A weak monobasic acid has K_a = 1.8x 10^-5 and limiting molar conductivity 390.5 S cm^2 mol^-1. Assuming alpha ll 1, the molar conductivity of its 0.10 M solution, in S cm^2 mol^-1, is closest to

JEE Main levelSingle correct optionDifficulty 2 of 3ec202

A weak monobasic acid has $K_{a} = 1.8 \times 1 0^{- 5}$ and limiting molar conductivity $390.5 S c m^{2} mo l^{- 1}$ . Assuming $α ≪ 1$ , the molar conductivity of its $0.10 M$ solution, in $S c m^{2} mo l^{- 1}$ , is closest to

Ostwald's dilution law with

α ≪ 1

K_{a} \approx c α^{2}

, so

α = K_{a} / c = 1.8 \times 1 0^{- 5} /0.10 = 1.8 \times 1 0^{- 4} = 0.0134

Λ_{m} = α Λ_{m}^{\circ} = 0.0134 \times 390.5 = 5.24 S c m^{2} mo l^{- 1}

. Using

α = K_{a} / c

without the square root gives

0.0703