Conductivity & Kohlrausch's Law
Electrochemistry Notes: Conductivity ($\kappa$), $\Lambda_m$, and Dilution Effects
1. Conductivity ($\kappa$)
Conductivity (or specific conductance), represented by kappa ($\kappa$), is the conductance of a solution of 1 cm length and 1 cm² cross-sectional area. It is the reciprocal of resistivity ($\rho$).
$$ \kappa = \frac{1}{\rho} = \frac{l}{A} \times \frac{1}{R} = G \times G^* $$
Where:
- $G = 1/R$ is Conductance (Siemens, S)
- $G^* = l/A$ is the Cell Constant ($cm^{-1}$)
- Unit of $\kappa$: $S \cdot cm^{-1}$ or $\Omega^{-1} cm^{-1}$
2. Molar & Equivalent Conductivity
Molar Conductivity ($\Lambda_m$)
Conducting power of all ions produced by 1 mole of electrolyte in solution.
$$ \Lambda_m = \frac{\kappa \times 1000}{Molarity (C)} $$
Unit: $S \cdot cm^2 \cdot mol^{-1}$
Equivalent Conductivity ($\Lambda_{eq}$)
Conducting power of all ions produced by 1 gram-equivalent of electrolyte.
$$ \Lambda_{eq} = \frac{\kappa \times 1000}{Normality (N)} $$3. Variation with Concentration
- Conductivity ($\kappa$): Decreases upon dilution because the number of ions per unit volume decreases.
- Molar Conductivity ($\Lambda_m$): Increases upon dilution because inter-ionic attraction decreases (Strong Electrolytes) or degree of dissociation increases (Weak Electrolytes).
4. Kohlrausch's Law
Law of Independent Migration of Ions: At infinite dilution, the limiting molar conductivity of an electrolyte is the sum of the limiting ionic conductivities of the cation and the anion.
$$ \Lambda^\circ_m = \nu_+ \lambda^\circ_+ + \nu_- \lambda^\circ_- $$
Applications
- Calculation for Weak Electrolytes: $\Lambda^\circ_{CH_3COOH}$ can be found using strong electrolytes ($\Lambda^\circ_{CH_3COONa} + \Lambda^\circ_{HCl} - \Lambda^\circ_{NaCl}$).
- Degree of Dissociation ($\alpha$):
$$ \alpha = \frac{\Lambda_m}{\Lambda^\circ_m} $$ - Dissociation Constant ($K_a$):
$$ K_a = \frac{c\alpha^2}{1-\alpha} $$
Practice Quiz
Test your knowledge on Conductivity and Kohlrausch's Law.
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