Question

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

• A. $\Lambda_{ m 2}=2 \Lambda_{ m 1}$
• B. $\Lambda_{ m 2}=\Lambda_{ m 1} / 2$
• C. $\Lambda_{ m 2}=\Lambda_{ m 1}$
• D. $\Lambda_{ m 2}=4 \Lambda_{ m 1}$

Answer 1

The Correct Option is A

To find the relationship between the molar conductivities \(\Lambda_{m1}\) and \(\Lambda_{m2}\) of two solutions, we first need to understand the concept of molar conductivity and its relation to volume and moles.

Molar Conductivity (\(\Lambda_m\)): Molar conductivity is defined as the conductivity of a solution divided by the molar concentration of the solute. It is represented by the formula:

\(\Lambda_m = \frac{K}{C}\)

where \(K\) is the conductivity and \(C\) is the concentration of the solution in moles per liter (M).

In this problem, we are given two solutions:

• First solution has 10 moles in 20 mL, with molar conductivity \(\Lambda_{m1}\).
• Second solution has 20 moles in 80 mL, with molar conductivity \(\Lambda_{m2}\).

The question states that the conductivities (\(K\)) of these two cells are the same. Hence:

\(K_1 = K_2\)

For the first cell:

\(\Lambda_{m1} = \frac{K}{10 \text{ moles/20 mL in L}}\)

The concentration for the first solution:

\(C_1 = \frac{10 \text{ moles}}{0.020 \text{ L}} = 500 \text{ moles/L}\)

Substituting in the formula for molar conductivity:

\(\Lambda_{m1} = \frac{K}{500}\)

For the second cell:

\(\Lambda_{m2} = \frac{K}{20 \text{ moles/80 mL in L}}\)

The concentration for the second solution:

\(C_2 = \frac{20 \text{ moles}}{0.080 \text{ L}} = 250 \text{ moles/L}\)

Substituting in the formula for molar conductivity:

\(\Lambda_{m2} = \frac{K}{250}\)

Since the conductivities are the same, \(K_1 = K_2\), we can equate:

\(\frac{K}{250} = \Lambda_{m2}\) and \(\frac{K}{500} = \Lambda_{m1}\)

From these, we find:

\(\Lambda_{m2} = 2 \Lambda_{m1}\)

Thus, the correct answer is: \(\Lambda_{ m 2} = 2 \Lambda_{ m 1}\)