15. Balancing Chemical Equations

Why equations must balance

Atoms are not created or destroyed in a reaction (conservation of mass). So there must be the same number of each type of atom on both sides of the arrow.

This equation is not balanced:

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

Left: 2 H, 2 O. Right: 2 H, 1 O. An oxygen atom has disappeared, which is impossible.

Subscripts and coefficients

	Subscript	Coefficient
What it looks like	Small number after a symbol: the 2 in $H_{2} O$	Big number in front: the 3 in $3 H_{2} O$
What it means	Atoms inside one molecule	How many molecules
Can you change it to balance?	Never	Yes

How to count atoms

Multiply the coefficient by each subscript.

$3 H_{2} O$ : H $= 3 \times 2 = 6$ , O $= 3 \times 1 = 3$ .
$2Ca (OH)_{2}$ : Ca $= 2$ , O $= 2 \times 2 = 4$ , H $= 2 \times 2 = 4$ . The subscript after a bracket multiplies everything inside.

Step by step method

Write the correct formulas for every reactant and product.
Count the atoms of each element on both sides. A table helps.
Balance one element at a time by putting coefficients in front of formulas. Start with an element that appears in only one substance on each side.
Leave hydrogen and oxygen until last, and an element that is on its own (like $O_{2}$ or Mg) to the very end.
Recount everything. Make sure coefficients are in the simplest whole number ratio.

Worked exampleWater

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

O: 2 on the left, 1 on the right. Put 2 in front of $H_{2} O$ :

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

Now H: 2 on the left, 4 on the right. Put 2 in front of $H_{2}$ :

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

Atom	Left	Right
H	4	4
O	2	2

Balanced.

Reading a balanced equation

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

"Two molecules of hydrogen react with one molecule of oxygen to make two molecules of water." The coefficients give the ratio in which substances react.

Balancing equations

Why

Atoms conserved
Same atoms each side

Numbers

Subscript: never change
Coefficient: change this
Bracket multiplies inside

Method

Correct formulas first
Count atoms in a table
One element at a time
H and O last
Recount

Shortcuts

Polyatomic ions as one unit
Lowest common multiple

Quick summary

A balanced equation has the same number of each atom on both sides.
Change only coefficients (big numbers in front), never subscripts.
Count atoms by multiplying the coefficient by each subscript. A bracket subscript multiplies everything inside.
Balance one element at a time, leave H and O until last, then recount.
Treat unchanged polyatomic ions as one unit.

Quiz

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