Balancing Chemical Equations

Return to Equations Menu


Chemical equations do not come already balanced. This must be done before the equation can be used in a chemically meaningful way.

All chemical calculations to come must be done with a balanced equation.

A balanced equation has equal numbers of each type of atom on each side of the equation.

The The Law of Conservation of Mass is the rationale for balancing a chemical equation. The law was discovered by Antoine Laurent Lavoisier (1743-94) and this is his formulation of it, translated into English in 1790 from the Traité élémentaire de Chimie (which was published in 1789):

"We may lay it down as an incontestible axiom, that, in all the operations of art and nature, nothing is created; an equal quantity of matter exists both before and after the experiment; the quality and quantity of the elements remain precisely the same; and nothing takes place beyond changes and modifications in the combination of these elements."

A less wordy way to say it might be:

"Matter is neither created nor destroyed."

Therefore, we must finish our chemical reaction with as many atoms of each element as when we started.


Here is the example equation for this lesson:

H2 + O2 ---> H2O

It is an unbalanced equation (sometimes also called a skeleton equation). This means that there are UNEQUAL numbers at least one atom on each side of the arrow.

In the example equation, there are two atoms of hydrogen on each side, BUT there are two atoms of oxygen on the left side and only one on the right side.

Remember this: A balanced equation MUST have EQUAL numbers of EACH type of atom on BOTH sides of the arrow.

An equation is balanced by changing coefficients in a somewhat trial-and-error fashion. It is important to note that only the coefficients can be changed, NEVER a subscript.

The coefficient times the subscript gives the total number of atoms.

Three quick examples before balancing the equation.

(a) 2 H2 - there are 2 x 2 atoms of hydrogen (a total of 4).

(b) 2 H2O - there are 2 x 2 atoms of hydrogen (a total of 4) and 2 x 1 atoms of oxygen (a total of 2).

(c) 2 (NH4)2S - there are 2 x 1 x 2 atoms of nitrogen (a total of 4), there are 2 x 4 x 2 atoms of hydrogen (a total of 16), and 2 x 1 atoms of sulfur (a total of 2).


So, now to balancing the example equation:

H2 + O2 ---> H2O

The hydrogen are balanced, but the oxygens are not. We have to get both balanced. We put a two in front of the water and this balances the oxygen.

H2 + O2 ---> 2 H2O

However, this causes the hydrogen to become unbalanced. To fix this, we place a two in front of the hydrogen on the left side.

2 H2 + O2 ---> 2 H2O

This balances the equation.


Two things you CANNOT do when balancing an equation.

1) You cannot change a subscript.

You cannot change the oxygen's subscript in water from one to two, as in:

H2 + O2 ---> H2O2

True, this is a balanced equation, but you have changed the substances in it. H2O2 is a completely different substance from H2O. So, it's not the answer to the question that was asked.

2) You cannot place a coefficient in the middle of a formula.

The coefficient goes at the beginning of a formula, not in the middle, as in:

H2 + O2 ---> H22O

Water only comes as H2O and you can only use whole formula units of it.


Two more points:

1) Make sure that your final set of coefficients are all whole numbers with no common factors other than one. For example, this equation is balanced:

4 H2 + 2 O2 ---> 4 H2O

However, all the coefficients have the common factor of two. Divide through to eliminate common factors like this.

Technically, the equation just above is balanced, but only if you ignore the "no common factors other than one" rule. The correct answer has all common factors greater than one removed. If you were to answer a test question balanced as above, you will probably only get partial credit, if that.

2) NO fractions allowed in the answer, only whole numbers. For example:

H2 + Cl2 ---> (1/2)HCl

is an allowable step along the way to the answer, but it is not the answer.

The use of fractions in balancing is a powerful tool. Look for it in the solved examples.


Balance this equation: H2 + Cl2 ---> HCl

Remember that the rule is: A balanced equation MUST have EQUAL numbers of EACH type of atom on BOTH sides of the arrow.

The correctly balanced equation is:

H2 + Cl2 ---> 2 HCl

Placement of a two in front of the HCl balances the hydrogen and chlorine at the same time.


Balance this equation: O2 ---> O3

Hint: think about what the least common multiple is between 2 and 3. That's right - six.

The LCM tells you how many of each atom will be needed. Your job is to pick coefficients that get you to the LCM.

The correctly balanced equation is:

3 O2 ---> 2 O3

Practice Problems

How many oxygens are indicated: 3 Ca(NO3)2

Balance these equations:

Zn + HCl ---> ZnCl2 + H2

KClO3 ---> KCl + O2

S8 + F2 ---> SF6

Fe + O2 ---> Fe2O3

C2H6 + O2 ---> CO2 + H2O

Answers to the above problems


The last problem above involved the use of fractional coefficients. Balance these three equations using ONLY fractional coefficients:

S8 + F2 ---> SF6

C4H10 + O2 ---> CO2 + H2O

S8 + O3 ---> SO2

Answers to the three fractional coefficient problems

Be careful on using fractions. For example, (1/2)H2O is not a correct use of fractions. Why not? (1/2)H2 = one H atom, but (1/2)O = one half of one atom. You cannot split atoms in chemical reactions.

Generally speaking, fractions are mostly used with diatomics (with O2 is the most common). However, as you delve into this, you will sometimes see something like (1/2)H2O ussed in a balancing step, but you will never see it as the answer.

Want more balancing practice? Here's Balancing Worksheet #1 with 50 problems and answers.

Want still more? Here's Balancing Worksheet #2 with 60 more problems and answers.

Return to Equations Menu