Introduction:

Conductance of electrolytic solutions is a fundamental concept in Class 12 Chemistry Chapter 2 Electrochemistry that explains how ionic solutions conduct electricity. Unlike metallic conductors that use electrons, electrolytic solutions conduct current through the movement of ions dissolved in the solution. This topic is crucial for understanding electrochemical cells, battery technology, and various industrial applications.

The ability of an electrolyte to conduct electricity depends on several factors including the concentration of ions, temperature, nature of the electrolyte, and the degree of dissociation. Understanding these principles helps explain phenomena from simple salt solutions to complex electrochemical processes in biological systems.

Types of Conductivity in Electrolytic Solutions

Specific Conductivity (κ)

Specific conductivity or conductivity is defined as the conductance of a unit volume of solution placed between two electrodes with unit area of cross-section and unit distance apart. It represents the intrinsic ability of the solution to conduct electricity.

Formula: κ = G × (l/A) = G × K

Where:

κ = specific conductivity (S cm⁻¹)

G = conductance (S)

l = distance between electrodes (cm)

A = area of electrodes (cm²)

K = cell constant (cm⁻¹)

Key Points:

SI unit: S m⁻¹ (commonly expressed as S cm⁻¹)

Specific conductivity decreases with dilution due to fewer ions per unit volume.

Depends on the nature and concentration of electrolyte

Molar Conductivity (Λₘ)

Molar conductivity is defined as the conductance of all ions produced by one mole of an electrolyte dissolved in solution. It provides information about the efficiency of ionic conduction per mole of electrolyte.

Formula: Λₘ = κ × 1000/c

Where:

Λₘ = molar conductivity (S cm² mol⁻¹)

κ = specific conductivity (S cm⁻¹)

c = molar concentration (mol L⁻¹)

Behavior with Dilution:

Strong electrolytes: Molar conductivity increases slowly with dilution

Weak electrolytes: Molar conductivity increases sharply with dilution due to increased ionization.

Equivalent Conductivity (Λₑq)

Equivalent conductivity represents the conductance of all ions produced by one gram-equivalent of electrolyte.

Formula: Λₑq = κ × 1000/Cₑq

Where Cₑq is the equivalent concentration.

Relationship: Λₘ = n × Λₑq (where n is the valency)

Cell Constant and Conductivity Measurement

Cell Constant (K)

The cell constant is a geometric factor that depends only on the physical dimensions of the conductivity cell.

Formula: K = l/A

Where:

l = distance between electrodes (cm)

A = effective area of electrodes (cm²)

Important Features:

Independent of temperature, electrolyte type, or concentration

Must be determined by calibration using standard solutions

Different cell constants suit different conductivity ranges

Common Cell Constants:

K = 0.01 cm⁻¹: Ultrapure water, distilled water

K = 0.1 cm⁻¹: Drinking water, low conductivity solutions

K = 1.0 cm⁻¹: Industrial water, moderate conductivity

K = 10.0 cm⁻¹: High concentration electrolytes, concentrated solutions

Conductivity Measurement:

Specific Conductivity = Measured Conductance × Cell Constant

The conductometer measures conductance, which is then multiplied by the cell constant to obtain true conductivity.

Strong vs Weak Electrolytes

Strong Electrolytes

Strong electrolytes undergo complete or nearly complete ionization in solution.

Characteristics:

Complete dissociation into ions

High conductivity at all concentrations

Molar conductivity varies slightly with concentration

Examples: NaCl, KBr, HCl, NaOH, H₂SO₄

Variation with Dilution:

The relationship follows Kohlrausch's equation: Λₘ = Λ°ₘ - A√c

Where:

Λ°ₘ = limiting molar conductivity

A = constant depending on electrolyte type

c = concentration

Weak Electrolytes

Weak electrolytes undergo partial ionization in solution.

Characteristics:

Partial dissociation into ions

Lower conductivity compared to strong electrolytes

Molar conductivity increases sharply with dilution

Examples: CH₃COOH, NH₄OH, H₂CO₃

Degree of Dissociation:

α = Λₘ/Λ°ₘ

Where α represents the fraction of molecules dissociated.

Kohlrausch's Law of Independent Migration of Ions

Statement

Kohlrausch's law states that at infinite dilution, each ion migrates independently and contributes individually to the total molar conductivity, regardless of the nature of other ions present.

