The molar conductivity of $0.007 \mathrm{M}$ acetic acid is $20 \mathrm{S}{ \mathrm{cm}}^2{ \mathrm{mol}}^{-1}.$ What is the dissociation constant of acetic acid? Choose the correct option.

$$\begin{gathered} {\mathrm{\lambda }}_{{\mathrm{H}}^{+}}^{\circ }=350 \mathrm{S} {\mathrm{cm}}^2 {\mathrm{mol}}^{-1} \\ {\mathrm{\lambda }}_{{\mathrm{CH}}_3{\mathrm{COO}}^{-}}^{\circ }=50 \mathrm{S} {\mathrm{cm}}^2 {\mathrm{mol}}^{-1} \end{gathered}$$

• A

  $1.75\times {10}^{-4} \mathrm{mol}{ \mathrm{L}}^{-1}$
• B

  $2.50\times {10}^{-4} \mathrm{mol}{ \mathrm{L}}^{-1}$
• Correct answer
  C

  $1.75\times {10}^{-5} \mathrm{mol}{ \mathrm{L}}^{-1}$
• D

  $2.50\times {10}^{-5} \mathrm{mol}{ \mathrm{L}}^{-1}$

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