Thermodynamics Lecture on Delta G Calculation

Key Concepts

• Gibbs Free Energy (G): A state function similar to enthalpy (H).
  • State Function: Depends only on current state, not on the path taken.
  • Change in state function: Final state minus initial state.

Calculating Delta G

Methods for Finding Delta G

1. From Standard Free Energies of Formation

   • Similar to Delta H from standard enthalpies of formation.
   • Important to consider the reaction involved and the phases of compounds (gas, liquid, solid).
   • Use fractional coefficients to represent elements in their natural states if necessary.
   • Example reactions:
     • Ammonia gas formation from N2 and H2.
     • Sodium hydrogen carbonate from Na, H2, C (as graphite), and O2.
   • Standard free energy of formation for elements in their natural state is zero.

2. Using Hess's Law

   • Delta G for reactions that add up to the overall reaction can be summed.
   • Pathway independence of Gibbs free energy allows combination of reactions.
   • Method involves flipping and scaling reactions to achieve desired reaction.

Applying Delta G Calculations

• Example Problem: Combustion of benzene (C6H6) to CO2 and H2O.
  • Balance the equation carefully considering the coefficients.
  • Calculate Delta G for the entire reaction as written.
  • Determine per mole basis by dividing by the coefficient of interest.

Relationship with Other Thermodynamic Quantities

Delta G and Equilibrium Constant (K)

• Equation: ΔG = -RT ln K
  • R = 8.314 J/(K·mol)
  • T in Kelvin
• Conversion between kilojoules and joules is crucial.

Delta G and Cell Potential (E°)

• Equation: ΔG = -nFE°
  • n = number of moles of electrons
  • F = Faraday's constant = 96485.34 C/mol
• Consider units and conversion between energy scales.

Non-Standard Conditions

• Equation: ΔG = ΔG° + RT ln Q
  • Q = reaction quotient
  • At standard conditions, Q = 1, and ΔG = ΔG°.
  • At equilibrium, Q = K, and ΔG = 0.

Example Problems

1. Finding Equilibrium Constant
   • Use Delta G of formation to find reaction's Delta G.
   • Relate Delta G to K using ΔG = -RT ln K.
2. Standard Cell Potential from Free Energies
   • Find Delta G for redox reaction using free energies of formation.
   • Relate to standard cell potential using ΔG = -nFE°.
   • Compare calculated potential to standard reduction potentials.

Conclusion

• Understanding the properties and calculation methods for Delta G is crucial for predicting reaction spontaneity and understanding equilibrium.
• Relationships between Delta G, equilibrium constants, and cell potentials are foundational concepts in thermodynamics and electrochemistry.