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A reaction where it starts off with more energy and releases energy is exergonic, but there's no way to determine the sign of delta H without further information. We need to know how much energy was added as heat, how much work was done on/by the system, and the conditions it is under (eg. constant temperature and/or pressure, or at standard conditions). Knowing that the reaction releases energy is only part of figuring out the sign of delta H; you may have to use relationships like delta H = delta U + P*delta V or delta G = delta H - T*delta S
That is not enough information. To determine the sign of delta H, we need to know what whether its under constant heat or temperature, how much heat is released or added and how much work has been done. The amount of energy alone will not tell us much about the change in enthalpy of the entire system.
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