Gibbs Free Energy Calculations

Concept of Gibbs Free Energy

The Gibbs Free Energy formula allows chemists to determine the spontaneity of a chemical reaction by using enthalpy (), entropy (), and temperature (T) values. The sign of indicates whether a reaction is spontaneous under given conditions.

• Formula:

• : Reaction is spontaneous.

• : Reaction is nonspontaneous.

• : System is at equilibrium.

Example Calculation

For a reaction with kJ and J/K, calculate at 298 K:

• Convert to kJ: J/K kJ/K

• Apply the formula:

• Since , the reaction is nonspontaneous at 298 K.

Temperature Conditions and Spontaneity

Effect of Temperature on Spontaneity

The spontaneity of a reaction can depend on temperature, especially when and have the same sign. The temperature at which a reaction becomes spontaneous can be calculated by setting :

• If and , reaction is spontaneous at high temperatures.

• If and , reaction is spontaneous at low temperatures.

Example: Temperature Dependence

Given kJ, J/K, calculate the temperature above which the reaction is spontaneous:

• Convert to kJ: $82= 0.082$ kJ/K

• Set :

• Reaction is spontaneous above 378 K.

Gibbs Free Energy of Reaction

Calculating from Standard Free Energies of Formation

The standard Gibbs free energy change of a reaction () can be calculated using the standard free energies of formation () of reactants and products:

• Elements in their standard state have .

Example Calculation

For the reaction:

• Given values:

  • kJ/mol

  • kJ/mol

  • kJ/mol

• Calculation:

kJ

• Negative indicates a spontaneous reaction under standard conditions.

Practice Problems

Sample Calculations

• Calculate for at 25°C, given kJ/mol and J/K.

• Determine if a reaction is spontaneous under standard conditions, and at what temperature it becomes spontaneous.

• Given and for nickel, predict if it will melt at a given temperature and pressure.

HTML Table: Standard Gibbs Free Energies of Formation

The following table summarizes standard Gibbs free energies of formation for selected substances (values in kJ/mol):

Key Terms

• Gibbs Free Energy (): Thermodynamic quantity indicating the maximum reversible work obtainable from a system at constant temperature and pressure.

• Spontaneous Reaction: A reaction that occurs without external input; .

• Standard State: The most stable form of a substance at 1 atm and 25°C.

Additional info: The notes include practice problems and tables for standard Gibbs free energies of formation, which are essential for mastering thermodynamic calculations in General Chemistry.