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: Set up the equilibrium table:
If $S$ mol/L dissolves, we get $2S$ of silver ions and $S$ of oxalate ions.

Step 2: Solve:
$K_{sp} = 4S^3$. Divide by 4 and take the cube root. This gives $S = (K_{sp}/4)^{1/3}$, which is option (C). The salt has the $\text{A}_2\text{B}$ type, so the factor is 4 and the root is a cube root.

Final Answer:
$S = \left(\frac{K_{sp}}{4}\right)^{1/3}$. \[ \boxed{S = \sqrt[3]{\frac{K_{sp}}{4}}} \]