Q5 / 160 · AP EAMCET 2010 · Chemistry

The $\mathrm{pH}$ of $0.01 \mathrm{M}$ solution of acetic acid is 5.0. What are the values of $\left[\mathrm{H}^{+}\right]$and $K_a$ respectively?

  • Correct answer
    A
    $1 \times 10^{-5} \mathrm{M}, 1 \times 10^{-8}$
  • B
    $1 \times 10^{-5} \mathrm{M}, 1 \times 10^{-9}$
  • C
    $1 \times 10^{-4} \mathrm{M}, 1 \times 10^{-8}$
  • D
    $1 \times 10^{-3} \mathrm{M}, 1 \times 10^{-8}$

Solution

Given, $\mathrm{pH}$ of $0.01 \mathrm{M} \mathrm{CH}_3 \mathrm{COOH}$ solution $=5.0$ Concentration, $C$ of the solution $=0.01 \mathrm{M}$ $\left[\mathrm{H}^{+}\right]=1 \times 10^{-\mathrm{pH}}$ $=1 \times 10^{-5} \mathrm{~mol} / \mathrm{L}=1 \times 10^{-5} \mathrm{M}$ Since, acetic acid is a weak acid and for weak acid, $\left[\mathrm{H}^{+}\right]=\sqrt{K_a \cdot C}$ $\left[\mathrm{H}^{+}\right]^2=K_a \cdot C$ $K_a=\frac{\left[\mathrm{H}^{+}\right]^2}{C}$ $=\frac{\left(1 \times 10^{-5}\right)^2}{0.01}$ $=1 \times 10^{-8}$

Hence, the correct answer is option: 'A'.

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