Electrochemistry - Conductance of Electrolytic Solutions

Resistance ($R$): The opposition to the flow of current. It is directly proportional to length ($l$) and inversely proportional to the area of cross-section ($A$): $R = \rho \frac{l}{A}$, where $\rho$ is resistivity.

Conductance ($G$): The ease with which current flows through a conductor. It is the reciprocal of resistance: $G = \frac{1}{R}$. Unit: $S$ (Siemens) or $\Omega^{-1}$.

Conductivity (Specific Conductance, $\kappa$): The inverse of resistivity: $\kappa = \frac{1}{\rho}$. It represents the conductance of a solution of $1\text{ cm}$ length and $1\text{ cm}^2$ area of cross-section.

Cell Constant ($G^*$): For a given cell, it is the ratio of the distance between electrodes ($l$) to the area of the electrodes ($A$): $G^* = \frac{l}{A}$. Also, $\kappa = G \times G^*$.

Molar Conductivity ($\Lambda_m$): The conducting power of all the ions produced by dissolving one mole of an electrolyte in solution: $\Lambda_m = \frac{\kappa}{C}$.

Variation with Concentration: $\kappa$ always decreases with a decrease in concentration (dilution) because the number of ions per unit volume decreases. However, $\Lambda_m$ increases with dilution as the total volume containing one mole of electrolyte increases.

Kohlrausch's Law of Independent Migration of Ions: At infinite dilution, the limiting molar conductivity of an electrolyte is the sum of the individual contributions of its constituent ions: $\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$.

Degree of Dissociation ($\alpha$): For weak electrolytes, the ratio of molar conductivity at concentration $C$ to the limiting molar conductivity: $\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$.