# Gibbs Energy change and Equilibrium

Free Energy Change (ΔG):

• The two thermodynamic quantities which affect the spontaneity of a reaction are enthalpy (H) and entropy (S).
• The free energy is the amount of work that a thermodynamic system can perform
• The free energy of a substance such as its enthalpy or entropy is a characteristic property of the substance.
• In any reaction, the change in free energy, ΔG, is the difference in free energies of products and reactants.
ΔG = Gproducts – Greactants
• Gibbs showed that the sign of ΔG can be used to determine whether a reaction is spontaneous or not. For a reaction carried out at constant temperature and pressure:
• If ΔG is negative, the forward reaction is spontaneous.
• If ΔG is positive, the forward reaction is non-spontaneous. Instead, the reverse reaction will be spontaneous.
• If ΔG is zero, the system is at equilibrium. There is not tendency for the net reaction to take place in either direction.

Relationship between ΔG, ΔH and ΔS:

• ΔG is made up of two terms: an energy term and an entropy term.
ΔG = ΔH (energy term) – TΔS (entropy term)
Where T is the temperature in Kelvin.
• One of these is the enthalpy change due to the making and breaking of bonds, ΔH.
• The other is the product of the change in randomness, ΔS, times the absolute temperature T.

Standard Free Energy Change:

Using the equation ΔG = ΔH – TΔS, we can calculate the standard free energy change for the reaction, ΔGθ

This is defined as the free energy change when all the species involved in the reaction are at unit concentrations (for gases 1 atm, and 1M for ions or molecules in aqueous solution).

Standard Free Energy Change ΔGθ and Equilibrium Constant (Keq):

The standard free energy change can be defined as the free energy change for a process at 298K in which the reactants in their standard states are converted into the products in their standard states.

Standard free energy change ΔGθ is related to the equilibrium constant (Keq) by the relation:

ΔGθ  = − 2.303RT logKeq