Question

Concentration of the Ag⁺ ions in a saturated solution of Ag₂C₂O₄ is 2.2 × 10^–4 mol L^–1. Solubility product of Ag₂C₂O₄ is

• A. 2.42 × 10^–8
• B. 2.66 × 10^–12
• C. 4.5 × 10^–11
• D. 5.3 × 10^–12

Answer 1

The Correct Option is D

To calculate the solubility product (\(K_{sp}\)) of Ag₂C₂O₄, we first need to understand its dissolution process in water.

The dissociation of Ag₂C₂O₄ in a saturated solution is represented by the equation: 

\(\text{Ag}_2\text{C}_2\text{O}_4 (s) \rightleftharpoons 2\text{Ag}^+ (aq) + \text{C}_2\text{O}_4^{2-} (aq) \\)

Given that the concentration of \(\text{Ag}^+\) ions is \(2.2 \times 10^{-4}\) mol L^–1, we can use this information to find the concentration of \(\text{C}_2\text{O}_4^{2-}\) ions because all are related to the stoichiometry of the dissolution equation.

For every mole of Ag₂C₂O₄ that dissolves, it produces 2 moles of \(\text{Ag}^+\) ions and 1 mole of \(\text{C}_2\text{O}_4^{2-}\) ions. Therefore, when the concentration of \(\text{Ag}^+\) is \(2.2 \times 10^{-4}\) mol L^–1, the concentration of \(\text{C}_2\text{O}_4^{2-}\) is :

\([\text{C}_2\text{O}_4^{2-}] = \frac{2.2 \times 10^{-4}}{2} = 1.1 \times 10^{-4} \ \text{mol L}^{-1}\)

The solubility product expression (\(K_{sp}\)) for Ag₂C₂O₄ is:

\(K_{sp} = [\text{Ag}^+]^2[\text{C}_2\text{O}_4^{2-}] \\)

Substituting the concentrations into the \(K_{sp}\) expression gives:

\(K_{sp} = (2.2 \times 10^{-4})^2 \times (1.1 \times 10^{-4})\)

• \((2.2 \times 10^{-4})^2 = 4.84 \times 10^{-8}\)
•  

Rounding it to two significant figures, the solubility product (\(K_{sp}\)) is approximately:

5.3 × 10^–12

Therefore, the correct answer is 5.3 × 10^–12.