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All spontaneous processes have an increase in entropy. In other words, heat will always flow from hot to cold and never cold to hot spontaneously. So, S(universe) >0 for spontaneous process (2nd law of thermo.). We also know that delta H is negative for exothermic reactions and that delta G = delta H - T*delta S. So, H will be negative and S will be positive. Thus, G will be negative and spontaneous.
Conceptually, it makes sense for exothermic reactions to be spontaneous as the release of energy makes the system more stable. Endothermic reactions on the other hand require an input of energy and thus, are not naturally occurring.
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