Chemical equations: Non-integer coefficients

When we write a balanced chemical equation, we indicate how much is needed of each substance in the reaction. Like this chemical reaction, where, two carbon atoms and one oxygen molecule form two carbon monoxide molecules. The number in front of each substance in a chemical equation is called the coefficient. The coefficients show the ratio between the number of carbon atoms, oxygen molecules, and carbon monoxide molecules in the reaction. Why two carbon atoms, and two molecules of carbon monoxide?

Because oxygen atoms come two by two, in oxygen molecules. There are no single oxygen atoms in the air. Therefore, two oxygen atoms is the minimum we can start with. Let's say we want to form a certain number of carbon monoxide molecules. How many oxygen molecules are needed?

Simple. To form two molecules of carbon monoxide, we need one oxygen molecule - half the number. And to form ten carbon monoxide molecules, we need half that number of oxygen molecules: five. In order to form one carbon monoxide molecule, you will need... one half of an oxygen molecule!

Wait a minute, half a molecule? We just said that there were no single oxygen atoms! Actually, they're not the same. The oxygen atoms are still bound together two by two. The coefficient "0.5" only shows that it's "half as many" molecules, not that the molecules themselves are cut in half.

One half of an oxygen molecule in the chemical equation, is not the same as a single oxygen atom. Does it seem complicated? Let's look at one more example. Iron oxide and carbon form pure iron and carbon dioxide. Let's ask the question, "How many carbon atoms are needed for each unit of iron oxide in the reaction?" We need to balance the equation.

The iron oxide contains two iron and three oxygen. After the reaction, the three oxygen atoms show up in carbon dioxide. So, how many carbon dioxide molecules are needed to get three oxygen atoms on the right-hand side? Each carbon dioxide molecule contains two oxygen atoms, so it needs to be... one and a half molecules!

1.5 molecules with two oxygen atoms each, makes three oxygen atoms. Exactly the number we needed. As in the previous example, it is not the actual molecule that is halved. It's the number of molecules that is 1.5 times as large as the number of iron oxide units. Let's finish balancing the equation.

How many carbon atoms are needed to form 1.5 molecules of carbon dioxide? That's right: "1.5 carbon atoms". Does that mean the atoms are cut in half? No, there are no half atoms. However: for each Fe-two O-three, we need one and a half times as many carbon atoms.

And finally, two iron atoms on the right hand side, and the equation is balanced: One formula unit of iron oxide plus "one and a half" carbon atoms gives us two iron atoms plus "one and a half" molecules of carbon dioxide. If you want whole numbers in the equation, you can simply double the coefficients of all the substances. But if the question is, "How many carbon atoms are needed for each formula unit of iron oxide?" the answer is, "One and a half!"