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.

Weak electrolytes are only partly associated with solutions. The degree of dissociation of weak electrolytes in an aqueous solution

is inversely proportional to the initial concentration of the electrolyte

The correct answer is option 1. is inversely proportional to the initial concentration of the electrolyte.

Let us break down the concept of the degree of dissociation (\(\alpha\)) for weak electrolytes in detail:

Degree of Dissociation (\(\alpha\)): It is defined as the fraction of the total number of electrolyte molecules that dissociate into ions. For a weak electrolyte, this is less than 1 because not all of the electrolyte molecules dissociate.

Equilibrium and Dissociation

Weak Electrolytes: These are substances that do not fully dissociate in solution. Instead, they establish an equilibrium between the undissociated molecules and the ions formed.

For example, consider a weak acid (\(HA\)) that dissociates in water:

\(HA \leftrightarrow H^+ + A^- \)

Equilibrium Constant (\(K_a\)): The equilibrium constant for this dissociation reaction is given by:

\(K_a = \frac{[H^+][A^-]}{[HA]}\)

Here, \( [H^+] \) and \( [A^-] \) are the equilibrium concentrations of the ions, and \( [HA] \) is the concentration of the undissociated acid at equilibrium.

Effect of Initial Concentration

Initial Concentration (\(C\)): This is the concentration of the weak electrolyte before dissociation begins.

Relationship with Degree of Dissociation: According to the equation derived from the equilibrium constant:

\(\alpha = \sqrt{\frac{K_a}{C}}\)

Here, \( \alpha \) is the degree of dissociation, \( K_a \) is the dissociation constant, and \( C \) is the initial concentration of the electrolyte.

Inversely Proportional Relationship

Inversely Proportional: As shown in the equation, \(\alpha\) (the degree of dissociation) is inversely proportional to the square root of the initial concentration (\(C\)):

Higher Initial Concentration: If the initial concentration of the electrolyte is high, the degree of dissociation (\(\alpha\)) is lower because the equilibrium position is less favorable towards ion formation.

Lower Initial Concentration: If the initial concentration is low, the degree of dissociation is higher because the equilibrium shifts more towards the dissociated ions, making it easier for the electrolyte to dissociate.

Practical Implications

Dilution: When you dilute a solution of a weak electrolyte, the initial concentration decreases. According to the inverse proportionality, this results in an increased degree of dissociation. Thus, as the solution becomes more dilute, more of the electrolyte dissociates into ions.

Summary

To summarize, the degree of dissociation (\(\alpha\)) of a weak electrolyte in aqueous solution is inversely proportional to its initial concentration (\(C\)). This means that as the concentration of the electrolyte decreases, its degree of dissociation increases. This relationship is fundamental to understanding the behavior of weak electrolytes in different concentration