Equivalent Conductivity Calculation

The degree of dissociation of a weak electrolyte equals the ratio of its molar conductivity at a given concentration to its molar conductivity at infinite dilution, α = Λ_m/Λ°_m. This follows from Arrhenius's theory, since only the dissociated fraction of acetic acid contributes free ions to conduction. Substituting the given data, α = 49/390 = 0.1256, which rounds to about 0.126. This means roughly 12.6 percent of the acetic acid molecules are ionised at this dilution, consistent with acetic acid being a weak acid. Option 0.063 wrongly halves the correct ratio. Option 0.13 is a loose rounding but less precise than 0.126. Option 0.50 grossly overestimates dissociation, which would describe a moderately strong acid rather than acetic acid. This calculation directly applies Kohlrausch's law and Arrhenius theory from NCERT electrochemistry. Working through the logic step by step, rather than memorising the result, makes it clear why weak acid governs the behaviour seen here. A common JEE pitfall is to ignore the role of degree of dissociation, yet it is exactly this factor that distinguishes the correct answer from the tempting alternatives. Plausibility check: a value near 0.13 is physically reasonable for a dilute weak acid, and using it in the dissociation-constant expression reproduces the known K_a near 1.8 × 10^-5, confirming consistency.