Lecture Notes: Galvanic Cells and Free Energy Changes

Key Concepts

• Galvanic Cells: Electrochemical cells that convert chemical energy into electrical energy through spontaneous redox reactions.
• Oxidation and Reduction:
  • Oxidation occurs at the anode.
  • Reduction occurs at the cathode.
• Standard Conditions:
  • 1 molar concentration of reactants and products.
  • Temperature: 25°C (298K).
  • Standard cell potential: 1.10 volts.

Chemical Reactions in the Cell

• Zinc is oxidized to zinc two plus ions at the anode.
• Copper two plus ions are reduced to solid copper at the cathode.

Gibbs Free Energy and Cell Potential

• Standard Free Energy Change (ΔG°):
  • Calculated from standard cell potential: ΔG° = -nFE°.
  • ΔG° for the cell ≈ -212 kJ/mol.
• Equation for Free Energy Change:
  • ΔG = ΔG° + RTlnQ
  • Where R is the gas constant (8.314 J/mol·K), T is temperature in Kelvin, and Q is the reaction quotient.

Reaction Quotient (Q)

• Expression: Concentration of products / concentration of reactants, excluding solids.
• Standard Conditions: Q = 1; at this point, ΔG = ΔG°.

Changes During Reaction

• As the reaction proceeds:
  • Q Increases: More products are formed, increasing the concentration of zinc two plus ions and decreasing the concentration of copper two plus ions.
  • ΔG Changes: As Q increases, ΔG becomes less negative, approaching zero.
  • Example Calculation: If Q = 10,000, ΔG ≈ -189.2 kJ/mol.

Instantaneous Cell Potential

• Relation to ΔG: E = (ΔG/nF)
• As Q increases, cell potential decreases slightly but remains positive as long as the reaction is spontaneous.
• Example: If Q = 10,000, E ≈ 0.98 volts.

Equilibrium

• At equilibrium:
  • Q = K (equilibrium constant), for this cell K ≈ 1.58 x 10^37.
  • ΔG = 0, indicating no free energy difference between reactants and products.
  • Cell Potential (E): At equilibrium, E = 0 volts, indicating the cell is "dead".

Conclusion

• Understanding the relationship between the standard free energy change, reaction quotient, and cell potential helps in analyzing galvanic cells.
• Voltage generation and cell potential decrease as the reaction approaches equilibrium.
• This lecture emphasizes the thermodynamic aspect of galvanic cells, particularly focusing on free energy changes and its impact on cell functionality.