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Exothermic and endothermic refer to thermodynamic properties, that is delta H. Exergonic and endergonic refer to the Gibbs free energy. We say that a negative delta H indicates an exothermic reaction, but that does not mean it is exergonic (you would have to refer to the sign of delta G) and vice versa (+deltaH= endothermic but not necessarily endergonic). Exergonic and endergonic have nothing to do with how hot or cold something gets, rather it describes the rxn in a more chemical meaning (spontaneity of the rxn) . Similarly and inversley, exo and endothermic have nothing to do with the likeliness of a rxn.
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