If the molar conductivity (Λₘ) of a 0.050 mol L⁻¹ solution of a monobasic weak acid is 90 S cm² mol⁻¹, its extent (degree) of dissociation will be
[Assume Λ₊⁰ = 349.6 S cm² mol⁻¹ and Λ_-⁰ = 50.4 S cm² mol⁻¹]

CONCEPT:

Molar Conductivity (Λ_m) and Degree of Dissociation (α)

• Molar conductivity (Λ_m) of an electrolyte is the conductivity of a solution containing one mole of electrolyte, divided by the molar concentration.
• For a weak electrolyte, the molar conductivity at any concentration (Λ_m) is related to the molar conductivity at infinite dilution (Λ_m⁰) by the degree of dissociation (α).
• The degree of dissociation (α) is calculated using the formula:

  α = Λ_m / Λ_m⁰

• For a monobasic weak acid, the molar conductivity at infinite dilution is given by:

  Λ_m⁰ = Λ₊⁰ + Λ_-⁰

EXPLANATION:

• Calculate Λ_m⁰:
  • Λ_m⁰ = Λ₊⁰ + Λ_-⁰
  • = 349.6 S cm² mol^-1 + 50.4 S cm² mol^-1
  • = 400 S cm² mol^-1
• Calculate α:
  • α = Λ_m / Λ_m⁰
  • = 90 S cm² mol^-1 / 400 S cm² mol^-1
  • = 0.225

Therefore, the degree of dissociation (α) is 0.225, and the correct answer is Option 3.