Gibbs Free Energy and Thermodynamic Favorability

Delta G, or Gibbs free energy change, indicates a reaction's spontaneity. A negative delta G means the reaction is spontaneous and releases free energy to surroundings, called an exergonic reaction. A positive delta G means the reaction is nonspontaneous and absorbs free energy, called an endergonic reaction. When delta G equals zero, the system is at equilibrium with forward and reverse driving forces balanced.

Delta G depends on both enthalpy and entropy changes and temperature. When delta H is negative and delta S is positive, delta G is always negative, making the reaction spontaneous at all temperatures. When both are negative, the reaction is spontaneous only at low temperatures. When both are positive, spontaneity occurs only at higher temperatures. When delta H is positive and delta S is negative, delta G is always positive, making the reaction nonspontaneous at all temperatures.

The standard free energy change equals negative RT times the natural logarithm of the equilibrium constant. If delta G naught is less than zero, the equilibrium constant is greater than 1, favoring product formation. If delta G naught is greater than zero, the equilibrium constant is less than 1, favoring the reverse reaction. This relationship links these two essential thermodynamic properties and allows deriving one from the other.

For any reaction mixture composition, delta G equals the standard free energy plus RT times the natural log of the reaction quotient. When Q is less than the equilibrium constant K, the reaction proceeds forward until equilibrium is reached. When Q exceeds K, the reaction proceeds in reverse. At equilibrium, Q equals K and delta G equals zero, indicating no net driving force in either direction.

Exergonic reactions have negative delta G values and release free energy to surroundings, proceeding spontaneously. Endergonic reactions have positive delta G values and absorb free energy from surroundings, occurring nonspontaneously. The magnitude of delta G reflects the driving force strength. Larger negative delta G values indicate stronger spontaneity, while larger positive values indicate greater resistance to the forward reaction.

When both delta H and delta S are positive, the reaction is temperature-dependent. At low temperatures, the negative TΔS term is small, making delta G positive and the reaction nonspontaneous. At higher temperatures, the TΔS term becomes large enough to overcome the positive delta H, making delta G negative and the reaction spontaneous. This explains why some endothermic reactions become favorable only at elevated temperatures.

Under nonstandard conditions with pressures other than 100 kPa or concentrations other than 1 M, delta G is calculated using the standard free energy change plus RT times the natural log of the reaction quotient. This equation shows how actual reaction conditions deviate from standard states. The reaction quotient Q allows predicting whether a reaction will proceed forward or reverse to reach equilibrium under any given set of conditions.