Question

The solubility of salt \(\text{AX}_2\) is \(6\times 10^{-12} \text{mol dm}^{-3}\). What is solubility product of the salt ?

• A. \(2.06\times 10^{-24}\)
• B. \(2.48\times 10^{-24}\)
• C. \(4.32\times 10^{-34}\)
• D. \(8.64\times 10^{-34}\)

Hint:

For AX2, Ksp = 4 s^3, where s is the molar solubility.

Answer 1

The Correct Option is D

Step 1: Write the ion concentrations:
Per formula unit dissolved: one $\text{A}^{2+}$ and two $\text{X}^-$ ions.
So $[\text{A}^{2+}] = 6\times10^{-12}$ M and $[\text{X}^-] = 12\times10^{-12}$ M.

Step 2: Multiply directly:
$K_{sp} = (6\times10^{-12})(12\times10^{-12})^2$.
$(12\times10^{-12})^2 = 144\times10^{-24}$.
$K_{sp} = 6\times144\times10^{-36} = 864\times10^{-36} = 8.64\times10^{-34}$.

Step 3: Why not the others:
Exponent -24 would come from forgetting to cube the power of ten. The value $4.32\times10^{-34}$ comes from using $K_{sp}=2s^3$, which is the wrong stoichiometry for a 1:2 salt.

Final Answer:
$K_{sp} = 8.64\times10^{-34}$, option (D). \[ \boxed{8.64\times 10^{-34} \text{ (D)}} \]