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How can you determine limiting molar conductivity, $\left( \wedge {{{}^\circ }_{m}} \right)$ for strong electrolyte and weak electrolyte?

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Last updated date: 13th Jun 2024
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Answer
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Hint: Molar conductivity varies with the concentrations of the electrolyte which can be determined by the equation which includes concentration quantity.

Complete step by step answer:
Let us understand about the molar conductivity of a solution first.
Molar conductivity is the conducting power of one mole of ions formed by dissolving electrolyte in the solution. It determines the efficiency of electrolyte to conduct electricity in the given solution. It can never be constant.

Kohlrausch law-
Molar conductivity of a solution at a given concentration is the conductance of volume V of a solution containing one mole of electrolyte kept between two electrodes with an area of cross section A and distance of unit length.
${{\wedge }_{m}}=\dfrac{K}{C}$
where,
C = concentration
K = specific conductivity
${{\wedge }_{m}}$= molar conductivity
This can also be written as,
${{\wedge }_{m}}$ = KV
where,
V = volume

Limiting molar conductivity for strong and weak electrolytes-
The limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte. This implies the conductivity of the solution at infinite dilution.
To find out the limiting molar conductivity of a strong and weak electrolyte we need to plot a graph of conductivity v/s square root of concentration for the electrolytic solution.
As strong electrolytes always dissociate at infinite dilutions, we can extrapolate the line and can assume the linear plot for them according to the Kohlrausch law.
However the same can’t be used for weak electrolytes as they have lower molar conductivities and lower degree of dissociation at higher concentrations. Thus, we cannot extrapolate the graph at zero concentrations as it's very steep.

Note: Limiting molar conductivities for strong and weak electrolytes depends on the concentration which itself is the reason for the differences. The name suggests the power of dissociation and its conduction (i.e. strong for strong electrolytes and so on).