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Because the pressure is not changing, none of the heat being released is going into the surroundings. This would make the change a closed system and all of the heat released in a reaction would equal the enthalpy of the reaction.
I'm pretty sure enthalpy is really just a convention created by scientists to make calculations convenient (most reactions occur at constant pressure). It is really hard to explain the equations related to enthalpy from a conceptual standpoint. This one can be derived, but it requires the First Law of Thermo and some relatively difficult math.
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