At 300 K, the conductivity of 0.01 mol dm^-3 aqueous solution of acetic acid is $19.5\times {10}^{-5}\mathrm{mho}{\mathrm{cm}}^{-1}$ and limiting molar conductivity of acetic acid at the same temperature is $390\mathrm{mho}{\mathrm{cm}}^2{\mathrm{mol}}^{-1}$. The degree of dissociation of acetic acid is

Concentration (C) = 0.01 mol dm⁻³ = 10 mol m⁻³.

Conductivity (K) = 19.5 × 10⁻⁵ S cm⁻¹ = 19.5 × 10⁻³ S m⁻¹

Limiting molar conductivity(∧^∘m) = 390 S cm² mol⁻¹ = 390×10⁻⁴ S m² mol⁻¹
$\mathrm{Molar} \mathrm{Conductivity} \left({\wedge }^{\mathrm{m}}\right)=\frac{\mathrm{K}}{\mathrm{C}}=\frac{19.5\times {10}^{-3} \mathrm{S} {\mathrm{m}}^{-1}}{10 \mathrm{mol} {\mathrm{m}}^{-3}}=19.5\times {10}^{-4} \mathrm{S} {\mathrm{m}}^2 {\mathrm{mol}}^{-1}$

The degree of dissociation is determined as:

$\mathrm{Degree} \mathrm{of} \mathrm{dissociation} \left(\mathrm{\alpha }\right)=\frac{{\wedge }^{\mathrm{m}}}{{\wedge }_{\mathrm{m}}^0}=\frac{19.5\times {10}^{-4} \mathrm{S} {\mathrm{m}}^2 {\mathrm{mol}}^{-1}}{390\times {10}^{-4} \mathrm{S} {\mathrm{m}}^2 {\mathrm{mol}}^{-1}}=0.05=5.0\times {10}^{-2}$