Question

The $K_a$ of acetic acid is $2\times {10}^{-5}$. What is the $pH$ of a $0.5M$ solution of acetic acid?

• A. 1
• B. 2
• C. 2.5
• D. 3

Answer 1

Answer: (C)

2.5

Since acetic acid is a weak acid, $C{H}_{3}COOH\leftrightharpoons C{H}_{3}CO{O}^{-}+H^{+}$

Initially $0.500$

At equilibrium $0.5-CCC$

$K_a=\frac{C^2}{0.5-C}=2\times {10}^{-5}$

Ignoring $C$ in the denominator as $0.5>>C$ for weak acid $C{H}_{3}COOH$

$C^2=0.5\times 2\times {10}^{-5}$

$⟹C=10\times {10}^{-6}$

$⟹C=3.16\times {10}^{-3}$

Hence, $\left[H^{+}\right]=3.16\times {10}^{-3}$

$\therefore pH=-\log (3.16\times {10}^{-3})=2.5$

Hence, option $C$ is correct.