Based on experimental measurements of enthalpy changes, Swiss chemist G.H. Hess suggested in 1840 that the addition of chemical equations yields a net chemical equation whose enthalpy change is the sum of the individual positive and negative enthalpy changes.

Formulated by the chemist Germain Hess, this is an application of the first law of thermodynamics to physical chemistry. Thermodynamics tells us that energy is conserved; Hess confirmed that this applies to chemical reactions.

Hess's law is that the total enthalpy change accompanying a chemical change is the same regardless of the route by which that change takes place.

In other words, the creation of any particular chemical product(s) will involve precisely the same transfer of heat energy regardless of what you start with, and regardless of which steps you take to reach the final product(s).

Hess's law is used in determining experimentally the enthalpy changes of reactions which cannot be directly measured themselves (such as the formation of magnetic iron oxide, Fe3O4), and for calculating enthalpy changes without the need for experiment. This is done by determining the enthalpy changes of formation of the products and reactants. This is best illustrated by a Hess cycle:

REACTANTS -- PRODUCTS \ / ELEMENTS
Either the change from reactants to products cannot be measured, for whatever practical reason, or you don't have time to carry out the experiment. But the change from the basic chemical elements to the reactants, and from the elements to the products, can be measured. Going from the elements directly to the products involves exactly the same enthalpy change as going from the elements via the reactants. The difference between the enthalpy change of direct formation of products from elements, and of direct formation of reactants from elements, is thus equal to the enthalpy change of the reactants forming the products.

A simple way of imagining it is to consider the change [elements-reactants] as equal to 1, [reactants-products] as equal to 2, and [elements-products] as equal to 3. Obviously, 1 + 2 = 3, so 3 - 1 = 2. In other words, [enthalpy change of formation of products, 3] minus [enthalpy change of formation of reactants, 2] equals [enthalpy change of reaction, 1].

Hess's law is thus an extremely useful tool in physical chemistry.


Worked example:

Say you want to calculate the enthalpy change for the combustion of methane. The equation for this reaction is:

CH4 + 2O2 = CO2 + 2H2O.

The appropriate Hess cycle is:

CH4 + 2O2 -- CO2 + 2H2O \ / C + 2H2 + 2O2
To calculate the enthalpy change you need to know the enthalpies of formation of the products (carbon dioxide and water) and the reactant (methane). Oxygen does not have an enthalpy change of formation because it's an element - it takes zero energy to "transform" it to the state it's already in.

The enthalpy change of formation of carbon dioxide is -393.5 kJ mol-1. The enthalpy change of formation of water is -285.8 kJ mol-1, which then has to be doubled because there are two moles of water in the equation. All together this comes to -965.1 kJ mol-1. The enthalpy change of formation of methane is -74.8 kJ mol-1. Subtract this from the above total (the products) and you get -890.3 kJ mol-1. This is the enthalpy change of combustion of methane. Its strongly negative value means that it gives out a lot of energy, which is what you would expect for a combustion reaction.


Reference: Michael Volkins (general editor), Nuffield Advanced Chemistry, 2000

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