Resistance of 0.2 M solution of an electrolyte is $50 \Omega$. The specific conductance of the solution is $1.4 \mathrm{~S} \mathrm{~m}^{-1}$. The resistance of 0.5 M solution of the same electrolyte is $280 \Omega$. The molar conductivity of 0.5 M solution of the electrolyte in $\mathrm{S} \mathrm{m}^{2} \mathrm{~mol}^{-1}$ is:

JEE Main · 2014 · 06 Apr 2014 · Offline · Redox Reactions and Electrochemistry

Resistance of 0.2 M solution of an electrolyte is

50Ω

. The specific conductance of the solution is

1.4 S m^{- 1}

. The resistance of 0.5 M solution of the same electrolyte is

280Ω

. The molar conductivity of 0.5 M solution of the electrolyte in

S m^{2} mol^{- 1}

is:

Answer: (C)

First pin down the cell constant from the

0.2

M solution:

\frac{ℓ}{A} = κ R = 1.4 \times 50 = 70

^{- 1}

. For the

0.5

M solution the same cell gives

κ = \frac{1}{R} \cdot \frac{ℓ}{A} = \frac{70}{280} = 0.25

S/m. Molar conductivity is

Λ_{m} = \frac{κ}{C}

with

C = 0.5

= 500

mol/m

^{3}

, so

Λ_{m} = \frac{0.25}{500} = 5 \times 1 0^{- 4}

S m

^{2}

mol

^{- 1}

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option