 ## Hess's Law

Many chemical reactions are difficult to carry out in the lab under normal conditions. The reasons for this are varied but might include:
• the reaction might be very slow and take a long time to complete.
• there maybe unwanted side reactions taking place This means that we cannot measure the enthalpy changes for these reactions directly. Luckily we can use Hess's law to calculate the enthalpy changes for these reactions.

Hess's Law is simply an extension of the law of conservation of energy, that is that energy cannot be created or destroyed only change from one form to another. As an example consider the image opposite. Here the change A→B is an exothermic reaction with an enthalpy change (ΔH1) of -1000kJ. Now imagine that for some reason the change A→B cannot be carried out directly. However the change A→C and C→B is possible with enthalpy changes of ΔH2= -400kJ and ΔH3= -600kJ. This route from A→B simply goes through an intermediate C. However the important fact is that both reactions, the direct route A→B and the other route through intermediate C both start and end up at the same place. They both start at A and end up at B.

In essence this is Hess's law. Hess's law states that:

The enthalpy change for a reaction depends only on the initial and final states of the reaction and is independent of the route by which the reaction occurs.

So in our example:

• the direct route A→B has an enthalpy change of ΔH1= -1000kJ.
• the indirect route A→C has an enthalpy change of ΔH2= -400kJ and C→B has an enthalpy change of ΔH3= -600kJ.
Or we could write ΔH1 = ΔH2 + ΔH3.
That is the sum of the two enthalpy changes, ΔH2 + ΔH3 is the same as the direct route ΔH1. Which is just another way of saying that the enthalpy change for a reaction is equal to the sum of the enthalpy changes for any individual steps, as long as you start and end points are the same. That's all there is to Hess's law!

### Worked examples using Hess' law

Examiners often ask you to calculate the enthalpy change for a reaction using either enthalpies of combustioncHo) or enthalpies of formationn(ΔfHo). If you are not sure what these enthalpy changes represent then click the links to do a little research before continuing.

### Using enthalpies of combustion (ΔcHo) to calculate an enthalpy change

substance Enthalpy of combustion/kJmol-1
C(s) -394
H2(g) -286
CH4(g) -890

Example 1 - Calculate the enthalpy of formation of methane (CH4(g)) using the enthalpies of combustion given in the table opposite.

All the questions you are likely to be asked to solve are all done the same way. So follow the method below and you can't go wrong!
Step 1 - You must write the equation for the reaction you are being asked to calculate the enthalpy change for. In this case we have to calculate the enthalpy of formation of methane. An equation for this enthalpy change is given below:

##### C(s) + 2H2(g) → CH4(g)
To calculate this enthalpy change we need the enthalpies of combustion of all the element and compound present in this equation, a quick check in the table shows that you have all these enthalpies of combustion. Now all we need to do is draw a simple energy cycle using the data we have. Some students get confused on how to start these cycles, but if you are using enthalpies of combustion, which we are here, then the cycle goes "downwards"! ### Using enthalpies of formation (ΔfHo) to calculate an enthalpy change

The other type of problem you are likely to meet is where you have to use enthalpies of formation to calculate an enthalpy change.

substance Enthalpy of formation/kJmol-1
NH3(g) -46
NO(g) 90
H2O(l) -286
As before the first step is to write out the equation you have been asked to find the enthalpy change for.
Example 2- Calculate the enthalpy change for the following reaction using the enthalpy of formation(ΔfHo) data in the table.
##### 4NH3(g) + 5O2(g) → 4NOg) + 6H2O(l)
As before in order to calculate the enthalpy of reaction (ΔrxnH) we need to know the enthalpy of formation ( (ΔfH) for all the substances in our equation. Looking at the table we have all the information we need, remember the enthalpy of formation of an element is by definition 0.
When we drew the energy cycle above using enthalpies of combustion (ΔcHo) we drew the cycle "downwards" from our equation. This time using enthalpies of formation (ΔfHo) we will work "upwards" towards our equation. ## Key Points

The hardest part of getting started with a Hess's law energy cycle is knowing where to start - remember that if you are given enthalpies of combustion data to calculate an unknown enthalpy change your energy cycle goes "downwards". If you are given enthalpies of formation data to calculate an unknown enthalpy change your energy cycle goes "upwards". 