Voltaic Cell and Free Energy

Key Concepts

• Voltaic Cell: A device that converts chemical energy into electrical energy through a spontaneous redox reaction.
• Free Energy (ΔG): Indicates the spontaneity of a reaction. For a spontaneous reaction, ΔG is negative.
• Cell Potential (E): The voltage or potential difference of the cell, measurable using a voltmeter.

Important Equations

• Relationship between free energy and cell potential:
  • ΔG = -nFE
    • ΔG: Change in free energy
    • n: Moles of electrons transferred
    • F: Faraday’s constant
    • E: Cell potential (voltage)

Details

• Spontaneous Reactions:
  • ΔG is negative.
  • E is positive (for a voltaic cell).

Calculating Faraday's Constant (F)

• Charge of One Electron: 1.602 x 10^-19 coulombs.
• Avogadro's Number: 6.022 x 10^23 electrons/mole.
• Faraday's Constant: 96,472 C/mol (rounded to 96,500 C/mol for calculations).

Standard Cell Potential (E°)

• Defined under standard conditions:
  • Pure solids (e.g., Zinc and Copper)
  • 1 M concentration solutions
  • Temperature: 25°C
• E° for the example cell: 1.10 volts (or joules per coulomb).

Calculating Standard Change in Free Energy (ΔG°)

• Use the formula ΔG° = -nFE°.
• Example Calculation:
  • n = 2 moles of electrons
  • F = 96,500 C/mol
  • E° = 1.10 V (J/C)
  • ΔG° = -212 kJ (negative indicates spontaneity)

Observations

• ΔG° and E° have opposite signs:
  • Positive E° suggests a spontaneous reaction, as ΔG° is negative.
• Unit Conversion: Ensure units cancel appropriately to result in joules (or kilojoules).