That is a *fantastic* question.
The difference is between delta G of the *system* and delta G° (the energy of formation) of the individual components.
For a *system* at equilibrium, delta G is zero. There is no net change of energy.
If the equilibrium constant was 1 (concentration of the products = concentration of reactants) then we could *also* say that the delta G° (delta G of formation) of the products is equivalent to that of the reactants.
But most of the time, the equilibrium constant is greater (or lower) than 1 (depending on which direction you draw the equation). That means one component is more *stable* than the other, and we can relate their relative stabilities to the equilibrium by using the Gibbs free energy equation, delta G° = RT ln K. If we know the equilibrium constant at a given temperature we can rearrange the equation to solve for the difference in energies.
Does that make sense?
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