Hess's Law (Three-Step Sum)

Enthalpy is a state function: it depends only on where the chemistry starts and where it ends, never on the route. So if you can reach the target reaction by adding up a chain of steps whose enthalpies you already know, their sum is the answer. Reverse a step and you flip the sign of its ΔH; double a step and you double its ΔH. Only two steps? Enter 0 for the third.

Germain Henri Hess published this in 1840 in St Petersburg, and the date is the remarkable part — it is before the first law of thermodynamics was stated. Joule's paddle-wheel measurements, Mayer's paper, and Helmholtz's 1847 formulation of energy conservation were all still to come. Hess had no theory of energy conservation to lean on; he simply measured heats of neutralisation with a calorimeter, noticed that the totals were the same whichever order he ran the reactions in, and stated the constancy of heat summation as an empirical law. It later turned out to be a corollary of the first law, which is a fair definition of a good experimentalist.

Worked case: the enthalpy of formation of acetylene cannot be measured directly — you cannot make 2C(s) + H₂(g) → C₂H₂(g) happen in a calorimeter — but its combustion can. Route it: 2C + 2O₂ → 2CO₂ at 2(−393.5) = −787.0 kJ/mol; H₂ + ½O₂ → H₂O at −285.8 kJ/mol; and the reversed combustion 2CO₂ + H₂O → C₂H₂ + 5/2 O₂ at +1299.6 kJ/mol. Sum: −787.0 − 285.8 + 1299.6 = +226.8 kJ/mol, matching the tabulated +227 kJ/mol. Acetylene is one of the few hydrocarbons with a positive formation enthalpy, which is exactly why an oxy-acetylene torch burns hot enough to cut steel.