Balancing a chemical equation

Why balance?

In the last chapter, we learned the law of conservation of mass. In a reaction, atoms are not made or destroyed. They are only rearranged. So the number of atoms of each element must be the same on both sides of the equation. An equation with this property is balanced.

Look at the skeletal equation for water:

The left side has $2$ atoms of oxygen, and the right side has only $1$. It is not balanced. An atom would have vanished.

How to balance: hit and trial

We put a coefficient, a whole number, in front of a formula. It multiplies all the atoms in that formula. We never change the small numbers in the formula.

1. Write the skeletal equation with the correct formulae.
2. Count the atoms of each element on both sides.
3. Begin with the element that is in the fewest formulae. Put a coefficient to match the atoms.
4. Balance the other elements, and count again. Balance an element that is alone last.
5. Check that the coefficients are the smallest whole numbers.

Example 1: water.

Oxygen: $2$ on the left, $1$ on the right. Put $2$ before $\text{H}_2\text{O}$: now oxygen is $2$ and $2$. But hydrogen on the right is now $4$. Put $2$ before $\text{H}_2$.

Example 2: iron and steam.

Oxygen: $1$ on the left, $4$ on the right. Put $4$ before $\text{H}_2\text{O}$. Now hydrogen on the left is $8$. Put $4$ before $\text{H}_2$ on the right. Iron: $1$ on the left and $3$ on the right. Put $3$ before $\text{Fe}$.

Check: Fe $3 = 3$, H $8 = 8$, O $4 = 4$.

Example 3: methane burning.

Check: C $1 = 1$, H $4 = 4$, O $4 = 2 + 2$.

You should find that $1, 5, 3, 4$ balances it, and that doubling every number keeps it balanced.

A group of atoms as one

When a group such as $\text{SO}_4$ or $\text{OH}$ is the same on both sides, we can count it as one unit. In $\text{Na}_2\text{SO}_4 + \text{BaCl}_2 \rightarrow \text{BaSO}_4 + 2\,\text{NaCl}$, the group $\text{SO}_4$ is $1$ on both sides.

Practise with new numbers

Try it in Python

This program balances an equation by trying small coefficients.

Remember these

• A balanced equation has the same number of atoms of each element on both sides.
• Balance with coefficients, which are whole numbers in front of formulae. Never change a formula.
• Count the atoms before and after.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Balance $\text{Ca} + \text{O}_2 \rightarrow \text{CaO}$.

2. Is $\text{H}_2 + \text{Cl}_2 \rightarrow 2\,\text{HCl}$ balanced?

3. Why can we not balance the equation for water by writing $\text{H}_2\text{O}_2$?

4. Balance $\text{N}_2 + \text{O}_2 \rightarrow \text{NO}$.