Specific and Molar Conductivity — Revision Notes

⚡ 30-Second Revision

Conductance (G): — $G = 1/R$, Unit: S
Specific Conductivity ($\kappa$): — $\kappa = G \times G^*$, Unit: $\text{S cm}^{-1}$ or $\text{S m}^{-1}$
**Cell Constant ($G^*$):** $G^* = l/A$, Unit: $\text{cm}^{-1}$ or $\text{m}^{-1}$
Molar Conductivity ($\Lambda_m$): — $\Lambda_m = \frac{\kappa \times 1000}{C}$ (for $\kappa$ in $\text{S cm}^{-1}$, $C$ in $\text{mol L}^{-1}$), Unit: $\text{S cm}^2 \text{mol}^{-1}$
Effect of Dilution on $\kappa$: — Decreases (fewer ions/unit volume)
Effect of Dilution on $\Lambda_m$: — Increases (reduced interionic attraction/increased dissociation)

2-Minute Revision

Specific and molar conductivity are key measures of an electrolyte solution's ability to conduct electricity. **Specific conductivity ($\kappa$)** is the conductance of a unit volume ($1\,\text{cm}^3$) of the solution.

It's an intrinsic property, measured in $\text{S cm}^{-1}$, and depends on the concentration of ions and their mobility. Crucially, $\kappa$ decreases with dilution because there are fewer ions in a fixed unit volume.

**Molar conductivity ($\Lambda_m$)** represents the total conducting power of all ions from one mole of electrolyte. It's calculated as $\Lambda_m = (\kappa \times 1000) / C$ (where $C$ is molarity in $\text{mol L}^{-1}$), with units of $\text{S cm}^2 \text{mol}^{-1}$.

Unlike $\kappa$, $\Lambda_m$ increases with dilution. For strong electrolytes, this is due to reduced interionic attraction, increasing ionic mobility. For weak electrolytes, dilution enhances the degree of dissociation, producing more ions from the same mole of electrolyte.

The **cell constant ($G^* = l/A$)** is a geometric factor for a conductivity cell, used to convert measured conductance ($G$) to specific conductivity ($\kappa = G \times G^*$).

5-Minute Revision

Let's consolidate our understanding of specific and molar conductivity, which are fundamental to electrolytic conductance.

1. Basic Definitions:

Resistance (R): — Opposition to current flow ($\Omega$).
Conductance (G): — Ease of current flow, $G = 1/R$ (S).
Resistivity ($\rho$): — Resistance of unit length and area ($\Omega \text{ cm}$).
Specific Conductivity ($\kappa$): — Reciprocal of resistivity, $\kappa = 1/\rho$. It's the conductance of $1\,\text{cm}^3$ of solution ($\text{S cm}^{-1}$). It's an intrinsic property.

**2. Cell Constant ($G^*$):**

For a conductivity cell, $G^* = l/A$, where $l$ is electrode distance and $A$ is electrode area ($\text{cm}^{-1}$).
It relates specific conductivity to measured conductance: $\kappa = G \times G^*$. You often determine $G^*$ using a standard $\text{KCl}$ solution of known $\kappa$.

3. Molar Conductivity ($\Lambda_m$):

The conducting power of all ions from one mole of electrolyte in a given volume.
Formula: $\Lambda_m = \frac{\kappa \times 1000}{C}$, where $\kappa$ is in $\text{S cm}^{-1}$ and $C$ is in $\text{mol L}^{-1}$. Unit: $\text{S cm}^2 \text{mol}^{-1}$.

4. Effect of Dilution (Crucial Distinction!):

Specific Conductivity ($\kappa$): — Decreases with dilution for both strong and weak electrolytes. Why? Because dilution means fewer ions per unit volume ($1\,\text{cm}^3$), reducing charge carriers.
Molar Conductivity ($\Lambda_m$): — Increases with dilution for both strong and weak electrolytes. Why?

