Conductance in Electrolytic Solutions — Revision Notes

⚡ 30-Second Revision

Resistance ($R$): — Opposition to current flow ($\Omega$).
Conductance ($G$): — $1/R$ (S).
Resistivity ($\rho$): — Resistance of unit length/area ($\Omega \cdot m$).
Conductivity ($\kappa$): — $1/\rho = G \cdot G^*$ ($S \cdot m^{-1}$ or $S \cdot cm^{-1}$). $G^* = l/A$ (cell constant).
Molar Conductivity ($\Lambda_m$): — $kappa/C$. If $\kappa$ in $S \cdot cm^{-1}$, $C$ in $mol \cdot L^{-1}$, then $\Lambda_m = \frac{\kappa \times 1000}{C}$ ($S \cdot cm^2 \cdot mol^{-1}$).
Limiting Molar Conductivity ($\Lambda_m^0$): — $\Lambda_m$ at infinite dilution.
Kohlrausch's Law: — $\Lambda_m^0 = \nu_+ \lambda_+^0 + \nu_- \lambda_-^0$.
Degree of Dissociation ($\alpha$): — $\alpha = \Lambda_m / \Lambda_m^0$.
Weak Electrolyte Dissociation Constant ($K_a$): — $K_a = \frac{Calpha^2}{1-alpha}$.
Trends: — $\kappa$ decreases with dilution. $\Lambda_m$ increases with dilution (for both strong and weak electrolytes).

2-Minute Revision

Conductance in electrolytic solutions is about ion movement. Key terms are Resistance ($R$), its reciprocal Conductance ($G$), Resistivity ($\rho$), and its reciprocal Conductivity ($\kappa$). Conductivity is an intrinsic property, related to measured conductance by the cell constant ($G^* = l/A$), so $\kappa = G \cdot G^*$.

Molar conductivity ($\Lambda_m$) normalizes conductivity per mole of electrolyte, calculated as $\Lambda_m = \frac{\kappa \times 1000}{C}$ (with $\kappa$ in $S \cdot cm^{-1}$ and $C$ in $mol \cdot L^{-1}$).

A crucial concept is how these values change with dilution: $\kappa$ decreases because fewer ions are in a unit volume, while $\Lambda_m$ increases because ions move more freely and weak electrolytes dissociate more.

Kohlrausch's Law is vital for weak electrolytes, allowing calculation of their limiting molar conductivity ($\Lambda_m^0$) indirectly from strong electrolytes, and subsequently their degree of dissociation ($\alpha = \Lambda_m / \Lambda_m^0$) and dissociation constant ($K_a$).

Remember to pay close attention to units and conversions in numerical problems.

5-Minute Revision

Electrolytic solutions conduct electricity via ion migration. We quantify this using several terms. **Resistance ($R$)** is the opposition to current flow, measured in Ohms ($\Omega$). Its reciprocal is **Conductance ($G$)**, measured in Siemens (S).

**Resistivity ($\rho$) is the intrinsic resistance of a material, and its reciprocal is Conductivity ($\kappa$)**, also known as specific conductance. $\kappa$ is measured in $S \cdot cm^{-1}$ or $S \cdot m^{-1}$.

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

**Molar conductivity ($\Lambda_m$)** is the conducting power of one mole of electrolyte. It's calculated as $\Lambda_m = \frac{\kappa \times 1000}{C}$ (if $\kappa$ is in $S \cdot cm^{-1}$ and $C$ in $mol \cdot L^{-1}$, giving $\Lambda_m$ in $S \cdot cm^2 \cdot mol^{-1}$). A key trend is that $\kappa$ decreases with dilution (fewer ions per unit volume), but $\Lambda_m$ increases with dilution (ions move more freely, and weak electrolytes dissociate more).

Kohlrausch's Law of Independent Migration of Ions is critical for weak electrolytes. It states that at infinite dilution, $\Lambda_m^0$ (limiting molar conductivity) is the sum of the limiting ionic conductivities of its constituent ions ($\Lambda_m^0 = \nu_+ \lambda_+^0 + \nu_- \lambda_-^0$).

This allows us to calculate $\Lambda_m^0$ for weak electrolytes indirectly (e.g., $\Lambda_m^0(CH_3COOH) = \Lambda_m^0(CH_3COONa) + \Lambda_m^0(HCl) - \Lambda_m^0(NaCl)$). Once $\Lambda_m^0$ is known, the **degree of dissociation ($\alpha$)** for a weak electrolyte at a given concentration can be found: $\alpha = \Lambda_m / \Lambda_m^0$.

From $\alpha$, the **dissociation constant ($K_a$)** can be calculated using $K_a = \frac{Calpha^2}{1-alpha}$.

Example: A $0.05,M$ solution of an electrolyte has a resistance of $31.6,\Omega$ in a cell with a cell constant of $0.367,cm^{-1}$. Calculate its molar conductivity.

