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 statement is not correct?

Dilution of a weak electrolyte solution does not affect the either equivalent conductance or molar conductance

The correct answer is option 4. Dilution of a weak electrolyte solution does not affect either the equivalent conductance or molar conductance.

Let us explain each statement in detail to understand why one of them is not correct:

1. When the solution of weak electrolyte is diluted, specific conductivity decreases

Specific Conductivity: Specific conductivity (or conductivity) is the ability of a solution to conduct electricity, measured in Siemens per meter (S/m). It depends on the concentration of ions in the solution.

Effect of Dilution: When a weak electrolyte is diluted, the concentration of ions decreases because the total amount of dissolved substance is spread over a larger volume. Consequently, the specific conductivity decreases because there are fewer ions to carry the electric current.

2. When the solution of weak electrolyte is diluted, molar conductivity increases

Molar Conductivity: Molar conductivity (\(\Lambda_m\)) is the conductivity of a solution divided by its molar concentration. It is a measure of how well a particular concentration of a solute contributes to the overall conductivity.

Effect of Dilution: For a weak electrolyte, dilution increases the degree of dissociation (\(\alpha\)), meaning more ions are present in the solution. Since molar conductivity is calculated as conductivity divided by concentration, as the concentration decreases (due to dilution) and the degree of dissociation increases, the molar conductivity increases.

3. Equivalent conductance of a weak electrolyte solution on dilution increases

Equivalent Conductance: Equivalent conductance (\(\Lambda_e\)) is the conductance of a solution containing one equivalent of the electrolyte, and it is affected by the concentration of ions in the solution.

Effect of Dilution: As a weak electrolyte solution is diluted, the degree of dissociation increases. This results in more ions being present, which increases the equivalent conductance. Essentially, equivalent conductance increases because the number of charge carriers (ions) rises with dilution.

4. Dilution of a weak electrolyte solution does not affect either equivalent conductance or molar conductance

Misconception: This statement is incorrect because dilution does affect both equivalent conductance and molar conductance. As explained earlier:

Equivalent Conductance: Increases with dilution due to increased ionization of the weak electrolyte.

Molar Conductance: Also increases with dilution because molar conductivity takes into account the increased degree of dissociation.

Summary

In summary:

Specific Conductivity decreases with dilution because the concentration of ions decreases. Molar Conductivity increases with dilution because the degree of dissociation increases, leading to more ions contributing to the conductivity. Equivalent Conductance increases with dilution for the same reason—more dissociation leads to more ions.

Thus, the statement "Dilution of a weak electrolyte solution does not affect either equivalent conductance or molar conductance" is incorrect because both properties are affected by dilution.