* Strong Electrolytes: Interionic attractions decrease upon dilution, allowing ions to move more freely, increasing their mobility and thus total conductance per mole. * Weak Electrolytes: Dilution increases the degree of dissociation ($\alpha$), producing more ions from the one mole of electrolyte, significantly boosting total conductance per mole.

Example: A $0.05\,\text{M}$ $\text{NaCl}$ solution has a specific conductivity of $0.005\,\text{S cm}^{-1}$. Calculate its molar conductivity. $\Lambda_m = \frac{0.005 \times 1000}{0.05} = \frac{5}{0.05} = 100\,\text{S cm}^2 \text{mol}^{-1}$.

Remember to always check units and apply the correct conversion factors, especially the '1000' in the molar conductivity formula.

Prelims Revision Notes

Specific and Molar Conductivity: NEET Quick Recall

1. Fundamental Concepts:

Resistance (R): — Opposition to current flow. Unit: Ohm ($\Omega$).
Conductance (G): — Ease of current flow. $G = 1/R$. Unit: Siemens (S) or $\Omega^{-1}$.
Resistivity ($\rho$): — Resistance of a unit cube of material. Unit: $\Omega \text{ cm}$ or $\Omega \text{ m}$.
Specific Conductivity ($\kappa$): — Reciprocal of resistivity. Conductance of $1\,\text{cm}^3$ of solution. Unit: $\text{S cm}^{-1}$ or $\text{S m}^{-1}$.

**2. Cell Constant ($G^*$):**

Geometric factor of a conductivity cell: $G^* = l/A$ (distance between electrodes / area of electrodes).
Unit: $\text{cm}^{-1}$ or $\text{m}^{-1}$.
Relationship: $\kappa = G \times G^*$.
Determined using standard solutions (e.g., $\text{KCl}$) of known $\kappa$.

3. Molar Conductivity ($\Lambda_m$):

Conducting power of all ions from one mole of electrolyte.
Formula (most common for NEET): $\Lambda_m = \frac{\kappa \times 1000}{C}$

* $\kappa$ in $\text{S cm}^{-1}$ * $C$ (concentration) in $\text{mol L}^{-1}$ (Molarity) * $\Lambda_m$ in $\text{S cm}^2 \text{mol}^{-1}$

Alternative Formula (SI units): $\Lambda_m = \kappa / C$

* $\kappa$ in $\text{S m}^{-1}$ * $C$ in $\text{mol m}^{-3}$ ($1\,\text{M} = 1000\,\text{mol m}^{-3}$) * $\Lambda_m$ in $\text{S m}^2 \text{mol}^{-1}$

4. Effect of Dilution (CRITICAL for NEET):

Specific Conductivity ($\kappa$): — DECREASES with dilution for both strong and weak electrolytes. (Reason: Fewer ions per unit volume).
Molar Conductivity ($\Lambda_m$): — INCREASES with dilution for both strong and weak electrolytes.

* Strong Electrolytes: Due to decreased interionic attractions, leading to increased ionic mobility. * Weak Electrolytes: Due to increased degree of dissociation, producing more ions from one mole of electrolyte.

5. Factors Affecting Conductivity:

Nature of Electrolyte: — Strong vs. Weak (degree of dissociation).
Concentration: — Number of ions per unit volume.
Temperature: — Increases ionic mobility (kinetic energy).
Nature of Solvent/Viscosity: — Affects dissociation and ionic movement.

6. Common Mistakes to Avoid:

Confusing the effect of dilution on $\kappa$ vs. $\Lambda_m$.
Incorrect unit conversions, especially the factor of 1000.
Mixing up formulas for $\kappa$ and $\Lambda_m$.

Vyyuha Quick Recall

Kappa Decreases, Lambda Increases with Dilution. (KDI-LID)

Kappa ($\kappa$) Decreases with Dilution.
Lambda ($\Lambda_m$) Increases with Dilution.