Question

in aqueous solution the ag⁺ ion forms a complex with two cyanide anions. write the formation constant expression for the equilibrium between the hydrated metal ion and the aqueous complex. under that, write the balanced chemical equation for the first step in the formation of the complex. k_f = write the first step: first step:

Explanation:

Step1: Determine the complex formation reaction

The hydrated silver ion is $\ce{Ag+(aq)}$ (or can be considered as $\ce{[Ag(H2O)n]+}$ but for simplicity, we use $\ce{Ag+}$), and it forms a complex with two cyanide ions ($\ce{CN-}$) to form $\ce{[Ag(CN)2]-}$. The overall complex formation reaction is: $\ce{Ag+(aq) + 2CN-(aq) <=> [Ag(CN)2]-(aq)}$.

Step2: Write the formation constant expression

The formation constant ($K_f$) is the ratio of the concentration of the complex to the product of the concentrations of the reactants, each raised to their stoichiometric coefficients. So, $K_f = \frac{[\ce{[Ag(CN)2]-}]}{[\ce{Ag+}][\ce{CN-}]^2}$.

Step3: Determine the first step in complex formation

The first step in the formation of the complex $\ce{[Ag(CN)2]-}$ involves the reaction of the hydrated silver ion with one cyanide ion to form the intermediate $\ce{[Ag(CN)]}$. The balanced chemical equation for the first step is: $\ce{Ag+(aq) + CN-(aq) <=> [Ag(CN)](aq)}$.

Answer:

For the formation constant expression: $K_f = \frac{[\ce{[Ag(CN)2]-}]}{[\ce{Ag+}][\ce{CN-}]^2}$

For the first step: $\ce{Ag+(aq) + CN-(aq) <=> [Ag(CN)](aq)}$