Chemistry - Chemical Equilibrium Question with Solution | TestHub

(i) ${\mathrm{Ag}}^{+}+{\mathrm{NH}}_3\rightleftharpoons {\left[\mathrm{Ag}\left({\mathrm{NH}}_3\right)\right]}^{+};k_1=3.5\times 10^{-3}$ (ii) ${\left[\mathrm{Ag}\left({\mathrm{NH}}_3\right)\right]}^{+}+{\mathrm{NH}}_3\rightleftharpoons {\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\right]}^{+},k_2=1.7\times 10^{-3}$ on the basis of above reaction $$\begin{array}{rl}& k_1=\frac{{\left[\mathrm{Ag}\left({\mathrm{NH}}_3\right)\right]}^{+}}{\left[{\mathrm{Ag}}^{+}\right]\left[{\mathrm{NH}}_3\right]}\\ & k_2=\frac{{\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\right]}^{+}}{{\left[\mathrm{Ag}\left({\mathrm{NH}}_3\right)\right]}^{+}\left[{\mathrm{NH}}_3\right]}\end{array}$$ For the formation of ${\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\right]}^{+}$ $${\mathrm{Ag}}^{+}+2{\mathrm{NH}}_3\rightleftharpoons {\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\right]}^{+}$$ Formation constant $(K)=\frac{{\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2\right]}^{+}}{\left[{\mathrm{Ag}}^{+}\right]{\left[{\mathrm{NH}}_3\right]}^2}$ From eq. (i) and (ii) $$K=k_1\times k_2=3.5\times 10^{-3}\times 1.7\times 10^{-3}=5.95\times 10^{-6}\approx 6.08\times 10^{-6}$$