CHXI07:EQUILIBRIUM
314768
If \({\text{A}}{{\text{g}}^ + } + 2{\text{N}}{{\text{H}}_3} \rightleftharpoons {\left[ {{\text{Ag}}{{\left( {{\text{N}}{{\text{H}}_3}} \right)}_2}} \right]^ + };{{\text{K}}_{\text{1}}}{\text{ = 1}}{\text{.7}} \times {\text{1}}{{\text{0}}^{\text{7}}}\)
\({\text{A}}{{\text{g}}^ + } + {\text{C}}{{\text{l}}^{ - 1}} \rightleftharpoons {\text{AgCl}};{{\text{K}}_2} = 5.4 \times {10^9}\)
\({\text{Then for AgCl}} + 2{\text{N}}{{\text{H}}_3} \rightleftharpoons {\left[ {{\text{Ag}}{{\left( {{\text{N}}{{\text{H}}_3}} \right)}_2}} \right]^ + } + {\text{C}}{{\text{l}}^ - }\) equilibrium constants will be
1 \(0.31 \times 10^{-2}\)
2 \(3.2 \times 10^{2}\)
3 \(9.18 \times 10^{16}\)
4 \(1.00 \times 10^{-17}\)
Explanation:
For reaction
\(\mathrm {\mathrm{Ag}^{+}+2 \mathrm{NH}_{3} \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+} ; K_{1}=1.7 \times 10^{7}}\)
For \(\mathrm {\mathrm{Ag}^{+}+\mathrm{Cl}^{-} \rightleftharpoons \mathrm{AgCl} ; K_{2}=5.4 \times 10^{9}}\)
Thus for
\({\text{AgCl}} \rightleftharpoons {\text{A}}{{\text{g}}^{\text{ + }}}{\text{ + C}}{{\text{l}}^{\text{ - }}}\)
\({{{\text{K'}}}_{\text{2}}}{\text{ = }}\frac{{\text{1}}}{{{{\text{K}}^{\text{2}}}}}{\text{ = }}\frac{{\text{1}}}{{{\text{5}}{\text{.4}} \times {\text{1}}{{\text{0}}^{\text{9}}}}}\)
Now for the reaction
\(\rm {\mathrm{AgCl}+2 \mathrm{NH}_{3} \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}+\mathrm{Cl}^{-}}\)
\(\mathrm {K=K_{1} \times K_{2}^{\prime}=1.7 \times 10^{7} \times \dfrac{1}{5.4 \times 10^{9}}=0.31 \times 10^{-2}}\)
