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Ch.17 - Additional Aspects of Aqueous Equilibria
Chapter 17, Problem 68

Using the value of Ksp for Ag2S, Ka1 and Ka2 for H2S, and Kf = 1.1 * 10^5 for AgCl2^-, calculate the equilibrium constant for the following reaction: Ag2S (s) + 4 Cl^- (aq) + 2 H^+ (aq) ⇌ 2 AgCl2^- (aq) + H2S (aq)

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1
Identify the relevant equilibrium reactions and their constants: (1) Ag2S (s) ⇌ 2 Ag^+ (aq) + S^2- (aq) with Ksp, (2) H2S (aq) ⇌ H^+ (aq) + HS^- (aq) with Ka1, (3) HS^- (aq) ⇌ H^+ (aq) + S^2- (aq) with Ka2, and (4) Ag^+ (aq) + 2 Cl^- (aq) ⇌ AgCl2^- (aq) with Kf.
Write the expression for the equilibrium constant of the target reaction: K_target = [AgCl2^-]^2 [H2S] / ([Cl^-]^4 [H^+]^2).
Express the equilibrium constant for the target reaction in terms of the given constants: K_target = (Ksp * Kf^2) / (Ka1 * Ka2).
Substitute the given values of Ksp, Ka1, Ka2, and Kf into the expression for K_target.
Simplify the expression to find the numerical value of the equilibrium constant for the target reaction.