Conductance Of Electrolytic Solutions

Conductance and Conductivity

Electrical resistance ($R$) is a measure of a material's opposition to current flow. The resistance of any object is directly proportional to its length ($l$) and inversely proportional to its cross-sectional area ($A$).

$R = \rho \frac{l}{A}$

Example 2.4: Molar Conductivity Calculation

Problem. The resistance of a conductivity cell filled with $0.1\text{ mol L}^{-1}$ KCl solution is $100\ \Omega$. If the resistance of the same cell when filled with $0.02\text{ mol L}^{-1}$ KCl solution is $520\ \Omega$, calculate the conductivity and molar conductivity of $0.02\text{ mol L}^{-1}$ KCl solution. (Given: Conductivity of $0.1\text{ mol L}^{-1}$ KCl solution is $1.29\text{ S m}^{-1}$).

Variation of Conductivity with Concentration

When you dilute an electrolyte solution, its behavior changes. Conductivity ($\kappa$) always decreases with dilution for both strong and weak electrolytes. This is because the number of ions per unit volume carrying the current decreases as you add more solvent.

Example 2.7: Applying Kohlrausch's Law

Problem. Calculate $\Lambda_m^\circ$ for $\text{CaCl}_2$ and $\text{MgSO}_4$ using Kohlrausch law of independent migration of ions. (Given limiting ionic conductivities in $\text{S cm}^2\text{ mol}^{-1}$: $\lambda^\circ(\text{Ca}^{2+}) = 119.0$, $\lambda^\circ(\text{Cl}^-) = 76.3$, $\lambda^\circ(\text{Mg}^{2+}) = 106.0$, $\lambda^\circ(\text{SO}_4^{2-}) = 160.0$)