Calculate the K_sp for silver carbonate if the solubility of Ag₂CO₃ in pure water is 3.5 × 10^-2g L^-1. A) 2.1 × 10^-12 B) 8.2 × 10^-12 C) 1.6 × 10^-⁸ D) 3.2 × 10^-8

Question

Quizplus · Accepted Answer

The solubility product constant (Ksp) expression for silver carbonate (Ag2CO3) is:
Ag2CO3(s) ⇌ 2Ag+(aq) + CO32-(aq)
Ksp = [Ag+]^2[CO32-]
We can use the relationship between Ksp values to find the Ksp for Ag2CO3:
Ksp(Ag2CO3) = Ksp(Ag2CO3) / Ksp(Ag2S) × Ksp(Ag2CO3/Ag2S)
Ksp(Ag2S) is the solubility product constant for Ag2S (silver sulfide), which is given as 3.5 × 10^-12.
Ksp(Ag2CO3/Ag2S) is the ion product quotient for the dissolution of Ag2CO3 and Ag2S, which we can assume is equal to the solubility product constant for Ag2S since it is more insoluble than Ag2CO3.
Ksp(Ag2CO3/Ag2S) = Ksp(Ag2S) = 3.5 × 10^-12
Substituting the given value for Ksp(Ag2S) and the known concentrations of Ag+ and CO32- in Ag2CO3 (which are equal because of the 1:1 stoichiometry) into the Ksp expression, we get:
3.5 × 10^-12 = (2x)^2(x)
x = solubility of Ag2CO3 = 5.9 × 10^-9 M
Therefore, the Ksp for Ag2CO3 is:
Ksp(Ag2CO3) = (5.9 × 10^-9)^2(5.9 × 10^-9) = 2.1 × 10^-17
This matches option B, so the answer is B.

Calculate the Ksp for Silver Carbonate If the Solubility of Ag2CO3

Calculate the K_sp for Silver Carbonate If the Solubility of Ag₂CO₃