Question

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

(Given \[\ce{\lambda^{\circ}_{(H^+)}}\] = 349.6 S cm² mol⁻¹ and \[\ce{\lambda^{\circ}_{(CH_3COO^-)}}\] = 40.95 S cm² mol⁻¹)

Answer 1

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

α = `Lambda_m/Lambda^circ`    ... (1)

Where,

α = Degree of dissociation of the electrolyte

Λ_m = Molar conductivity

Λ° = 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:

\[\ce{\Lambda^{\circ}_{\text{acetic acid}} = \lambda^{\circ}_{(H^+)} + \lambda^{\circ}_{(CH_3COO^-)}}\]

 = 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) = `Lambda_m/Lambda^circ`

= \[\ce{\frac{39.05}{390.7}}\]

= 0.0999

≅ 0.1

Hence, the degree of dissociation is 0.1.