Question

The solubility product of sparingly soluble salt BA is \(4\times 10^{-13}\). Calculate the \([\text{A}^-]\) if \([\text{B}^+]\) is \(1\times 10^{-6} \text{M}\).

• A. \(2\times 10^{-7} \text{M}\)
• B. \(3\times 10^{-7} \text{M}\)
• C. \(4\times 10^{-7} \text{M}\)
• D. \(5\times 10^{-7} \text{M}\)

Hint:

For BA, Ksp is the product of the two ion concentrations.

Answer 1

The Correct Option is C

Step 1: Write the Ksp expression
The salt dissociates as \(BA \rightleftharpoons B^+ + A^-\). So \(K_{sp} = [B^+][A^-]\).

Step 2: Substitute
\[ [A^-] = \frac{K_{sp}}{[B^+]} = \frac{4\times 10^{-13}}{1\times 10^{-6}} = 4\times 10^{-7}\ \text{M} \]

Step 3: Check
Other options such as \(2\times 10^{-7}\) would need \(K_{sp} = 2\times 10^{-13}\), which does not match the given data.

Final Answer:
The concentration of A- is 4 x 10^-7 M. \[ \boxed{\text{(C)}\ 4\times 10^{-7}\ \text{M}} \]