Hess's law
Hess's law says the total heat of a reaction is the same whether it happens in one bold step or many small ones along the way. Picture hiking from a valley to a mountaintop: the change in your altitude depends only on where you start and where you finish, never on whether you marched straight up or wandered along switchbacks. Reaction enthalpy works the same way — the path is irrelevant; only the endpoints matter.
Because of this, you can add reactions together like equations in algebra and add their enthalpy changes right along with them. If a reaction is hard to measure directly, you can build it out of easier reactions whose enthalpies are already known, then sum them up to get the answer. Reverse a step and you simply flip the sign of its enthalpy.
The deeper reason is that enthalpy is a state function — it depends only on the state of the materials, not the route taken. Hess's law is really just that fact, dressed for practical use. It lets chemists pin down heats of reaction that no thermometer could ever catch directly, by routing around them through known steps.
Carbon burning straight to CO₂ is easy to measure; carbon burning only halfway to CO is not. So you measure CO₂ formation and the burning of CO, then subtract to get carbon's reaction to CO — without ever doing it directly.
Add known reactions to reach an unknown one — enthalpies add right along.
Hess's law is named after Germain Hess, who stated it in 1840 — before the first law of thermodynamics was fully formulated. It only works for state functions, so it applies to enthalpy (ΔH) and internal energy (ΔU), but never to heat or work counted along a particular path.