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.

The increase in equivalent conductance of a weak electrolyte solution with dilution is attributed to

both 1 and 2

The correct answer is option 3. both 1 and 2.

Let us delve into the reasons why the equivalent conductance of a weak electrolyte increases with dilution.

Equivalent Conductance (\( \Lambda \)): Equivalent conductance is defined as the conductance of a solution containing one equivalent of electrolyte, placed between two electrodes one centimeter apart.

For weak electrolytes, such as acetic acid (\( CH_3COOH \)), the increase in equivalent conductance with dilution can be explained by two main factors:

1. Increase in Degree of Dissociation:

Weak Electrolytes: Weak electrolytes do not fully dissociate in solution. Instead, they exist in equilibrium between the undissociated molecules and the dissociated ions.

Degree of Dissociation (\( \alpha \)): The degree of dissociation is the fraction of the total number of electrolyte molecules that dissociate into ions. For a weak electrolyte, the degree of dissociation increases as the solution is diluted.

Effect of Dilution: According to Le Chatelier's principle, diluting the solution shifts the dissociation equilibrium towards the dissociated ions. Therefore, more molecules dissociate into ions as the dilution increases.

Impact on Conductance: As more ions are produced, the number of charge carriers in the solution increases, leading to an increase in the equivalent conductance.

2. Increase in Ionic Mobility:

Inter-ionic Attraction: In a concentrated solution, the ions are closer together, leading to stronger inter-ionic attractions. These attractions impede the movement of ions, reducing their mobility.

Effect of Dilution: Diluting the solution reduces the concentration of ions, thereby decreasing the inter-ionic attractions. This reduction allows the ions to move more freely.

Ionic Mobility: With less hindrance, the mobility of the ions increases. Higher mobility of ions results in higher conductance because ions can travel more efficiently through the solution.

To summarize, the increase in equivalent conductance of a weak electrolyte solution with dilution is due to:

Increased Degree of Dissociation: More molecules dissociate into ions as the solution is diluted, leading to more charge carriers.

Increased Ionic Mobility: The ions move more freely in a dilute solution due to decreased inter-ionic attractions, enhancing the mobility and therefore the conductance.

Therefore, both the increase in the degree of dissociation and the increase in ionic mobility contribute to the rise in equivalent conductance with dilution for weak electrolytes.

So, the correct answer is: both 1 and 2.