The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is ${\mathrm{\Lambda }}_{{\mathrm{m}}_1}$ and that of 20 moles another identical cell having 80 mL NaCl solution is ${\mathrm{\Lambda }}_{{\mathrm{m}}_2}$, The conductivities exhibited by these two cells are same.

The relationship between ${\mathrm{\Lambda }}_{{\mathrm{m}}_2}\text{ and }{\mathrm{\Lambda }}_{{\mathrm{m}}_1}$ is

The relationship between the molar conductivities (Λ_m) of the two cells can be understood by considering how conductivity depends on the concentration of the solution. Molar conductivity (Λ_m) is given by the formula:

Λ_m = κ / C

Where κ is the conductivity and C is the concentration of the solution.

For identical conductivity cells, the conductivity is proportional to the molar concentration. Therefore, the molar conductivity will vary based on the concentration of the NaCl solution.

GIVEN

• The first cell has 10 moles of NaCl in 20 mL solution (concentration C₁ = 10 / 20 = 0.5 mol/L).
• The second cell has 20 moles of NaCl in 80 mL solution (concentration C₂ = 20 / 80 = 0.25 mol/L).

Now, since the conductivities of the two cells are the same (κ₁ = κ₂), the molar conductivity is inversely proportional to the concentration. Thus, we have:

Λ_m ∝ 1 / C

Therefore, the molar conductivity for the second cell will be:

Λ_m2 = 2 Λ_m1

Final Answer

Hence, the correct answer is:

Λ_m2 = 2 Λ_m1