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Basically a state function is something that depends only on its current equilibrium state, not on how it got there. So for chemical reactions, this means that we can just add/subtract the overall enthalphies, and don't have to worry about the intermediate steps that a reaction may have gone through to reach equilibrium.
Adding on to the previous explanation, something that is not a state function would be work. Going from one place to another may done differently, and therefore different amounts of work may be required to get from one place to another. On the other hand, enthalpy has no such possibilities for alternative methods. Rather, because a reaction simply changes enthalpy directly there is no need to take such differences into account. The “how” of something does not matter in the case of enthalpy.
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