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Enthalpy is considered a state function because it is NOT path dependent. Enthalpy is defined as delta H which is the change in H (which we can refer to as H final - H initial)! Therefore it's a state function because we care about the final and initial (since delta H is the difference in H), rather than the path it took! Heat isn't a state property because it's a form of energy in transit. You can kind of think of it as work if that makes more sense. work is also a form of energy in transit. They occur when there's a change in the system, but not at the initial or final state. Meaning they ARE path dependent, and therefore aren't state functions/properties! I hope this helps! :)
Enthalpy is the amount of heat released or absorbed at a constant pressure whereas heat is one way that energy can be transferred between a system and its surroundings as a result of a temperature difference. Like Angela mentioned, heat is a path dependent function while enthalpy is a state function. It's almost like displacement and distance. You can put in a lot more energy depending on the steps you take to achieve the final state, but all enthalpy cares about is the difference between an initial state and final state.
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