 # Hess' Law

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## Hess' Law

#### Energy cycles

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

#### Application of Hess' law

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 = ΔHc o Carbon (Graphite) = -393.5 kJmol-1

ΔH3 = ΔHc o Hydrogen = -285.8 kJmol-1

ΔH4 = ΔHc 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

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