Balancing Chemical Equations

The big idea

When you balance a chemical equation, you are not changing the reaction. You are making the written counts of atoms match what chemistry already does in real life. The law of conservation of mass says matter is not created or destroyed in a normal chemical reaction, so the same atoms must appear before and after.

Think of an equation like a recipe card. You can make more cakes by changing how many batches you bake, but you cannot turn sugar into flour. In chemistry, a coefficient is the big number in front of a formula that changes how many molecules (or, for ionic compounds like rust, formula units) you have. A subscript is the small number inside the formula that tells you what one molecule or formula unit is made of.

What you'll learn

• Why the same number of each atom must be on both sides
• How coefficients are different from subscripts
• A step-by-step method for balancing any equation
• How to check whether an answer is really balanced

Why atoms have to match

1. Reactants and products The left side of an equation shows the substances you start with. The right side shows what you make. Atoms can be rearranged, but they do not disappear or appear out of nowhere.
2. Count each atom To see if an equation is balanced, count the atoms of each element on both sides. If the counts match, the equation is balanced.
3. Mass stays the same If the atoms are the same before and after, the total mass is the same too. That is why the law of conservation of mass works in a closed system.

This picture shows why $2\mathrm{H_2} + \mathrm{O_2} \rightarrow 2\mathrm{H_2O}$ is balanced.

On the left, you can count 4 hydrogen atoms and 2 oxygen atoms. On the right, you count the same numbers. The equation is balanced because the atoms are just rearranged, not changed into different atoms.

Balanced equations keep the same atoms on both sides.

How to balance an equation

1. Write the correct formulas first Start with the right chemical formulas, not the names. If the formula is wrong, the equation will never balance.
2. Count each element Make a quick tally of every atom on the left and on the right. Look for the element that does not match.
3. Change coefficients only Put numbers in front of formulas to change the amount of each substance. Never change a subscript, because that would change the substance itself.
4. Save hydrogen and oxygen for last In many equations, these are easiest to balance after everything else. Then check again and use the smallest whole-number coefficients.

The trick is to change the count, not the formula.

Worked examples

1. Combustion of methane

Start with the unbalanced equation: $\mathrm{CH_4 + O_2 \rightarrow CO_2 + H_2O}$.

1. Carbon There is 1 C on the left and 1 C on the right, so carbon is already balanced.
2. Hydrogen There are 4 H atoms on the left but only 2 H atoms on the right. Put a 2 in front of water: $\mathrm{CH_4 + O_2 \rightarrow CO_2 + 2H_2O}$.
3. Oxygen The right side now has 4 O atoms total: 2 in $\mathrm{CO_2}$ and 2 in $\mathrm{2H_2O}$. Put a 2 in front of oxygen gas: $\mathrm{CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O}$.
4. Check C = 1, H = 4, O = 4 on both sides.

2. Formation of water

Start with $\mathrm{H_2 + O_2 \rightarrow H_2O}$.

1. Oxygen first Left side has 2 O atoms, right side has 1. Put a 2 in front of water: $\mathrm{H_2 + O_2 \rightarrow 2H_2O}$.
2. Hydrogen next The right side now has 4 H atoms, so put a 2 in front of hydrogen: $\mathrm{2H_2 + O_2 \rightarrow 2H_2O}$.
3. Check H = 4 and O = 2 on both sides.

3. Iron and oxygen

For iron(III) oxide, start with $\mathrm{Fe + O_2 \rightarrow Fe_2O_3}$.

1. Oxygen count Oxygen is 2 on the left and 3 on the right. The least common multiple of 2 and 3 is 6, so make 6 oxygen atoms on both sides.
2. Balance oxygen Put 3 in front of $\mathrm{O_2}$ and 2 in front of $\mathrm{Fe_2O_3}$: $\mathrm{Fe + 3O_2 \rightarrow 2Fe_2O_3}$.
3. Balance iron The right side now has 4 Fe atoms, so put 4 in front of Fe: $\mathrm{4Fe + 3O_2 \rightarrow 2Fe_2O_3}$.
4. Check Fe = 4 and O = 6 on both sides.

Every correct answer keeps each atom count the same.

Putting it together

$\text{atoms in reactants} = \text{atoms in products}$

Read it left to right: the numbers in front of formulas tell you how many molecules or formula units are reacting and forming. Those coefficients are also the mole ratios in the balanced equation.

A good balanced equation uses the smallest whole-number coefficients. For water, that final answer is $\mathrm{2H_2 + O_2 \rightarrow 2H_2O}$.

Read it left to right: two hydrogen molecules plus one oxygen molecule make two water molecules.

Check yourself

1. Why can you not change the subscript in $\mathrm{H_2O}$ to balance an equation? Answer Changing the subscript changes the substance, so you would no longer have water.
2. How many oxygen atoms are in $\mathrm{3O_2}$? Answer 6 oxygen atoms.
3. Is $\mathrm{CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O}$ balanced? Answer Yes. It has 1 C, 4 H, and 4 O atoms on both sides.

Common mistakes

• "I can fix it by changing a subscript." No. Changing a subscript changes the formula and makes a different substance.
• "A coefficient only changes the first atom." No. A coefficient multiplies every atom in the whole formula.
• "If the atoms match, the coefficients can be anything." No. Use the smallest whole-number coefficients.

Remember this

• Change coefficients, not subscripts. Coefficients change how many molecules you have. Subscripts change what the molecule is.
• Balanced means same atoms on both sides. That is the law of conservation of mass in a chemical equation.
• Count, change, check. Count atoms, change coefficients, then check again.