Consider the reaction:

A + B → C + D

Here we are only observing one possible reaction route from the reactants A and B to the products C and D. In fact there may be more than one possible route for this reaction to take.

Example:

According to the German scientist Hess, the total enthalpy change for a chemical reaction is independent of the route by which the reaction takes place.

If we take the example above then the enthalpy change of route 1 would equal the total of the enthalpy changes for route 2:

ΔH₁ = ΔH₂ + ΔH₃ + ΔH₄

The best way to calculate this is to use different routes as shown. Where we cannot measure enthalpy changes directly Hess' law is of great use.

Consider the following example for the formation of methane from carbon and hydrogen: We are unable to perform this reaction in the laboratory but we can use the values for the enthalpy of combustion for the elements and compound. (Note: O₂(g) is included on both sides of the equation in order to balance the equations. Its presence does not affect the enthalpy change.)

ΔH₂ = ΔH_c ^o Carbon (Graphite) = -393.5 kJmol^-1

ΔH₃ = ΔH_c ^o Hydrogen = -285.8 kJmol^-1

ΔH₄ = ΔH_c ^o Methane = -890.3 kJmol^-1

We can also use Hess's law to help calculate the average bond energy for C-H in methane:

ΔH₂ = -74.8 kJ mol¹

ΔH₃ = +715 kJ mol^-1

ΔH₄ = +218 kJ mol^-1

ΔH₁ = ΔH₃ + 4ΔH₄ - ΔH₂

ΔH₁ = +715 + 4(218) - (-74.8) = + 1661.8 kJ mol^-1

4 C-H bonds in methane therefore:

1 C-H bond = 1661.8/4 = +415.3 kJ mol^-1