Electrolytic Conductance — Revision Notes

⚡ 30-Second Revision

Conductance (G): — $G = 1/R$ (Units: S or $\Omega^{-1}$)
Conductivity ($\kappa$): — $\kappa = 1/\rho = G \cdot G^*$ (Units: $\text{S} \cdot \text{m}^{-1}$ or $\text{S} \cdot \text{cm}^{-1}$)
**Cell Constant ($G^*$):** $G^* = l/A$ (Units: $\text{m}^{-1}$ or $\text{cm}^{-1}$)
Molar Conductivity ($\Lambda_m$): — $\Lambda_m = \kappa/C$ (SI Units: $\text{S} \cdot \text{m}^2 \cdot \text{mol}^{-1}$)
Common Units for $\Lambda_m$: — $\Lambda_m = (\kappa \times 1000)/C$ (for $\kappa$ in $\text{S} \cdot \text{cm}^{-1}$, $C$ in $\text{mol/L}$, $\Lambda_m$ in $\text{S} \cdot \text{cm}^2 \cdot \text{mol}^{-1}$)
Kohlrausch's Law: — $\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$
Degree of Dissociation ($\alpha$): — $\alpha = \Lambda_m / \Lambda_m^\circ$
Effect of Temperature: — Electrolytic conductance increases with temperature.
Effect of Concentration: — $\kappa$ increases with concentration; $\Lambda_m$ decreases with concentration.

2-Minute Revision

Electrolytic conductance is the flow of electricity through solutions due to ion movement. It differs from metallic conductance, which involves electron flow. Key terms include resistance ($R$), its reciprocal conductance ($G$), resistivity ($\rho$), and its reciprocal conductivity ($\kappa$).

Conductivity is related to measured conductance by the cell constant ($G^* = l/A$), where $\kappa = G \cdot G^*$. Molar conductivity ($\Lambda_m$) normalizes conductivity by concentration ($C$), allowing comparison between electrolytes: $\Lambda_m = \kappa/C$.

Remember the common unit conversion: $\Lambda_m = (\kappa \times 1000)/C$ when $\kappa$ is in $\text{S} \cdot \text{cm}^{-1}$ and $C$ in $\text{mol/L}$. Factors like temperature (increases conductance), nature of electrolyte (strong vs.

weak), and concentration significantly affect conductance. Importantly, specific conductivity ($\kappa$) generally increases with concentration, while molar conductivity ($\Lambda_m$) decreases with concentration for both strong and weak electrolytes.

Kohlrausch's Law is vital for weak electrolytes, enabling calculation of their limiting molar conductivity ($\Lambda_m^\circ$) and degree of dissociation ($\alpha = \Lambda_m / \Lambda_m^\circ$) using strong electrolyte data.

5-Minute Revision

Electrolytic conductance is the phenomenon where ionic solutions conduct electricity via the migration of ions. This is distinct from metallic conduction, which relies on electron movement. The fundamental quantities are resistance ($R$, in $\Omega$) and its inverse, conductance ($G$, in S).

For a specific solution, its intrinsic ability to conduct is described by resistivity ($\rho$, in $\Omega \cdot \text{m}$) and its inverse, conductivity ($\kappa$, in $\text{S} \cdot \text{m}^{-1}$ or $\text{S} \cdot \text{cm}^{-1}$).

When measuring, we use a conductivity cell with a specific cell constant ($G^* = l/A$), such that $\kappa = G \cdot G^*$. To compare different electrolytes, we use molar conductivity ($\Lambda_m$), which is the conductivity normalized by the molar concentration ($C$).

The standard formula is $\Lambda_m = \kappa/C$. However, for practical NEET problems, using $\kappa$ in $\text{S} \cdot \text{cm}^{-1}$ and $C$ in $\text{mol/L}$ requires the formula $\Lambda_m = (\kappa \times 1000)/C$, yielding $\Lambda_m$ in $\text{S} \cdot \text{cm}^2 \cdot \text{mol}^{-1}$.

Several factors influence electrolytic conductance:

1
Nature of Electrolyte: — Strong electrolytes (e.g., NaCl) dissociate completely, providing more ions and higher conductance than weak electrolytes (e.g., $\text{CH}_3\text{COOH}$) which dissociate partially.
2
Concentration: — Specific conductivity ($\kappa$) generally increases with concentration due to more charge carriers per unit volume. However, molar conductivity ($\Lambda_m$) decreases with increasing concentration for both strong (due to increased interionic attraction) and weak electrolytes (due to decreased degree of dissociation).
3
Temperature: — Increasing temperature increases ion mobility and decreases solvent viscosity, thus increasing conductance.

