The value of the solubility product constant for Ag2CO3 is 8.5 * 10-12 and that of Ag2CrO4 is 1.1 * 10-12. From this data, what is the value of Kc for the reaction, Ag2CO3 (s) + CrO42 - (aq) → Ag2CrO4 (s) + CO32 - (aq)

A) 9.6 * 10-12

B) 7.7

C) 1.1 * 1023

D) 1.3 * 10-1

E) 9.4 * 10-24

B) 7.7

Explanation:

For the reaction Ag2CO3 (s) + CrO42 - (aq) → Ag2CrO4 (s) + CO32 - (aq)

Kc = (CO₃²⁻) / (CrO₄²⁻)

and the Ksp given are

Ag₂CO₃ ⇒ 2 Ag⁺ (aq) + CO₃²⁻ (aq) Ksp₁ = (Ag⁺) ² (CO₃²⁻)

Ag₂CrO₄ ⇒ 2 Ag⁺ (aq) + CrO₄²⁻ (aq) Ksp₂ = (Ag⁺) ² (CrO₄²⁻)

Where ( ...) indicate concentrations M

Notice if we divide the expressions for Ksp we get:

Ksp₁/Ksp₂ = (CO₃²⁻) / (CrO₄²⁻) = 8.5 x 10⁻¹² / 1.1 x 10⁻¹² = 7.7

which is the desired answer.