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Balancing Chemical Equations Using Coefficients

Welcome back. In the previous lesson, you wrote word equations by placing reactants on the left and products on the right. Chemical equations use the same structure, but replace names with chemical formulae.

This final lesson of the module introduces the rule that makes chemical equations scientifically accurate: the number of atoms of each element must be the same on both sides of the reaction arrow. You will learn to balance simple equations by adding coefficients — large numbers placed in front of formulae — while keeping every chemical formula unchanged.

Why equations must balance

During a chemical reaction, atoms are rearranged into new substances. They are not created or destroyed. This is the law of conservation of mass: if the same atoms are present before and after a reaction, the total mass stays the same.

For example, consider ammonia being made from nitrogen and hydrogen:

N_{2} + H_{2} \to N H_{3}

Count the atoms.

Element	Reactant side	Product side
Nitrogen, $N$	2	1
Hydrogen, $H$	2	3

The equation is not balanced: there are different numbers of nitrogen and hydrogen atoms on each side.

A balanced equation does not need the same number of molecules on each side. It needs the same number of each type of atom on each side.

The diagram compares the unbalanced equation $N_2 + H_2 \rightarrow NH_3$ with the balanced equation $N_2 + 3H_2 \rightarrow 2NH_3$, showing that both sides then contain two nitrogen atoms and six hydrogen atoms.

Coefficients: the numbers you are allowed to change

A coefficient is a whole number written in front of a chemical formula. It tells you how many particles or formula units of that substance are involved.

For example:

2 H_{2}

means two molecules of hydrogen. Each molecule contains two hydrogen atoms, so altogether there are:

2 \times 2 = 4

hydrogen atoms.

The coefficient applies to every atom in the formula. For water:

2 H_{2} O

means two water molecules. The atom totals are:

Hydrogen: $2 \times 2 = 4$
Oxygen: $2 \times 1 = 2$

A coefficient of $1$ is normally not written. Thus, $O_{2}$ really means $1 O_{2}$ .

The small numbers within formulae are called subscripts. They have a completely different job from coefficients.

Number type	Example	Meaning	Can you change it while balancing?
Coefficient	$2 H_{2} O$	Two water molecules	Yes
Subscript	$H_{2} O$	Two H atoms in each water molecule	No

Changing a subscript changes the substance itself. Water is $H_{2} O$ . If you change it to $H_{2} O_{2}$ , you have made hydrogen peroxide, which is a different chemical.

So the central rule is:

Change coefficients, never subscripts.

Introduction to Balancing Chemical Equations

Watch “Introduction to Balancing Chemical Equations” by Tyler DeWitt for a visual explanation of how atom counts change when coefficients are added.

Begin with balancing water. Notice that balancing oxygen first creates a new hydrogen mismatch, so the counts must be checked again. Then watch the numbers rule, which clearly distinguishes a coefficient from a subscript. Finish with the counting table for a practical atom-count method using ammonia.

A reliable balancing method

Balancing is usually a short process of counting, adjusting, and recounting.

Write the correct formulae for the reactants and products.
Count each element on both sides of the arrow.
Add a coefficient in front of one formula to fix an unequal atom count.
Recount every element. Adding a coefficient affects all atoms in that formula.
Continue until each element has equal counts on both sides.
Use the smallest whole-number coefficients that work.

A small table prevents mistakes, especially when an equation has more than one element.

Worked example: making water

Start with the unbalanced equation:

H_{2} + O_{2} \to H_{2} O

Count the atoms.

Element	Left side	Right side
Hydrogen	2	2
Oxygen	2	1

Hydrogen is balanced, but oxygen is not. There are two oxygen atoms on the left, so put a coefficient $2$ in front of water:

H_{2} + O_{2} \to 2 H_{2} O

Now recount.

Element	Left side	Right side
Hydrogen	2	$2 \times 2 = 4$
Oxygen	2	$2 \times 1 = 2$

Oxygen is now balanced, but hydrogen is not. Put a coefficient $2$ in front of hydrogen:

2 H_{2} + O_{2} \to 2 H_{2} O

Final check:

Element	Left side	Right side
Hydrogen	$2 \times 2 = 4$	$2 \times 2 = 4$
Oxygen	2	$2 \times 1 = 2$

The equation is balanced.

Worked example: making ammonia

Now return to the ammonia equation:

N_{2} + H_{2} \to N H_{3}

The nitrogen atoms are unequal: there are two on the left but only one on the right. Put a coefficient $2$ in front of ammonia:

N_{2} + H_{2} \to 2 N H_{3}

This fixes nitrogen, but it changes hydrogen on the product side. The counts are now:

Element	Left side	Right side
Nitrogen	2	$2 \times 1 = 2$
Hydrogen	2	$2 \times 3 = 6$

To make six hydrogen atoms on the left, place a $3$ in front of $H_{2}$ :

N_{2} + 3 H_{2} \to 2 N H_{3}

Check the final counts:

Element	Left side	Right side
Nitrogen	2	2
Hydrogen	$3 \times 2 = 6$	$2 \times 3 = 6$

Every element balances, so the equation is complete.

Balanced chemical equations - Atoms, elements and compounds - AQA - GCSE Chemistry (Single Science) Revision - AQA - BBC Bitesize

BBC Bitesize explains the conservation-of-mass reason for balancing and works through the same ammonia equation one careful step at a time.

In the subsection “Balancing an equation,” read the explanation and worked table. Focus on how the atom counts are checked after each new coefficient, rather than trying to balance both elements at once.

Common mistakes to avoid

Changing subscripts

This is the most important error to avoid.

Incorrect attempt:

H_{2} + O_{2} \to H_{2} O_{2}

The atom counts may look equal, but $H_{2} O_{2}$ is not water. The equation now describes a different reaction involving a different substance.

Correct balancing keeps the formula for water unchanged:

2 H_{2} + O_{2} \to 2 H_{2} O

Forgetting that a coefficient multiplies the whole formula

In:

3 H_{2}

there are $3 \times 2 = 6$ hydrogen atoms, not three.

Similarly, in:

2 N H_{3}

there are two nitrogen atoms and six hydrogen atoms. The coefficient $2$ multiplies both $N$ and $H_{3}$ .

Stopping after fixing one element

In the ammonia example, putting $2$ before $N H_{3}$ balanced nitrogen but caused hydrogen to become unequal. Always recount all elements after every change.

Writing unnecessary coefficient $1$

This is correct but usually not written:

1 N_{2} + 3 H_{2} \to 2 N H_{3}

The standard form is simpler:

N_{2} + 3 H_{2} \to 2 N H_{3}

Final checking routine

Before deciding an equation is balanced, use this checklist:

The chemical formulae have not been changed.
Every added number is a coefficient in front of a formula.
Each element has the same number of atoms on both sides.
The coefficients are the smallest whole numbers possible.
Any coefficient of $1$ has been omitted.

Key takeaways

Chemical equations must balance because atoms are conserved during a chemical reaction. Balancing does not mean making the formulas look similar; it means ensuring that each element has the same total number of atoms before and after the reaction.

Use coefficients to change the number of molecules or formula units:

2 H_{2} + O_{2} \to 2 H_{2} O

Never change subscripts, because they define the identity of a substance. With careful atom counting and a final check of every element, you can balance simple chemical equations accurately.

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