A 0.010 M solution of a weak monobasic acid HA is placed in a conductivity cell of cell constant 0.39 cm^-1 and shows a resistance of 1000 Omega. The limiting molar conductivity of HA is 390 S cm^2 mol^-1. The pH of the solution is

JEE Advanced levelSingle correct optionDifficulty 3 of 3ec201

A $0.010 M$ solution of a weak monobasic acid HA is placed in a conductivity cell of cell constant $0.39 c m^{- 1}$ and shows a resistance of $1000 Ω$ . The limiting molar conductivity of HA is $390 S c m^{2} mo l^{- 1}$ . The pH of the solution is

κ = G^{*} / R = 0.39/1000 = 3.9 \times 1 0^{- 4} S c m^{- 1}

Λ_{m} = 1000 κ / c = 1000 \times 3.9 \times 1 0^{- 4} /0.010 = 39 S c m^{2} mo l^{- 1}

α = 39/390 = 0.10

, so

[H X^{+}] = c α = 0.010 \times 0.10 = 1.0 \times 1 0^{- 3} M

and

pH = 3

. Taking the acid as fully dissociated gives pH 2.