What is percent dissociation of acetic acid in it's $0.01 \mathrm{M}$ solution if dissociation constant of acid is $1.34 \times 10^{-6}$ ?

• A

  $13.4 \%$
• B

  $4.02 \%$
• C

  $2.68 \%$
• Correct answer
  D

  $1.15 \%$

Solution

$\begin{aligned} & \mathrm{K}_{\mathrm{a}}=\frac{\mathrm{C} \alpha^2}{1-\alpha} \quad 1-\alpha \simeq 1 \\ & \mathrm{~K}_{\mathrm{a}}=\mathrm{Co}^2 \\ & \alpha=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{C}}} \\ & \% \alpha=\sqrt{\frac{\mathrm{K}_{\mathrm{a}}}{\mathrm{C}}} \times 100=\sqrt{\frac{1.34 \times 00^{-6}}{0.01}} \times 100 \\ & =1.15 \% \\ & \end{aligned}$

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