The Reaction Fraction

Once you understand how to read a reaction, stoichiometry is a simple idea. Let’s start with the same, example reaction:

2 C4H10 + 13 O2 → 8 CO2 + 10 H2O

Which you should read as:

2 moles of butane react with 13 moles of oxygen to make

8 moles of carbon dioxide and 10 moles of water.

This means that for every 2 moles of butane, the reaction uses 13 moles of oxygen. So, logically, 4 moles of butane would require 26 moles of oxygen. We can also relate amounts on the right side (the product side) of the reaction. When the reaction produces 8 moles of carbon dioxide, it also makes 10 moles of water. So, logically, if the reaction produced 16 moles of CO2, it would also make 20 moles of H2O. And, of course, we can relate the right and left sides of the reaction. So, if the reaction uses 4 moles of butane it would produce 16 moles of CO2.

Naturally, the world isn’t always that neat. We rarely have exactly 2 or 4 moles of butane, so we need to be able to use the reaction with numbers that are “messy.” That’s where the reaction fraction comes in.

The Reaction Fraction is simply the ratio between chemicals in the balanced reaction.

Let’s look at a specific example to see what that means.

How many moles of water are produced when 3.76 moles of butane burn?

As always, we start with the given fact on the left side, then use the factor label method to “fix” the units that are incorrect.

So, we'll put "what we don't want" on the bottom of the fraction and what we "do want" on the top of the fraction. That will give us this:

The numbers for that fraction come from the balanced reaction, so filling those numbers in, gives us:

Which we can now solve (remembering that numbers on the top are multiplied and numbers on the bottom are divided.

Let's do another example:

If butane is burned and it produces 9.08 moles of water, how many moles of oxygen were used?

Again we'll start with the basic structure of the problem (known on the left, fraction, needed on the right):

Then we'll put the units into the fraction

Then we'll put the numbers from the balanced reaction into the fraction

Then we'll solve