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Gibbs Free Energy (or Available Energy), ΔG° , is a Thermodynamic property like Enthalpy (ΔH°) and Entropy (ΔS°). So it has the same mathematical analysis as the other Thermodynamic properties. The property can be understood to represent the available energy to perform work (meaning do something) that a substance has. There is no substance that does not have some free energy so this is another Thermodynamic property that has a arbitrary condition as:
ΔG°f = 0 kJ/mol for elements in the phase that they are in at standard state conditions (25°C, 1atm). (Same as (ΔH°)
Even though Gibbs Free energy is used for physical process, it is most often used in chemical reaction to determine if the reaction does proceed spontaneously or not. The ΔG° rxn needs to be a NEGATIVE value for the reaction to be spontaneous (meaning proceed without surrounding energy "help" or input). This statement can be understood better if you remember that Gibbs Free Energy is energy that can be used by the material. So since in all Thermodynamics, Δ means Final (or products if in rxn) - initial (or reactants if in rxn),the energy (energy "push") that is needed to make the reactants into products has to come from somewhere. As the reactants turn into products some of the Free energy of the reactant (free energy of reactants is decreasing) is converted/put into the products (free energy of products is increasing). In mathematical form, that would occur when ΔG° is less than zero (or a negative value).
How do you calculate ΔG°, three methods.1st Year Students including Honors and CP DO NOT DO INFO BELOW
1. ΔG° = ΔH° - T ΔS°. T in K not °C or °F
2. Modified Hess' Law
3. Standard Free Energy of Formation (same as ΔH°)
Good video on Entropy and Gibbs Free Energy, Watch [Crash Course Video on Entropy (but also Gibbs Free Energy)]