Question

The solubility of sparingly soluble, salt \(\mathrm{AX}_2\) is \(1.5 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3}\). What is its solubility product?

• A. \(1.65\times 10^{-7}\)
• B. \(1.35\times 10^{-8}\)
• C. \(2.25\times 10^{-8}\)
• D. \(1.15\times 10^{-7}\)

Hint:

For AX2 the solubility product is four times the cube of the solubility.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
\(\text{AX}_2\rightleftharpoons\text{A}^{2+}+2\text{X}^{-}\). If solubility is \(s\), then \([\text{A}^{2+}]=s\) and \([\text{X}^{-}]=2s\).

Step 2: Expression
\(K_{sp}=s\times(2s)^{2}=4s^{3}\).

Step 3: Calculation
\(K_{sp}=4\times(1.5\times10^{-3})^{3}=4\times3.375\times10^{-9}=1.35\times10^{-8}\).

Step 4: Compare the options
Option (B).

Final Answer:
The solubility product is \(1.35\times10^{-8}\). \[ \boxed{\text{(B) }1.35\times 10^{-8}} \]