Hess’ Law continued

Hess’ Law is stated in the following way:

When one reaction can be written as the sum of two or more 

other reactions, then the heat of that reaction is the 

sum of the heats of the other reactions. 

In simple English, that means that if you start with the same reactants and end with the same products the overall heat (given off or taken in) should be the same. However it also leads us to some mathematical problems.

For instance:

The idea behind a problem like this is that if we can add up the three lower reactions so that they start and end with the same reactants and products as the reaction at the top, then we should be able to add the heats of those reactions to get the heat of the reaction at the top.

Just to be clear, lets add the reactions as they are and see what we get. As we do this, it is important to understand that this is like adding equations in algebra. In algebra, anything on the left side of the equal sign stays on the left and anything on the right stays on the right. The difference here is that we have an arrow instead of an equal sign.

So, if we add the three reactions, we will get

2 H_{2 (g)} + O_{2 (g)} + N₂O_{5 (g)} + H₂O _(l) + 1/2 N_{2 (g)} + 3/2 O_{2 (g)} + 1/2 H_{2 (g)} → 2 H₂O _(l) + 2 HNO_{3 (l)} + HNO_{3 (l)}

Combining "like terms" would give us

5/2 H_{2 (g)} + 5/2 O_{2 (g)} + N₂O_{5 (g)} + H₂O _(l) → 2 H₂O _(l) + 3 HNO_{3 (l)}

Cancelling the water which appears on both sides would leave

5/2 H_{2 (g)} + 5/2 O_{2 (g)} + N₂O_{5 (g)} → H₂O _(l) + 3 HNO_{3 (l)}

This is (obviously) not the reaction we want, so we'll need to try a different approach.