The molar conductance of an infinitely dilute solution of ammonium chloride was found to be $185~\mathrm{S~cm}^2~\mathrm{mol}^{-1}$ and the ionic conductance of hydroxyl and chloride ions are 170 and $70~\mathrm{S~cm}^2~\mathrm{mol}^{-1}$, respectively. If molar conductance of 0.02 M solution of ammonium hydroxide is $85.5~\mathrm{S~cm}^2~\mathrm{mol}^{-1}$, its degree of dissociation is given by $x \times 10^{-1}$. The value of x is ______. (Nearest integer)

JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Redox Reactions and Electrochemistry

The molar conductance of an infinitely dilute solution of ammonium chloride was found to be

185 S cm^{2} mol^{- 1}

and the ionic conductance of hydroxyl and chloride ions are 170 and

70 S cm^{2} mol^{- 1}

, respectively. If molar conductance of 0.02 M solution of ammonium hydroxide is

85.5 S cm^{2} mol^{- 1}

, its degree of dissociation is given by

x \times 1 0^{- 1}

. The value of x is ______. (Nearest integer)

Answer: 3

At infinite dilution the molar conductance of ammonium chloride is the sum of its ionic conductances, so the ammonium ion contributes

185 - 70 = 115 S c m^{2} mo l^{- 1}

. By Kohlrausch's law the limiting molar conductance of ammonium hydroxide is the sum of the ammonium and hydroxide contributions,

115 + 170 = 285 S c m^{2} mo l^{- 1}

. The degree of dissociation is the ratio of the measured molar conductance to this limiting value,

α = \frac{85.5}{285} = 0.3 = 3 \times 1 0^{- 1}

. The value of

x

3

JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Integer answer