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I think the free energy of activation refers to delta G. The activation energy is how much energy must be supplied to break the bonds of the reactants.
Activation energy, Ea, is the energy that's needed to get over an energy barrier during a transition step. The free energy of activation refers to Gibbs free energy, and it is what is used when we are looking at the energy barriers of chemical reactions/ allows us to determine how likely a reaction is to occur.
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