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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?
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The correct answer is:
$1 \times 10^{-5} \mathrm{M}, 1 \times 10^{-8}$
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,
$\left[\mathrm{H}^{+}\right]=\sqrt{K_a \cdot C}$
$\left[\mathrm{H}^{+}\right]^2=K_a \cdot C$
$K_a=\frac{\left[\mathrm{H}^{+}\right]^2}{C}$
$=\frac{\left(1 \times 10^{-5}\right)^2}{0.01}$
$=1 \times 10^{-8}$
$=5.0$
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,
$\left[\mathrm{H}^{+}\right]=\sqrt{K_a \cdot C}$
$\left[\mathrm{H}^{+}\right]^2=K_a \cdot C$
$K_a=\frac{\left[\mathrm{H}^{+}\right]^2}{C}$
$=\frac{\left(1 \times 10^{-5}\right)^2}{0.01}$
$=1 \times 10^{-8}$
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