CSEC Chemistry: The Mole and Electrolysis, the Faraday Constant and Performing Relevant Calculations

Introduction

• Explore the relationship between the mole concept and electrolysis.
• Focus on calculating the mass of substances discharged at electrodes during electrolysis.

Faraday's Discovery

• Michael Faraday's work in 1834 established the proportional relationship between the mass of substances discharged and the quantity of electricity in an electrolysis process.

Key Formula:

• m ∝ Q
  • Q = quantity of electricity (coulombs)
  • m = mass of substance

Understanding Coulombs

• Measure of electric charge: calculated as the product of electric current (I) and time (t).
• Formula: Q = I × t
  • I = electric current (amperes)
  • t = time (seconds)

Faraday Constant

• 96500 C/mol: Charge of one mole of electrons (Avogadro's number of electrons).
• Importance in determining the charge needed to discharge ions at electrodes.

Ion Discharge

• Singly charged ion: requires 96500 C for 1 mol of electrons to be transferred.
  • Example Equations:
    • X⁺ + e⁻ → X
    • Y → Y⁺ + e⁻
• Doubly charged ion: requires 2 × 96500 C.
  • Example Equations:
    • X²⁺ + 2e⁻ → X
    • Y → Y²⁺ + 2e⁻

General Rule

• For 1 mol of ion X or Y to be discharged, n × 96500 C (and n mol of electrons) must be transferred.

Example Calculations

Example 1: Magnesium Deposition

• Problem: Determine the mass of magnesium deposited at the cathode with 2 amperes through molten magnesium chloride for 30 minutes.
  • Q = It
  • Q = 2 A × (30 × 60)s = 3600 C
• Reaction: Mg²⁺ + 2e⁻ → Mg
  • 2 mol electrons for 1 mol of magnesium (24g)
  • 3600 C transferred, find moles of Mg deposited:
    • 3600 / (2 × 96500) ≈ 0.01865 mol
  • Mass of Mg = 24 g/mol × 0.01865 mol ≈ 0.45 g

Example 2: Chlorine Gas Liberation

• Problem: Determine the mass of chlorine gas liberated with the passage of 4.32 × 10⁴ C.
• Reaction: 2Cl⁻ → Cl₂(g) + 2e⁻
  • 2 × 96500 C liberates 1 mol Cl₂
  • C liberated = 4.32 × 10⁴ / (2 × 96500) ≈ 0.224 mol Cl₂
  • Mass of Cl₂ = 71 g/mol × 0.224 mol ≈ 15.904 g

Conclusion

• The relationship between mole concept and electrolysis helps perform critical calculations involving electric current and mass of substances in electrochemical processes.
• Faraday's constant is a foundational aspect in understanding the charge-mass relationship in electrolysis.