How can I do Hess's law with fractions?
Usually with ease.
Let's take a simple one, formation of water:
Now you have been given an enthalpy value for the reaction. What does it mean? It means that
If I wanted to represent the reaction a bit more economically I could write:
Quite clearly the same energy transfer occurs, but here only the 1 mole of product results (and of course 1/2 the energy). This last reaction represents (by definition)
So, what's the message? That enthalpies are extensive quantities, and depend on the amounts of reactants and products. And when you do heat summations with Hess' law, you add and subtract together the actual numerical quantities of reactions, and double/treble/halve the enthalpies associated with them if required.