Chemistry · Study Guide

Balancing Chemical Equations: A Step-by-Step Method

A balanced chemical equation has the same number of atoms of each element on both sides — this reflects the Law of Conservation of Mass: atoms are rearranged in a chemical reaction, never created or destroyed. Balancing means finding the right coefficients (the numbers placed in front of each formula) so both sides match exactly.

The Rule That Matters Most

You can only change the COEFFICIENTS (the big numbers in front of a formula, like the $2$ in $2H_2O$ ) — never the SUBSCRIPTS (the small numbers inside a formula, like the $2$ in $H_2O$ ). Changing a subscript changes what substance the formula represents entirely; changing a coefficient just changes how many molecules of that same substance you have.

A Repeatable Method

1. List how many atoms of each element appear on each side.
2. Balance one element at a time, usually starting with whichever element appears in the fewest different molecules.
3. Balance oxygen and hydrogen last if they appear in multiple compounds — they're usually easiest to fix once everything else is set.
4. Recount every atom on both sides at the end to confirm the equation is truly balanced before moving on.

Worked Example — Combustion of Propane

Problem

Balance:

C_3H_8 + O_2 \rightarrow CO_2 + H_2O

Balance carbon

The left side has

3

carbon atoms (from

C_3H_8

), so the right side needs

3

CO_2

molecules:

C_3H_8 + O_2 \rightarrow 3CO_2 + H_2O

Balance hydrogen

The left side has

8

hydrogen atoms. Each

H_2O

supplies

2

, so

4

molecules of

H_2O

are needed:

C_3H_8 + O_2 \rightarrow 3CO_2 + 4H_2O

Balance oxygen last

Now count oxygen on the right:

3CO_2

supplies

3 \times 2 = 6

oxygen atoms, and

4H_2O

supplies

4 \times 1 = 4

more — a total of

10

oxygen atoms. Since each

O_2

molecule supplies

2

atoms,

5

molecules of

O_2

are needed on the left.

Final balanced equation

C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O

Check

Carbon:

3 = 3

. Hydrogen:

8 = 8

. Oxygen: left

5 \times 2 = 10

; right

(3 \times 2) + (4 \times 1) = 10

. Every element matches — the equation is balanced.

Common Mistakes

Changing a subscript instead of a coefficient to try to "balance" an element — this actually changes the chemical identity of the substance and produces a wrong (and often meaningless) equation.
Balancing oxygen or hydrogen first when they appear in several different molecules — it's almost always easier to lock those in last, once every other element is already fixed.
Stopping as soon as one element looks balanced without re-checking every element at the end. A genuinely balanced equation has to work for ALL elements simultaneously.
Leaving coefficients as fractions in a final answer (e.g. $\frac{5}{2}O_2$ ) instead of multiplying every coefficient in the whole equation by $2$ to clear it — a standard balanced equation uses whole-number coefficients.

Practice

Balance:

H_2 + O_2 \rightarrow H_2O

2H_2 + O_2 \rightarrow 2H_2O

Check: H:

4=4

. O:

2=2

Balance:

N_2 + H_2 \rightarrow NH_3

N_2 + 3H_2 \rightarrow 2NH_3

Check: N:

2=2

. H:

6=6

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