To write the equilibrium expression for the given reaction, we need to consider the concentrations of the reactants and products. For the reaction:
[tex]\[ \text{Ag}^+_{(aq)} + 2 \text{NH}_3{(aq)} \longleftrightarrow \text{Ag(NH}_3\text{)}_{2(aq)}^+ \][/tex]
The equilibrium constant, [tex]\( K \)[/tex], is given by the ratio of the concentration of the products to the concentration of the reactants, each raised to the power of their respective stoichiometric coefficients.
So for the reaction:
[tex]\[ \text{Ag}^+_{(aq)} + 2 \text{NH}_3_{(aq)} \longleftrightarrow \text{Ag(NH}_3\text{)}_{2(aq)}^+ \][/tex]
The equilibrium expression [tex]\( K \)[/tex] is:
[tex]\[
K = \frac{[\text{Ag(NH}_3\text{)}_{2}^+]}{[\text{Ag}^+][\text{NH}_3]^2}
\][/tex]
Therefore, the correct equilibrium expression for the reaction is:
[tex]\[ K = \frac{[\text{Ag(NH}_3\text{)}_{2}^+]}{[\text{Ag}^+][\text{NH}_3]^2} \][/tex]
Among the given options, this matches:
[tex]\[ K=\frac{\left[\text{Ag}\left(\text{NH}_3\right)_2^{+}\right]}{\left[\text{Ag}^{+}\right]\left[\text{NH}_3\right]^2} \][/tex]
