.8\mathrm{M}$   

{If ${\mathrm{NH}}_3$ dissolves $\mathrm{AgCl}$ completely}

$$\begin{gathered} \Rightarrow \left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}^{+}\right]=\frac{1}{10\times 0.8\times {10}^4} \\ =1.25\times {10}^{-5}\mathrm{M} \end{gathered}$$