Question

The solubility product of a sparingly soluble salt AX is \(4.9 \times 10^{-13}\). What is its solubility in \(\text{mol dm}^{-3}\) ?

• A. \(2.4 \times 10^{-13}\)
• B. \(4.9 \times 10^{-7}\)
• C. \(7.0 \times 10^{-7}\)
• D. \(7.0 \times 10^{-13}\)

Hint:

For 1:1 salt → \(K_{sp} = s^2\)

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
For a binary sparingly soluble salt of the type AX, it dissociates into one cation and one anion. The solubility product (\(K_{sp}\)) is related to the molar solubility (\(s\)).
Step 2: Key Formula or Approach:
\[ \text{AX(s)} \rightleftharpoons \text{A}^+(\text{aq}) + \text{X}^-(\text{aq}) \] \[ K_{sp} = [\text{A}^+][\text{X}^-] = (s)(s) = s^2 \implies s = \sqrt{K_{sp}} \] Step 3: Detailed Explanation:
Given \(K_{sp} = 4.9 \times 10^{-13}\).
\[ s = \sqrt{4.9 \times 10^{-13}} = \sqrt{49 \times 10^{-14}} \] \[ s = 7.0 \times 10^{-7}\text{ moldm}^{-3} \] Step 4: Final Answer:
The molar solubility is \(7.0 \times 10^{-7}\text{ moldm}^{-3}\).