Given the solubility product constant (Ksp) for AgI is 8.3 x 10^-17 and the formation constant (Kf) for Ag(CN)₂⁻ is 1.0 x 10^21, calculate the equilibrium constant for the reaction AgI(s) + 2CN⁻(aq) ⇌ Ag(CN)₂⁻(aq) + I⁻(aq).

• A. 7.5 x 10^3
• B. 1.2 x 10^5
• C. 8.3 x 10^4
• D. 9.0 x 10^4

Answer: (C)

Verified step by step guidance

1. Identify the two reactions involved: the dissolution of AgI and the formation of Ag(CN)₂⁻. The dissolution reaction is AgI(s) ⇌ Ag⁺(aq) + I⁻(aq) with Ksp = 8.3 x 10^-17. The formation reaction is Ag⁺(aq) + 2CN⁻(aq) ⇌ Ag(CN)₂⁻(aq) with Kf = 1.0 x 10^21.
2. Write the overall reaction by combining the two reactions: AgI(s) + 2CN⁻(aq) ⇌ Ag(CN)₂⁻(aq) + I⁻(aq).
3. To find the equilibrium constant (K) for the overall reaction, use the relationship K = Kf / Ksp. This is because the overall reaction is the sum of the dissolution and formation reactions, and the equilibrium constant for the sum of reactions is the product of the constants of the individual reactions.
4. Substitute the given values into the equation: K = (1.0 x 10^21) / (8.3 x 10^-17).
5. Calculate the value of K by performing the division, which will give you the equilibrium constant for the overall reaction.