Hess’ Law, named after Germain Hess, is simply an application of the path independence of heat.
If we look at a simple heat of reaction graph, we remember that the heat of the reaction is simply the difference between the heat taken in and the heat given off. However, mathematically, that is the same as the difference between the heat of the reactants and the heat of the products. In fact, the only reason that we don’t work with it that way, is that it is impossible to directly measure how much heat something contains.
But, if we think of the heat of a reaction as simply the difference between the starting point and ending point then it becomes clear that the heat of the reaction should be path independent.
If that's true, then it shouldn't matter whether I get from the reactants to the products in one step (as above) or in more than one step.
If each of the “bumps” on the second graph above are separate steps in an overall process, then it should follow that if I put all of the individual heats together, I should get the overall heat.
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