Kohlrausch's Law is crucial: At infinite dilution, the molar conductivity of an electrolyte is the sum of the limiting molar conductivities of its individual ions ($\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$). This law is used to:

1
Calculate $\Lambda_m^\circ$ for weak electrolytes (e.g., $\Lambda_m^\circ(\text{CH}_3\text{COOH}) = \Lambda_m^\circ(\text{CH}_3\text{COONa}) + \Lambda_m^\circ(\text{HCl}) - \Lambda_m^\circ(\text{NaCl})$).
2
Determine the degree of dissociation ($\alpha$) of weak electrolytes: $\alpha = \Lambda_m / \Lambda_m^\circ$.
3
Calculate the dissociation constant ($K_a$) using $\alpha$: $K_a = C\alpha^2 / (1-\alpha)$.

*Example:* A $0.01,\text{M}$ solution of $\text{KCl}$ has a resistance of $150,Omega$. The cell constant is $0.90,\text{cm}^{-1}$. Calculate $\Lambda_m$. *Solution:* $G = 1/150 = 0.00667,\text{S}$. $\kappa = G \cdot G^* = 0.00667,\text{S} \times 0.90,\text{cm}^{-1} = 0.006003,\text{S} \cdot \text{cm}^{-1}$. $\Lambda_m = (0.006003 \times 1000)/0.01 = 600.3,\text{S} \cdot \text{cm}^2 \cdot \text{mol}^{-1}$.

Prelims Revision Notes

Electrolytic conductance is the measure of a solution's ability to conduct electricity due to ion movement. It's quantified by several terms. Resistance (R) is the opposition to current flow, measured in Ohms ($\Omega$).

Its reciprocal is conductance (G), measured in Siemens (S). The intrinsic property of a material is **resistivity ($\rho$)**, measured in $\Omega \cdot \text{m}$, and its reciprocal is **conductivity ($\kappa$)** or specific conductance, measured in $\text{S} \cdot \text{m}^{-1}$ or $\text{S} \cdot \text{cm}^{-1}$.

For a conductivity cell, the **cell constant ($G^*$)** is a geometric factor ($l/A$), and $\kappa = G \cdot G^*$.

**Molar conductivity ($\Lambda_m$)** is crucial for comparing electrolytes. It's the conductance of a solution containing one mole of electrolyte. The formula is $\Lambda_m = \kappa/C$, where $C$ is molar concentration. For practical calculations with $\kappa$ in $\text{S} \cdot \text{cm}^{-1}$ and $C$ in $\text{mol/L}$, use $\Lambda_m = (\kappa \times 1000)/C$, giving $\Lambda_m$ in $\text{S} \cdot \text{cm}^2 \cdot \text{mol}^{-1}$.

Factors affecting conductance:

1
Nature of Electrolyte: — Strong electrolytes (e.g., HCl) dissociate completely, providing more ions than weak electrolytes (e.g., $\text{CH}_3\text{COOH}$), hence higher conductance.
2
Concentration: — As concentration increases, $\kappa$ generally increases (more ions per unit volume). However, $\Lambda_m$ decreases for both strong (due to increased interionic attraction) and weak electrolytes (due to decreased degree of dissociation).
3
Temperature: — Conductance increases with temperature due to increased ion mobility and decreased solvent viscosity.

Kohlrausch's Law of Independent Migration of Ions: At infinite dilution, $\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$. This law is used to:

Calculate $\Lambda_m^\circ$ for weak electrolytes (e.g., $\Lambda_m^\circ(\text{CH}_3\text{COOH}) = \Lambda_m^\circ(\text{CH}_3\text{COONa}) + \Lambda_m^\circ(\text{HCl}) - \Lambda_m^\circ(\text{NaCl})$).
Determine the **degree of dissociation ($\alpha$)** for weak electrolytes: $\alpha = \Lambda_m / \Lambda_m^\circ$.
Calculate the **dissociation constant ($K_a$)** for weak electrolytes: $K_a = C\alpha^2 / (1-\alpha)$.

Key takeaway: Master the formulas, unit conversions, and the qualitative effects of factors on $\kappa$ and $\Lambda_m$. Practice numerical problems involving all these concepts.

Vyyuha Quick Recall

To remember the factors affecting electrolytic conductance: 'N.C.T.S.I.'

Nature of electrolyte (Strong vs. Weak)
Concentration ($\kappa$ up, $\Lambda_m$ down with concentration)
Temperature (Conductance up with temperature)
Solvent (Nature of solvent, viscosity)
Ion size and solvation (Effective size of hydrated ions)