0.12 Measuring energy changes in chemical reactions  (Page 6/8)

produces 393.5 kJ for one mole of carbon burned; hence q = -393.5 kJ. The reaction

produces 483.6 kJ for two moles of hydrogen gas burned, so q = -483.6 kJ. Therefore, more energy is available from the combustion of hydrogen fuel than from the combustion of carbon fuel. Because of this, we should not be surprised that conversion of the carbon fuel to hydrogen fuel requires the input of energy.

We can stare at the numbers for the heats of these reactions, 90.1 kJ, -393.5 kJ, -483.6 kJ, and notice a surprising fact. The first number 90.1 kJ, is exactly equal to the difference between the second number -393.5 kJ and the third number -483.6 kJ. In other words, the heat input in [link] is exactly equal to the difference between the heat evolved in the combustion of carbon ( [link] ) and the heat evolved in the combustion of hydrogen ( [link] ). This might seem like an odd coincidence, but the numbers from the data are too precisely equal for this to be a coincidence. Just as we do anytime we see a fascinating pattern in quantitative data, we should develop a model to understand this.

It is interesting that the energy of [link] is the difference between the energies in [link] and [link] , and not the sum. One way to view this is to remember that the energy of a reaction running in reverse must be the negative of the energy of the same reaction running forward. In other words, if we convert reactants to products with some change in energy, and then convert the products back to the reactants, the change in energy of the reverse process must be the negative of the change in energy in the forward process. If this were not true, we could carry out the reaction many times and generate energy, which would violate the Law of Conservation of Energy.

Let’s list all three reactions together, but in doing so, let’s reverse [link] :

What if we do both [link] and [link] at the same time?

Since O2 (g) is on both sides of this reaction, it is net neither a reactant nor product, so we could remove it without losing anything. [link] is then equivalent to [link] , except that we carried it out by doing two separate reactions. What if we do [link] in two steps, first doing [link] and then doing [link] ? That would be the same outcome as [link] so it must not matter whether we do [link] and [link] at the same time or one after the other. The reactants and products are the same either way.

What would be the energy of doing [link] and [link] either at the same time or in sequence? It must be the energy of [link] plus the energy of [link] , of course. So if we add these together using the above numbers, the energy of doing both reactions together is -393.5kJ + 483.6kJ = 90.1kJ. This is the energy of [link] and it is experimentally exactly the same as the energy of [link] .

This is a new observation. We have found that the energy of a single reaction ( [link] ) is equal to the sum of the energies of two reactions ( [link] and [link] ), which together give the same total reaction as the single reaction. When the separate reactions add up to an overall reaction, the energies of the separate reactions add up to the energy of the overall reaction.