Conductivity of electrolytes is measured by using conductivity cell which contains two electrodes separated by a fixed distance \(‘l’\) and have an area of cross-section \(A\) The resistance R of conductivity cell is given by the relation

\[R = \frac{\rho l}{A} = \frac{l}{\kappa A}\]

The quantity \(l/A\) for a particular conductivity cell is constant denoted by \(G^*\) and is called cell constant. The cell constant can be determined by using a \(KCl\) solution whose conductivity is known accurately at various concentrations. The cell constant \(G^* = l / A = R\kappa\). The conductances of different solutions can be determine by using Wheatstone bridge principle.  The specific conductance of a solution k is given by

\[\kappa =\frac{G}{R}\]

The total conductance of the solution is the product of specific conductance and volume of the solution \(\kappa ×V\). If the amount of electrolyte dissolved in solution is equal to the gram equivalent weight of the electrolyte, then the total conductance is known as equivalent conductance

\[\Lambda ­eq = 1000K /C\],

where C is the concentration of solution in gram equivalents per litre.

The unit of equivalent conductivity is ­\(\Omega^{−1}cm^2 eq^{−1}\) or \(Scm^2eq^{−1}\). If the amount of electrolyte dissolved in solution is equal to the gram molecular weight of electrolyte, then the total conductance is known as molar conductivity \((\Lambda_M)\).

The unit of molar conductivity is ­­\(\Omega^{−1}cm^2 mol^{−1}\). According to SI system, molar conductance is expressed

as \(S m^2 mol^{−1}\), if concentration is expressed in \(mol\text{ }m^3\). Specific conductance always decreases with the decrease in concentration both for strong and weak electrolytes due to the decrease in the number of ions per unit volume that carry the current in a solution.

Which of the following occurs to the molar conductivity of the solution, when a solution of a weak electrolyte is diluted?

It increases because a mole of the electrolyte produces more ions in a dilution

The correct answer is option 4. It increases because a mole of the electrolyte produces more ions in a dilution.

When a solution of a weak electrolyte is diluted, the molar conductivity (\(\Lambda_m\)) of the solution increases. Here's the detailed explanation for why this occurs:

Understanding Molar Conductivity (\(\Lambda_m\))

Molar Conductivity: It is defined as the conductivity (\(\kappa\)) of the solution divided by the molar concentration (\(C\)) of the electrolyte:

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

where \(\kappa\) is the specific conductivity (conductivity) of the solution and \(C\) is the concentration of the electrolyte.

Effects of Dilution on Molar Conductivity

Degree of Dissociation:

Weak Electrolytes: For weak electrolytes, the degree of dissociation (\(\alpha\)) increases with dilution. As the solution becomes more dilute, more molecules of the weak electrolyte dissociate into ions.

Increase in Ions: As the degree of dissociation increases, the number of ions in the solution rises.

Impact on Conductivity:

Specific Conductivity: Although specific conductivity decreases with dilution because the concentration of ions is lower, the increased degree of dissociation leads to more ions being present in the solution than would be expected if only the initial concentration were considered.

Molar Conductivity:

Molar conductivity is calculated as:

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

As dilution increases the degree of dissociation (\(\alpha\)), the number of ions per mole increases, which compensates for the decrease in specific conductivity, leading to an overall increase in molar conductivity.

Evaluating the Statements

1. It decreases because the weak electrolyte becomes weaker

This statement is incorrect. Dilution does not make the weak electrolyte weaker in a manner that affects molar conductivity directly. The electrolyte's inherent strength remains constant; it's the dissociation that changes.

2. It decreases because a given volume contains less electrolyte

This statement is incorrect. While it's true that a given volume contains less electrolyte in terms of concentration, molar conductivity increases due to the increased degree of dissociation.

3. It increases because a large volume of solution is involved in conducting electricity

This statement is incorrect. This statement is somewhat misleading. The increase in molar conductivity is due to the increased ionization rather than the volume of the solution.

4. It increases because a mole of the electrolyte produces more ions in a dilution

This statement is correct. This statement is correct. As the solution is diluted, the degree of dissociation of the weak electrolyte increases, which means that more ions are produced from each mole of the electrolyte. This results in an increase in molar conductivity.

Summary

The correct explanation for the increase in molar conductivity of a weak electrolyte solution with dilution is: It increases because a mole of the electrolyte produces more ions in a dilution.