Question

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

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

Answer 1

The degree of dissociation of a weak electrolyte is given by the following relation

α = Λ_m / Λ⁰ ... Equation (1)

where α is the degree of dissociation of the electrolyte, Λ_m is the molar conductivity and Λ⁰ is the molar conductivity at infinite dilution.

We are given that the ionic molar conductivity at infinite dilution of acetate and hydrogen ions are 349.8 and 40.9 S cm² mol^-1 respectively. Hence the limiting molar conductivity of acetic acid would be written as:

Λ⁰acetic acid = λ⁰(H⁺) + λ⁰(CH₃COO^-)

 = 40.9 + 349.8

= 390.7 cm² mol^-1

Now, since we are given that the molar conductivity of acetic acid is Λ_m = 39.05 S cm² mol^-1

Therefore, substituting the values in equation (1), we get:

Degree of dissociation of acetic acid = α = Λ_m/ Λ⁰ = `39.05/390.7 = 0.0999 " ≅ " 0.1`