
Generic plot showing to possible Gibbs free energy changes over time: the lower Gf position indicating a free energy change decrease, the higher Gf position indicating a free energy change increase.

Generic plot showing to possible Gibbs free energy changes over time: the lower Gf position indicating a free energy change decrease, the higher Gf position indicating a free energy change increase.

In thermodynamics, Gibbs free energy change, symbol ΔG, is the change Δ in Gibbs free energy G in a system in going from an initial state to a final state and is quantified by the difference of the latter over the former. This is stated mathematically as:

$\Delta G = G_f - G_i \,$

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Enthalpy and entropy
The expression for Gibbs free energy change, can be expanded, by substitution for the Gibbs function, in terms of initial and final values of enthalpy H and entropy S of the states of the system:

$\Delta G = (H - TS)_f - (H - TS)_i \,$

$\Delta G = H_f - TS_f - H_i + TS_i \,$

which states that Gibbs free energy change of a process can be studied in terms of the difference in the measures of the enthalpy and entropy of the system in the final state, Hf and Sf, as contrasted with the values of the enthalpy and entropy in the initial state, Hi and Si.

Further reading
● Anslyn, Eric V. and Dougherty, Dennis A. (2006). Modern Physical Organic Chemistry (pg. 68). University Science Books.