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A state function refers to a quantity that can be determined using the final and initial states only. State functions are path independent. Enthalpy is a state function because the delta H or change in enthalpy can be calculated using the final enthalpy and initial enthalpy. This is useful because it allows for us to add enthalpies when "adding" reactions together.
Expanding on the answer above, state functions are independent of how the final state of a system is reached. It's easier to understand if you think of an example such as hiking, which was what my TA told us. One hiker could take a winding path from point A to B, while another could make a straight beeline from A to B. In the end, the difference in height between the two points is still the same, regardless of how it took to get there. Furthermore, enthalpy itself is based on state properties such as internal energy, pressure, and volume, as given by the equation H = U + PV.
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