Calculate the degree of dissociation (α) of acetic acid if its molar conductivity (^m) is 39.05 S cm² mol^–1.

Given λ°(H⁺) = 349.6 S cm²mol^–1 and λ°(CH₃COO^–) = 40.9S cm² mol^–1

Given

limiting molar conductivity of H⁺ = 349.6 S cm²mol^-1

limiting molar conductivity of CH₃COO^- = 40.9 S cm²mol^-1

molar conductivity of acetic acid = 39.05 S cm²mol^-1

limiting molar conductivity of acetic acid =?

we know that limiting molar conductivity of a compound is the sum of limiting molar conductivities of its anion and cation.

So limiting molar conductivity of acetic acid

= (limiting molar conductivity of H⁺ )+ (limiting molar conductivity of CH₃COO^-)

= 349.6 S cm²mol^-1 + 40.9 S cm²mol^-1

= 390.5 S cm²mol^-1

We know that if α is the degree of dissociation then it is approximately equal to the ratio of molar conductivity to limiting molar conductivity

So,

⇒ α = 0.1