The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is $\Lambda_{\mathrm{m} 1}$ and that of 20 moles another identical cell heaving 80 mL NaCl solution is $\Lambda_{\mathrm{m} 2}$, The conductivities exhibited by these two cells are same. The relationship between $\Lambda_{\mathrm{m} 2}$ and $\Lambda_{\mathrm{m} 1}$ is

(A) $\Lambda_{\mathrm{m} 2}=2 \Lambda_{\mathrm{m} 1}$

(B) $\Lambda_{\mathrm{m} 2}=\Lambda_{\mathrm{m} 1} / 2$

(C) $\Lambda_{\mathrm{m} 2}=\Lambda_{\mathrm{m} 1}$

(D) $\Lambda_{\mathrm{m} 2}=4 \Lambda_{\mathrm{m} 1}$

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Redox Reactions and Electrochemistry

The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is

Λ_{m 1}

and that of 20 moles another identical cell heaving 80 mL NaCl solution is

Λ_{m 2}

, The conductivities exhibited by these two cells are same.
The relationship between

Λ_{m 2}

and

Λ_{m 1}

Answer: (A)

Molar conductivity is related to conductivity by:

Λ_{m} = κ \times \frac{1000}{M}

where

M

is molarity.

Since conductivities are equal (

κ_{1} = κ_{2}

\frac{Λ _{m_{1}}}{Λ _{m_{2}}} = \frac{M _{2}}{M _{1}}

For cell 1:

M_{1} = \frac{10 mol}{0.020 L} = 500

M

For cell 2:

M_{2} = \frac{20 mol}{0.080 L} = 250

\frac{Λ _{m_{1}}}{Λ _{m_{2}}} = \frac{250}{500} = \frac{1}{2}

Therefore,

Λ_{m_{2}} = 2 Λ_{m_{1}}

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Single correct option