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Since the positive and negative indicates whether energy is being absorbed or released for the reaction to take place, if the reaction absorbs heat in one direction, the reverse reaction will release heat since the bonds that were initially being broken are now being formed and vice versa.
Since reversing the equation would reverse the chemical process taking place, the sign of the enthalpy would change. For example, if you start with an exothermic reaction, the enthalpy would be negative because the reactants are releasing/losing heat to form the products. If you reverse this reaction, the products going to the reactants would be an endothermic reaction. The enthalpy would then be positive because the products are gaining heat to form the reactants.
It depends on whether the exothermic or endothermic reaction is favored. If the forward reaction is endothermic and is favored the delta H would be positive. If the reverse reaction is favored, the delta H becomes negative as the reverse reaction is exothermic.
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