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A state function is something that doesn't depend on the path taken to get to a certain state, but only depends on the initial and final states. Another state function is volume. For example, if a bucket first had 5 L of water, then someone added 3 L and then took away 6 L, you end up with 2 L, and the overall change in the beaker was that it lost 3 L of water, regardless of the fact that water was added then taken away. This shows how volume is additive, and so are enthalpies.
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