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 is wrong?

Unit of cell constant is cm s⁻¹

The statement that is wrong is (3) which says that the unit of cell constant is cm s−1. The correct unit of cell constant is cm⁻¹.

Specific conductance is the conductance of a solution of 1 cm3. The unit of specific conductance is siemens per meter (S m⁻¹).

Cell constant is the ratio of the distance between the electrodes to the area of the electrodes. The unit of cell constant is cm⁻¹.

Equivalent conductance is the conductance of a solution containing 1 equivalent of electrolyte. The unit of equivalent conductance is siemens per mho (S mho⁻¹).

The other statements are correct. The increase in the equivalent conductance of a strong electrolyte solution with dilution is attributed to the increase in ionic mobility. As the solution is diluted, the ions are less likely to interact with each other, which allows them to move more freely. This increase in ionic mobility leads to an increase in the equivalent conductance.