Conductivity & Kohlrausch's Law
Master the flow of ions. Decode Specific vs. Molar Conductivity, conquer the dilution traps, and use Kohlrausch's Law to unlock weak electrolytes.
Module Focus: The Resistance of Solutions
Electrolytic solutions conduct electricity due to the movement of free ions. Unlike metallic conductors, measuring their resistance ($R$) requires alternating current (AC) to prevent electrolysis, and a specially designed conductivity cell. From Resistance, we derive Conductance ($G$), and from Resistivity ($\rho$), we derive Specific Conductivity ($\kappa$). The most critical NEET applications lie in calculating how these values shift when the solution is diluted.
1. Conductance, Conductivity & Cell Constant
The reciprocal of resistance.
Units: $\Omega^{-1}$, Mho, or Siemens ($S$).
The reciprocal of resistivity ($\rho$). It is the conductance of exactly $1 \text{ cm}^3$ (or $1 \text{ m}^3$) of the solution.
Units: $S \text{ cm}^{-1}$ or $S \text{ m}^{-1}$.
The ratio of the distance between electrodes ($l$) to their cross-sectional area ($A$). It is a constant for any specific conductivity cell, regardless of the solution inside it.
Unit: $\text{cm}^{-1}$ or $\text{m}^{-1}$.
2. Molar ($\Lambda_m$) & Equivalent ($\Lambda_{eq}$) Conductivity
Because different solutions have different concentrations, comparing their specific conductivities ($\kappa$) isn't fair. We standardize them by dividing by concentration.
Conductance of a volume of solution containing exactly 1 mole of electrolyte placed between two massive parallel electrodes 1 cm apart.
Units: $S \text{ cm}^2 \text{ mol}^{-1}$
($\kappa$ must be in $S \text{ cm}^{-1}$ and $M$ in mol/L).
Conductance of a volume of solution containing exactly 1 gram-equivalent of electrolyte.
Units: $S \text{ cm}^2 \text{ eq}^{-1}$
($\kappa$ in $S \text{ cm}^{-1}$ and $N$ is Normality).
3. The Effect of Dilution (The Mega Trap)
What happens when you add water (dilute) to an electrolytic solution? Concentration ($\downarrow$) drops, Volume ($\uparrow$) increases. This is the most heavily tested theory concept in this chapter.
$\kappa$ measures the conductance of a fixed volume ($1 \text{ cm}^3$). When you dilute, the total number of ions increases, but the number of ions per unit volume drops drastically. Fewer ions per $cm^3$ = lower $\kappa$.
The formula is $\Lambda_m = \kappa \times V$. While $\kappa$ decreases, the Volume ($V$) containing that 1 mole of electrolyte increases much faster. Furthermore, ions move further apart, reducing inter-ionic attraction, so they move faster.
Strong electrolytes follow the Debye-HΓΌckel-Onsager equation: $\Lambda_m = \Lambda_m^\circ - A\sqrt{c}$. Weak electrolytes do not.
4. Kohlrausch's Law of Independent Migration
At infinite dilution, inter-ionic attractions completely vanish. Therefore, each ion migrates independently and contributes a definite value to the total molar conductivity of the electrolyte, regardless of the other ion present.
For an electrolyte $A_xB_y$ which dissociates as $A_xB_y \rightarrow xA^{y+} + yB^{x-}$:
Where $\lambda^\circ$ represents the limiting ionic conductivity of the individual cation or anion.
Applications of Kohlrausch's Law (High Yield Numericals)
Use strong electrolytes to algebraically construct the weak one. Example for Acetic Acid ($CH_3COOH$):
The ratio of molar conductivity at a given concentration ($\Lambda_m^c$) to its value at infinite dilution ($\Lambda_m^\circ$).
Once $\alpha$ is found, use Ostwald's dilution law formula. This is a guaranteed 4-marker if it appears.
NEET Grand Test: Conductivity
15 High-Yield Questions testing dilution effects, Kohlrausch math, and unit conversions.
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