Question

Consider the following data for KCl solution at a particular temperature:

What is the value of the limiting molar conductivity?

• A. 150.1 S cm\(^2\) mol\(^{-1}\)
• B. 149.2 S cm\(^2\) mol\(^{-1}\)
• C. 151.1 S cm\(^2\) mol\(^{-1}\)
• D. 152.1 S cm\(^2\) mol\(^{-1}\)

Hint:

The Debye-Hückel-Onsager plot is linear with \(\sqrt{C}\) on the x-axis.
Always convert the concentration \(C\) to \(\sqrt{C}\) before doing calculations, as using \(C\) directly is a common mistake in this type of problem.

Answer 1

The Correct Option is A

To find the limiting molar conductivity (\(\Lambda_0\)) of KCl at a particular temperature, we can use the given data of molar conductivities at different concentrations and apply Kohlrausch's Law of Independent Migration of Ions.

Kohlrausch's Law states that the molar conductivity of an electrolyte at infinite dilution (limiting molar conductivity) can be expressed as the sum of the individual contributions of the cations and anions:

\(\Lambda_0 = \lambda_0^+ + \lambda_0^-\)

However, in this problem, we will estimate \(\Lambda_0\) by extrapolating the data provided for the molar conductivity at different concentrations:

Here, the data shows molar conductivity (\(\Lambda_m\)) at concentrations 1 × 10^-4 mol L^-1 and 9 × 10^-4 mol L^-1\ with values 149.1 and 147.1 S cm² mol^-1 respectively.

1. To estimate \(\Lambda_0\), plot the molar conductivity against the square root of the concentration, which typically gives a straight line, following the equation:

\(\Lambda_m = \Lambda_0 - K c^{1/2}\)

1. Extrapolate the straight line to zero concentration (\(c = 0\)) to find \(\Lambda_0\).

Given the data:

Concentration (mol L-1)	Molar Conductivity (S cm2 mol-1)
1 × 10-4	149.1
9 × 10-4	147.1

1. Extrapolating using the linear relation would show that as the concentration approaches zero, the molar conductivity would approach 150.1 S cm² mol^-1.

Therefore, the limiting molar conductivity for KCl is:

150.1 S cm² mol^-1

Hence, the correct option is: 150.1 S cm² mol^-1.