Question

Which of the following is correct relationship between solubility and solubility product for silver oxalate ?

• A. \(S = \sqrt[3]{K_{sp}\times 4}\)
• B. \(S = \sqrt[3]{\frac{4}{K_{sp}}}\)
• C. \(S = \sqrt[3]{\frac{K_{sp}}{4}}\)
• D. \(S = \sqrt[4]{\frac{K_{sp}}{27}}\)

Hint:

Write the dissociation of Ag2C2O4 and express Ksp in terms of S.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Silver oxalate is \(\text{Ag}_2\text{C}_2\text{O}_4\). It dissociates as \(\text{Ag}_2\text{C}_2\text{O}_4 \rightleftharpoons 2\text{Ag}^+ + \text{C}_2\text{O}_4^{2-}\).

Step 2: Express ions in solubility S:
\([\text{Ag}^+] = 2S\) and \([\text{C}_2\text{O}_4^{2-}] = S\).

Step 3: Detailed Explanation:
\[ K_{sp} = (2S)^2\cdot S = 4S^3 \]
\[ S^3 = \frac{K_{sp}}{4} \Rightarrow S = \sqrt[3]{\frac{K_{sp}}{4}} \]
Option (A) multiplies instead of dividing, option (B) inverts the fraction, and option (D) has a fourth root, which does not follow from \(K_{sp} = 4S^3\).

Final Answer:
The correct relation is \(S = \sqrt[3]{K_{sp}/4}\), option (C). \[ \boxed{S = \sqrt[3]{\frac{K_{sp}}{4}}} \]