Q.The molar conductivity of a 0.5 mol dm⁻³ solution of $\text{AgNO}_3$ with electrolytic conductivity of $5.76\times10^{-3}\ \text{S cm}^{-1}$ at 298 K is

An electrolyte dissolved in a solvent such as water dissociates into free-moving cations and anions, and it is exactly these free ions that let the solution conduct an electric current when a field is applied — a fundamentally different conduction mechanism from the free-electron conduction of a metal. The conductivity cell — two platinum electrodes of area A, separated by distance l, immersed in the solution — obeys Ohm's law at constant temperature: $V = IR$, where R is the solution's resistance in ohms.

From this single relationship, three related quantities are built up. Resistivity (specific resistance), $\rho$, is defined through $R = \rho(l/A)$, and is the resistance of an electrolyte of unit length and unit cross-sectional area, with SI unit Ωm. Conductance, $C = 1/R$, is measured in siemens (S). Conductivity (specific conductance), $\kappa = 1/\rho$, is the conductance of exactly one cubic metre of the solution, with SI unit S m⁻¹ — a physical property of the solution itself, independent of the particular cell geometry used to measure it. …