Class 12 Chemistry Conductance of Electrolytic Solutions - Complete Study Notes
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:
The conductance of electrolytic solutions is a fundamental topic that bridges theoretical chemistry with practical applications. Understanding the different types of conductivity, the behavior of strong versus weak electrolytes, and Kohlrausch's law provides essential knowledge for electrochemistry. These concepts form the foundation for advanced topics in electrochemical cells, batteries, and analytical chemistry. Mastering this topic requires understanding the mathematical relationships, practicing numerical problems, and appreciating the real-world applications in technology and industry. The principles learned here apply directly to modern developments in energy storage, water treatment, and chemical analysis.