Question

The value of [H\(_3\)O\(^+\)] in mol lit\(^{-1}\) of 0.001 M acetic acid solution (\( K_a = 1.8 \times 10^{-5} \)) is _________.

• A. 1.34 × 10\(^{-1}\)
• B. 1.34 × 10\(^{-2}\)
• C. 1.34 × 10\(^{-3}\)
• D. 1.34 × 10\(^{-4}\)

Answer 1

The Correct Option is C

For acetic acid (weak acid), \( \text{CH}_3\text{COOH} \leftrightharpoons \text{H}^+ + \text{CH}_3\text{COO}^- \),
\[ K_a = \frac{[\text{H}^+][\text{CH}_3\text{COO}^-]}{[\text{CH}_3\text{COOH}]}. \] Initial concentration \( C = 0.001 \, \text{M} \), \( K_a = 1.8 \times 10^{-5} \).
Let \( [\text{H}^+] = x = [\text{CH}_3\text{COO}^-] \), \( [\text{CH}_3\text{COOH}] \approx 0.001 - x \approx 0.001 \).
\[ 1.8 \times 10^{-5} = \frac{x^2}{0.001} \quad \Rightarrow \quad x^2 = 1.8 \times 10^{-8} \quad \Rightarrow \quad x = \sqrt{1.8 \times 10^{-8}} \approx 1.3416 \times 10^{-3} \, \text{M}. \] Answer: 1.34 × 10\(^{-3}\) M.