Mathematical Expression: Λ°ₘ = λ°₊ + λ°₋

Where:

Λ°ₘ = limiting molar conductivity of electrolyte

λ°₊ = limiting molar conductivity of cation

λ°₋ = limiting molar conductivity of anion

Applications of Kohlrausch's Law

1. Calculation of Limiting Molar Conductivity for Weak Electrolytes

For acetic acid (CH₃COOH): Λ°ₘ(CH₃COOH) = λ°(H⁺) + λ°(CH₃COO⁻)

This can be calculated using strong electrolytes: Λ°ₘ(CH₃COOH) = Λ°ₘ(HCl) + Λ°ₘ(CH₃COONa) - Λ°ₘ(NaCl)

2. Determination of Degree of Dissociation

For weak electrolytes: α = Λₘ/Λ°ₘ

3. Calculation of Dissociation Constant

For a weak electrolyte: Kₐ = (Cα²)/(1-α)

Where C is the initial concentration.

Factors Affecting Conductance

1. Concentration

Specific conductivity: Increases with concentration (more ions per unit volume)

Molar conductivity: Decreases with concentration due to inter-ionic interactions

2. Temperature

Higher temperature increases ionic mobility

Generally increases all types of conductivity

Enhanced kinetic energy overcomes inter-ionic forces

Nature of Electrolyte

Strong electrolytes show higher conductivity than weak electrolytes

Multivalent ions contribute more to conductivity

Size and charge of ions affect mobility

Solvent Properties

Dielectric constant affects degree of dissociation

Viscosity influences ionic mobility

Temperature affects solvent properties

Important Formulas and Relationships

Basic Relationships:

Conductance and Resistance: G = 1/R

Specific Conductivity: κ = G × K = G × (l/A)

Molar Conductivity: Λₘ = κ × 1000/c

Kohlrausch's Law: Λ°ₘ = λ°₊ + λ°₋

Degree of Dissociation: α = Λₘ/Λ°ₘ

For Strong Electrolytes: Λₘ = Λ°ₘ - A√c

Unit Conversions:

Conductivity: S m⁻¹ = 100 × S cm⁻¹

Molar conductivity: S m² mol⁻¹ = 10⁴ × S cm² mol⁻¹

Solved Examples:

Example 1: Calculate Molar Conductivity

Given: κ = 0.001 S cm⁻¹, c = 0.01 mol L⁻¹

Solution:

Λₘ = κ × 1000/c = 0.001 × 1000/0.01 = 100 S cm² mol⁻¹

Example 2: Degree of Dissociation

For 0.025 mol L⁻¹ methanoic acid with Λₘ = 46.1 S cm² mol⁻¹ Given: λ°(H⁺) = 349.6 S cm² mol⁻¹, λ°(HCOO⁻) = 54.6 S cm² mol⁻¹

Solution: Λ°ₘ(HCOOH) = 349.6 + 54.6 = 404.2 S cm² mol⁻¹ α = Λₘ/Λ°ₘ = 46.1/404.2 = 0.114 = 11.4%

Practical Applications:

1. Water Quality Testing

Conductivity measurements determine the purity of water and concentration of dissolved salts. Pure water has very low conductivity, while contaminated water shows higher values.

2. Battery Technology

Understanding electrolyte conductivity is crucial for designing efficient batteries and fuel cells. Higher ionic conductivity leads to better battery performance.

3. Chemical Analysis

Conductometric titrations use conductivity changes to determine end points and analyze solution composition.

4. Industrial Processes

Monitoring electrolyte conductivity ensures proper conditions in electroplating, water treatment, and chemical manufacturing.

Important Points for Examinations

Key Concepts to Remember

Conductivity decreases with dilution, but molar conductivity increases

Strong electrolytes show complete ionization; weak electrolytes show partial ionization

Kohlrausch's law applies only at infinite dilution

Cell constant is independent of solution properties

Degree of dissociation increases with dilution for weak electrolytes

Common Mistakes to Avoid

Confusing specific conductivity with molar conductivity

Forgetting the factor of 1000 in molar conductivity calculations

Mixing up units in problem solving

Not considering temperature effects in conductivity measurements

Conclusion: