Hess's Law Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
Hess's law states that the enthalpy of a reaction obtained by combining several known reactions is the sum of their enthalpies, each multiplied by the coefficient (positive or negative) needed to reconstruct the target reaction. Combining carbon combustion (ΔH = −393.5 kJ/mol) with reversed carbon monoxide combustion (ΔH = −283.0 kJ/mol, coefficient −1) gives the enthalpy of formation of CO: −110.5 kJ/mol.
Explanation
Hess's law is a direct consequence of enthalpy being a state function: its total change between an initial and a final state depends only on those two states, never on the reaction pathway taken to go from one to the other. This lets you calculate the enthalpy of a reaction that's hard to measure directly (because it's too slow, incomplete, or dangerous to run in a lab) by breaking it down into a combination of other reactions whose enthalpies are already known and measured. A negative coefficient in this calculator represents a reversed reaction: if a known reaction goes from A to B with an enthalpy ΔH, the reverse reaction (from B to A) has an enthalpy of exactly −ΔH — this is the mechanism that, in this calculator's reference example, lets you subtract carbon monoxide combustion from carbon combustion to isolate the formation reaction of CO itself, a reaction that in practice is very difficult to isolate experimentally because it almost always produces a mixture of CO and CO2. This method complements our Charles's law calculator and the site's other chemistry tools dealing with gases: where those calculators relate a gas's pressure, volume, and temperature, Hess's law relates energy exchanges between several chemical reactions.
Example: enthalpy of formation of carbon monoxide
Inputs
Reaction 1 (C + O2 → CO2): ΔH1 = −393.5 kJ/mol, coefficient +1. Reaction 2 (CO + ½O2 → CO2): ΔH2 = −283.0 kJ/mol, coefficient −1 (reversed).
Calculation
Total ΔH = (1 × −393.5) + (−1 × −283.0) = −393.5 + 283.0 = −110.5 kJ/mol.
Result
The formation enthalpy of carbon monoxide (C + ½O2 → CO) is −110.5 kJ/mol, a value that matches published reference tables.
Frequently asked questions
Why can't the formation enthalpy of CO be measured directly?
When carbon is burned in the presence of oxygen, the reaction almost always produces a mixture of carbon monoxide (CO) and carbon dioxide (CO2), with no way to experimentally isolate a reaction that would produce pure CO alone. Hess's law works around this practical problem by combining two reactions that are much easier to measure in isolation (the complete combustion of carbon, and the combustion of already-formed CO) to deduce the enthalpy sought through calculation rather than direct measurement.
What does a negative coefficient represent in this calculator?
A negative coefficient means the reaction must be reversed (read right to left) to contribute to the target reaction, and its enthalpy then changes sign. A coefficient of −2, for example, means the reaction is both reversed AND counted twice (the equivalent of twice the reverse reaction), with a total enthalpy multiplied by −2.
Does Hess's law apply to quantities other than enthalpy?
Yes, it actually applies to any thermodynamic state function — Gibbs free energy or entropy, for example, follow exactly the same additivity principle along a broken-down reaction pathway. Enthalpy nonetheless remains by far the most common application in general chemistry, especially for combustion and formation reactions. Once this enthalpy is known, our specific heat calculator lets you estimate the temperature rise it would produce on a given mass of matter.