1
$G = 1/R = 1/31.6 = 0.03164,S$.
2
$\kappa = G \cdot G^* = 0.03164,S \times 0.367,cm^{-1} = 0.01160,S \cdot cm^{-1}$.
3
$\Lambda_m = \frac{\kappa \times 1000}{C} = \frac{0.01160 \times 1000}{0.05} = \frac{11.60}{0.05} = 232,S \cdot cm^2 \cdot mol^{-1}$.

Always double-check units and ensure correct application of formulas, especially the '1000' factor.

Prelims Revision Notes

Conductance in Electrolytic Solutions: NEET Quick Recall

1. Basic Definitions & Formulas:

Resistance ($R$): — Opposition to current flow. Unit: Ohm ($\Omega$).
Conductance ($G$): — Ease of current flow. $G = 1/R$. Unit: Siemens (S) or $\Omega^{-1}$ (mho).
Resistivity ($\rho$): — Specific resistance. $R = \rho \frac{l}{A}$. Unit: $\Omega \cdot m$ or $\Omega \cdot cm$.
Conductivity ($\kappa$): — Specific conductance. $\kappa = 1/\rho$. Unit: $S \cdot m^{-1}$ or $S \cdot cm^{-1}$.
**Cell Constant ($G^*$):** Geometric factor of a conductivity cell. $G^* = l/A$. Unit: $m^{-1}$ or $cm^{-1}$.

* Relationship: $\kappa = G \cdot G^*$. * Determination: $G^* = \kappa_{std} \cdot R_{std}$.

2. Molar Conductivity ($\Lambda_m$):

Conducting power of all ions from 1 mole of electrolyte.
Formula: $\Lambda_m = \kappa / C$.

* If $\kappa$ in $S \cdot cm^{-1}$ and $C$ in $mol \cdot L^{-1}$: $\Lambda_m = \frac{\kappa \times 1000}{C}$ (Unit: $S \cdot cm^2 \cdot mol^{-1}$). Crucial 1000 factor! * If $\kappa$ in $S \cdot m^{-1}$ and $C$ in $mol \cdot m^{-3}$: $\Lambda_m = \kappa / C$ (Unit: $S \cdot m^2 \cdot mol^{-1}$). (Note: $1,M = 1000,mol \cdot m^{-3}$)

3. Effect of Dilution:

Conductivity ($\kappa$): — Decreases with dilution. Reason: Number of ions per unit volume decreases.
Molar Conductivity ($\Lambda_m$): — Increases with dilution.

* Strong Electrolytes: Interionic attractions decrease, increasing ion mobility. * Weak Electrolytes: Degree of dissociation ($\alpha$) increases, producing more ions.

4. Limiting Molar Conductivity ($\Lambda_m^0$):

Molar conductivity at infinite dilution (zero concentration).
For strong electrolytes: Determined by extrapolating $\Lambda_m$ vs. $\sqrt{C}$ plot to $\sqrt{C}=0$ (linear relationship).
For weak electrolytes: Cannot be determined by extrapolation (non-linear plot).

5. Kohlrausch's Law of Independent Migration of Ions:

At infinite dilution, $\Lambda_m^0 = \nu_+ \lambda_+^0 + \nu_- \lambda_-^0$.

* $\nu_+, \nu_-$: stoichiometric coefficients of cation/anion. * $\lambda_+^0, \lambda_-^0$: limiting molar ionic conductivities.

Applications:

* Calculate $\Lambda_m^0$ for weak electrolytes: e.g., $\Lambda_m^0(CH_3COOH) = \Lambda_m^0(CH_3COONa) + \Lambda_m^0(HCl) - \Lambda_m^0(NaCl)$. * Calculate **Degree of Dissociation ($\alpha$)**: $\alpha = \Lambda_m / \Lambda_m^0$. * Calculate **Dissociation Constant ($K_a$)** for weak electrolytes: $K_a = \frac{Calpha^2}{1-alpha}$ (from Ostwald's dilution law).

6. Factors Affecting Conductance:

Nature of Electrolyte: — Strong (high $\Lambda_m$) vs. Weak (low $\Lambda_m$).
Concentration: — Affects $\kappa$ and $\Lambda_m$ as described above.
Temperature: — Increases ion mobility, generally increases $\kappa$ and $\Lambda_m$.
Nature of Solvent: — Viscosity, dielectric constant affect ion mobility and dissociation.
Size/Charge of Ions: — Smaller, less hydrated ions move faster; higher charge increases attraction to electrodes.

Vyyuha Quick Recall

To remember factors affecting electrolytic conductance: Nice Cats Try Solving Ions.

Nature of electrolyte (strong/weak)
Concentration
Temperature
Solvent properties (viscosity, dielectric constant)
Ion size and charge