For a strong electrolyte salt XY, the plot of _m versus √(c) has slope -90.0 S cm²mol⁻3/2L¹/2 at 298 K. At 0.01 M, _m=145.0 S cm²mol⁻¹. The limiting molar conductivity of Y⁻ ion, λ⁰_Y⁻ (in S cm²mol⁻¹), is: [Given λ⁰_X⁺=74.0 S cm²mol⁻¹]

Solution & Explanation

Concept: Debye-Huckel-Onsager (Kohlrausch) behaviour of a strong electrolyte: Λ_m = Λ°_m - A√c, so a plot of Λ_m versus √c is a straight line of slope -A and intercept Λ°_m. Given slope = -90.0, so A = 90.0, and at c = 0.01 M, √c = 0.1, Λ_m = 145.0. Find the limiting molar conductivity from the line: Λ°_m = Λ_m + A√c = 145.0 + 90.0 × 0.1 = 145.0 + 9.0 = 154.0 S cm² mol⁻¹. For the 1:1 salt XY, Kohlrausch's law of independent migration gives: Λ°_m(XY) = λ°(X⁺) + λ°(Y⁻). 154.0 = 74.0 + λ°(Y⁻). λ°(Y⁻) = 154.0 - 74.0 = 80.0 S cm² mol⁻¹. Hence λ°(Y⁻) = 80.0 — answer (A). Trap: the measured Λ_m at 0.01 M (145) is NOT the limiting value; you must add back A√c to reach infinite dilution before applying Kohlrausch's law.