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The Gibbs free energy of a system at any moment in time is defined as the enthalpy of the system minus the product of the temperature times the entropy of the system. The Gibbs free energy of the system is a state function because it is defined in terms of thermodynamic properties that are state functions.
Adding on to what others have said, we use Gibbs free energy to determine if a certain reaction is thermodynamically favorable. If the Gibbs free energy of a reaction is negative, then the reaction is thermodynamically favorable and spontaneous.
Gibbs free energy determines whether or not a reaction is spontaneous (or thermodynamically favorable) in a given direction. A reaction with a negative gibbs free energy is said to be spontaneous while a reaction with a positive gibbs free energy is non-spontaneous.
Thermodynamics mostly concerns state properties. These are things that focus on the final and initial values without much concern for what is happening in between. Gibbs Free Energy (delta G) is one of these state properties and also helps us to calculate other thermodynamic properties.
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