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In physical organic chemistry, a free-energy relationship or linear Gibbs energy relation relates the logarithm of a reaction rate constant or equilibrium constant for one series of reactions with the logarithm of the rate or equilibrium constant for a related series of reactions. Establishing free-energy relationships helps in the understanding of the reaction mechanism for a chemical reaction and allows the prediction of reaction rates and equilibrium constants.

The Brønsted catalysis equation describes the relationship between the ionization constant of a series of catalysts and the reaction rate constant for a reaction on which the catalyst operates. The Hammett equation predicts the equilibrium constant or reaction rate of a reaction from a substituent constant and a reaction type constant. The Edwards equation relates the nucleophilic power to polarisability and basicity.

It has been suggested that this name should be replaced by linear Gibbs energy relation, but at present there is little sign of acceptance of this change. The area of physical organic chemistry which deals with such relations is commonly referred to as 'Linear Free-Energy Relationships'

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