Balancing chemical equations

We must have the same number of atoms on both sides of a chemical equation's arrow. Why? If we didn't we would be creating or destroying atoms, and that's not possible. The Law Of Conservation Of Mass tells us that matter (in this case atoms) cannot be created nor destroyed.

So when we count up the number of atoms on each side of the arrow, they must be the same.


Also, the number of atoms of each element must be the same. In a chemical reaction, the atoms are rearranged, but they can't change from one element to another. A carbon atom in a reactant on the left side of the arrow remains a carbon when it changes to a product on the right side of the arrow. It doesn't suddenly become a different element.

Sidenote: when we have radioactive elements, changes happen in the nucleus of the atom that mean that an atom of a radioactive element can decay to form a different element. And in stars, at immense temperatures, the nuclei of two atoms may fuse together to make a heavier element. But in the chemistry lab, the elements remain as the same elements.

What we're doing when we balance an equation is making sure that we haven't lost or gained any atoms. Balancing equations is an essential skill in chemistry and will always be asked about in exams, so we do need to get to grips with it.


Before we begin, let's remember what a chemical formula tells us.
H₂ means that we have two atoms of hydrogen, H, joined together in a molecule.
H₂O (water) tells us that those two atoms have been joined by a single oxygen atom, O. We could write it H₂O₁ but the ones just clutter everything up. When we only have one atom, we leave out the one and let the element's symbol do the job of showing us that there is one atom.

Test yourself 1: how many atoms are in H₂SO₄ (sulfuric acid)?

Let's start with the very simple example of hydrogen reacting with oxygen to form water. We can write that first as a word equation, which helps us to keep the reactants and products in the right places.

hydrogen + oxygen → water

Now let's change those names into chemical formulae:

H₂ + O₂ → H₂O

Add up the numbers of atoms on each side of the arrow. We have 2 x hydrogen and 2 x oxygen on the left, while on the right we have 2 x hydrogen but only 1 x oxygen. We have lost an oxygen atom somewhere, and that is not allowed. The equation is unbalanced.

In order to balance equations, students are sometimes tempted to change the small numbers after the elements, like this

H₂ + O₂ → H₂O₂ (THIS IS WRONG)

The numbers of atoms now balance, so what's the problem? The problem is, we haven't made water any more, but a different substance called hydrogen peroxide, H₂O₂, and that is not what happens in the reaction.

Instead, what we have to do is put large numbers in front of the chemical formulae to show that we are using more than one reactant molecule or producing more than one product molecule. So a 2 in front of H₂ would represent two molecules of H₂, or 4 x hydrogen atoms in total.

We're ready to try a method for balancing, using a number of steps.

Step 1. Count the number of atoms on each side of the arrow. Make yourself a little table. Some elements may balance already. If they all do, then we don't need to go further, as the equation is already balanced.

H₂ + O₂ → H₂O
2 x H → 2 x H
2 x O → 1 x O

Here we can see that hydrogen is balanced, but oxygen is not.

Step 2. See which side is short of atoms. Oxygen is short of atoms on the right side of the arrow. To fix this, we add large numbers in front of the chemical formulae. Let's fix oxygen by adding a two in front of H₂O.

H₂ + O₂ → 2H₂O

Step 3. Update the count of atoms.

H₂ + O₂ → 2H₂O
2 x H → 4 x H
2 x O → 2 x O

Oops! In balancing the oxygen atoms, we have unbalanced the hydrogens. Let's repeat Step 2, and see if we can fix the hydrogens this time. We can put a large 2 in front of H₂ so that we are using two molecules of hydrogen:

2H₂ + O₂ → 2H₂O
4 x H → 4 x H
2 x O → 2 x O

Now both hydrogen and oxygen are balanced, and the recipe for making water is clear. We take two molecules of hydrogen and one molecule of oxygen, and they react together to make two molecules of water. We have the same number of atoms of each element on both sides of the arrow, so no atoms have been created and none destroyed. The Law Of Conservation Of Mass has been obeyed.

If the equations are simple, we will be able to balance very quickly using this method, but for more complex ones, we may need to cycle round Steps 2 and 3 several times until we achieve balance.

Here's another example: hydrogen reacting with chlorine to make hydrogen chloride.

hydrogen + chlorine → hydrogen chloride
H₂ + Cl₂ → HCl
2 x H → 1 x H
2 x Cl → 1 x Cl

Both hydrogen and chlorine are short of atoms on the right hand side. We need more hydrogen chloride molecules, so let's put a 2 in front of that.

H₂ + Cl₂ → 2HCl
2 x H → 2 x H
2 x Cl → 2 x Cl

That's done the trick. We have balanced the equation.

Test yourself 2. Nitrogen N₂ reacts with hydrogen H₂ to make ammonia NH₃. Write a balanced symbol equation for the reaction.

Answers to test yourself questions

1. 7. Two x hydrogen, one x sulfur, four x oxygen.
2. N₂ + H₂ → NH₃
   2 x H → 3 x H
   2 x N → 1 x N
   
   Nothing balances. We are short of N on the right hand side, so let's fix that by putting a 2 in front of NH₃.
   
   N₂ + H₂ → 2NH₃
   2 x H → 6 x H
   2 x N → 2 x N
   
   That's sorted the nitrogens, but we are short of hydrogens on the left hand side. We have two and need six. We can fix that by using 3 molecules of hydrogen.
   
   
   N₂ + 3H₂ → 2NH₃
   6 x H → 6 x H
   2 x N → 2 x N
   
   
   And now we're balanced.