Question

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

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

Answer 1

Answer: (A)

Given, $pH$ of $0.01\,M\, CH _{3} COOH$ solution
$=5.0$
Concentration, $C$ of the solution $=0.01\, M$
$\left[ H ^{+}\right] =1 \times 10^{- pH }$
$=1 \times 10^{-5} mol / L =1 \times 10^{-5} M$
Since, acetic acid is a weak acid and for weak acid,
$\left[ H ^{+}\right] =\sqrt{K_{a} \cdot C}$
$\left[ H ^{+}\right]^{2} =K_{a} \cdot C$
or $K_{a} =\frac{\left[ H ^{+}\right]^{2}}{C}$
$=\frac{\left(1 \times 10^{-5}\right)^{2}}{0.01}$
$=1 \times 10^{-8}$