Calculate the solubility of Ag₂CrO₄ [K_sp = 9.0 × 10^-12] in a 1.0 × 10^-2 M AgNO₃ solution. A) 1.3 × 10^-4 mol/L B) 2.3 × 10^-8 mol/L C) 9.0 × 10^-8 mol/L D) 9.0 × 10^-10 mol/L E) none of these

Question

Quizplus · Accepted Answer

The solubility of a salt is determined by its solubility product constant (Ksp) and the concentration of the ions in solution.

The balanced equation for the dissolution of AgS1U1B12S1U1B0CrOS1U1B14S1U1B0 is:

AgS1U1B12S1U1B0CrOS1U1B14S1U1B0 (s) ↔ Ag+ (aq) + S1U1B12− (aq) + CrO4 2− (aq) + S1U1B14− (aq)

The Ksp expression for this reaction is:

Ksp = [Ag+] [S1U1B12−] [CrO4 2−] [S1U1B14−]

We need to find the solubility of AgS1U1B12S1U1B0CrOS1U1B14S1U1B0 in a 1.0 × 10S1U1P1-2S1S1P0 M AgNOS1U1B13S1U1B0 solution, which means that [Ag+] = 1.0 × 10S1U1P1-2S1S1P0 M.

Let's assume that the solubility of AgS1U1B12S1U1B0CrOS1U1B14S1U1B0 is s mol/L. Then, at equilibrium, [Ag+] = s mol/L and [S1U1B12−] = [CrO4 2−] = [S1U1B14−] = s mol/L (since the stoichiometric coefficients are all 1).

Substituting into the Ksp expression:

Ksp = (s) (s) (s) (s) = s^4

Now, we can solve for s:

Ksp = 9.0 × 10S1U1P1-12S1S1P0
s^4 = 9.0 × 10S1U1P1-12S1S1P0
s = (9.0 × 10S1U1P1-12S1S1P0)1/4
s = 9.0 × 10S1U1P1-8S1S1P0 mol/L

Therefore, the solubility of AgS1U1B12S1U1B0CrOS1U1B14S1U1B0 in a 1.0 × 10S1U1P1-2S1S1P0 M AgNOS1U1B13S1U1B0 solution is 9.0 × 10S1U1P1-8S1S1P0 mol/L, which is choice (C).

Calculate the Solubility of Ag2CrO4 [Ksp = 9

Calculate the Solubility of Ag₂CrO₄ [K_sp = 9