Hess's Law

Enthalpy is a state function: it depends only on where you start and where you end, not on the route in between. Think of it like elevation. Climbing a mountain by a steep trail or a winding one gets you to the same height. A reaction's delta H works the same way — whether it happens in one step or ten, the total heat released or absorbed between the same reactants and the same products is identical.

That path independence is what makes Hess's Law work. If you have several known reactions with known delta H values, you can flip one (which flips the sign of its delta H) or multiply one by a factor (which scales its delta H by the same factor) so that, when you stack all the reactions and add them together, everything except the reactants and products of your target equation cancels out. Species that appear on both sides, or that cancel between steps, are intermediates — they show up in the known reactions but vanish from the final sum. Add up the adjusted delta H values and you get the delta H of the target reaction, even if that reaction is hard or impossible to run directly.

This connects back to energy diagrams and bond enthalpies from earlier in the unit: all of them are ways to total up the same kind of bookkeeping, just approached differently. Hess's Law is the general tool that justifies combining steps freely, which is exactly why you can build complicated reactions out of simpler measured ones and trust the arithmetic.