The overall formation mechanism of the diamminesilver(I) complex, , occurs in two distinct reversibl — Ionic Equilibrium Chemistry Question
Question
The overall formation mechanism of the diamminesilver(I) complex, $[Ag(NH_3)_2]^+$, occurs in two distinct reversible steps with successive equilibrium constants $K_1 = 1.6 \times 10^3$ and $K_2 = 6.8 \times 10^3$. What is the overall formation constant ($K_f$) for this complexation mechanism?
💡 Solution & Explanation
The stepwise formation reactions are: Step 1: $Ag^+ + NH_3 \rightleftharpoons [Ag(NH_3)]^+$ (Constant $K_1$). Step 2: $[Ag(NH_3)]^+ + NH_3 \rightleftharpoons [Ag(NH_3)_2]^+$ (Constant $K_2$). The overall reaction is the sum of these two steps: $Ag^+ + 2NH_3 \rightleftharpoons [Ag(NH_3)_2]^+$. When reactions are added, their equilibrium constants are multiplied. Therefore, $K_f = K_1 \times K_2 = (1.6 \times 10^3) \times (6.8 \times 10^3) = 10.88 \times 10^6 = 1.088 \times 10^7$.