Electrochemistry - Conductance in electrolytic solutions

Ohm's Law states that the current flowing through a conductor is directly proportional to the potential difference across it: $V = IR$.

Resistance ($R$) is given by $R = \rho \frac{l}{A}$, where $\rho$ is the resistivity, $l$ is the length, and $A$ is the area of cross-section. The unit is Ohm ($\Omega$).

Conductance ($G$) is the reciprocal of resistance: $G = \frac{1}{R}$. Its unit is $Siemens$ ($S$) or $\Omega^{-1}$.

Conductivity (Specific Conductance, $\kappa$) is the reciprocal of resistivity: $\kappa = \frac{1}{\rho} = G \times \frac{l}{A}$. It represents the conductance of $1$ $cm^3$ of the electrolytic solution.

Cell Constant ($G^*$) is defined as the ratio of distance between electrodes ($l$) to the area of cross-section ($A$): $G^* = \frac{l}{A}$. Thus, $\kappa = G \times G^*$.

Molar Conductivity ($\Lambda_m$) is the conducting power of all the ions produced by dissolving $1$ mole of an electrolyte in solution: $\Lambda_m = \frac{\kappa \times 1000}{M}$, where $M$ is Molarity.

Equivalent Conductivity ($\Lambda_{eq}$) is the conducting power of all the ions produced by dissolving $1$ gram equivalent of an electrolyte: $\Lambda_{eq} = \frac{\kappa \times 1000}{N}$, where $N$ is Normality.

Variation with Dilution: Conductivity ($\kappa$) decreases with dilution because the number of ions per unit volume decreases. However, Molar Conductivity ($\Lambda_m$) and Equivalent Conductivity ($\Lambda_{eq}$) increase with dilution.

Kohlrausch's Law states that 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 can be calculated as $\alpha = \frac{\Lambda_m^c}{\Lambda_m^\circ}$.