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Gibbs Free Energy

Gibbs Free Energy (∆G) is the energy that is available to do useful work in a spontaneous process (∆G < 0) or the work that is required to drive a non-spontaneous (∆G > 0) process. Heat energy cannot be completely transferred into work energy due to entropy.

  • The formula is: ∆G = ∆H - T∆S

Gibbs Free Energy Image

For example:

  • When a reaction is exothermic and the disorder increases, the reaction is -

    • Exothermic means ∆H° < 0.
    • Disorder increases means ∆S° > 0.
    • Looking at the equation ∆G° = ∆H° - T∆S°, we can conclude that ∆G° < 0 for all values of T. Therefore, the reaction is spontaneous at all temperatures.

  • When a reaction is exothermic and the disorder decreases, the reaction is -

    • Exothermic means ∆H° < 0.
    • Disorder decreases means ∆S° < 0.
    • Looking at the equation ∆G° = ∆H° - T∆S°, we can conclude that ∆G° < 0 for small values of T. Therefore, the reaction is spontaneous at low temperatures and not spontaneous at high temperatures.

Calculating Gibbs Free Energy (ΔG)​

The formula to calculate Gibbs Free Energy is:

  • ∆G°rxn = 𝚺 n ∆G°f(products) - 𝚺 m ∆G°f(reactants)

N and m are the stoichiometric coefficients of each product or reactant.

Similar to ∆S, If a reaction is carried out in a series of steps, ∆G for the overall reaction will be equal to the sum of the ∆G’s for the individual steps.

Crossover Temperature​

Crossover Temperature Image

When the equation ∆G° = ∆H° - T∆S° is at equilibrium, ∆G = 0. This point is the crossover of two lines as shown in the diagram below. The temperature at this crossover is usually the boiling point or melting point.