Variations of Conductivity with Concentration — Core Principles

Core Principles

Electrolytic solutions conduct electricity due to the movement of ions. The ability to conduct is quantified by specific conductivity ($kappa$) and molar conductivity ($Lambda_m$). Specific conductivity, the conductance of a unit volume, decreases with dilution for both strong and weak electrolytes because the number of ions per unit volume reduces.

Molar conductivity, the conductance of one mole of electrolyte, increases with dilution for both types. For strong electrolytes, this increase is due to reduced inter-ionic attractions and increased ionic mobility, following the Debye-Hückel-Onsager equation ($Lambda_m = \Lambda_m^\circ - A\sqrt{c}$).

For weak electrolytes, the increase is much steeper and primarily due to an increase in the degree of dissociation ($alpha$) as per Ostwald's Dilution Law, which produces more ions. Molar conductivity at infinite dilution ($Lambda_m^\circ$) is the maximum conductivity, obtainable by extrapolation for strong electrolytes, but requiring Kohlrausch's Law for weak electrolytes.

Understanding these variations is crucial for characterizing electrolytes and solving related numerical problems in NEET.

Important Differences

vs Strong Electrolytes vs. Weak Electrolytes (Conductivity Variation)

Aspect	This Topic	Strong Electrolytes vs. Weak Electrolytes (Conductivity Variation)
Specific Conductivity ($kappa$) with Dilution	Decreases (due to reduced ion density per unit volume)	Decreases (due to reduced ion density per unit volume)
Molar Conductivity ($Lambda_m$) with Dilution	Increases moderately (due to reduced inter-ionic attractions and increased ionic mobility)	Increases sharply (primarily due to increased degree of dissociation, producing more ions)
Plot of $Lambda_m$ vs. $sqrt{c}$	Linear, allows extrapolation to find $Lambda_m^\circ$ (Debye-Hückel-Onsager equation)	Non-linear, steep curve, extrapolation not possible to find $Lambda_m^\circ$
Primary factor for $Lambda_m$ increase on dilution	Increased ionic mobility (reduced inter-ionic forces)	Increased degree of dissociation (more ions formed)
Degree of Dissociation ($alpha$)	Approaches 1 (complete dissociation) even at moderate concentrations	Increases significantly with dilution, approaches 1 only at infinite dilution

While specific conductivity decreases with dilution for both strong and weak electrolytes due to reduced ion concentration per unit volume, their molar conductivity trends diverge significantly. Strong electrolytes show a moderate increase in molar conductivity with dilution, primarily due to enhanced ionic mobility as inter-ionic attractions diminish. In contrast, weak electrolytes exhibit a much sharper increase in molar conductivity upon dilution, predominantly because their degree of dissociation increases, generating a greater number of charge-carrying ions. This fundamental difference is also reflected in their respective $Lambda_m$ vs. $sqrt{c}$ plots and the methods used to determine their molar conductivity at infinite dilution.