High School Chemistry : Chemical Reactions
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Example Question #21 : Balancing Chemical Equations
Balance the following equation:
When balancing a chemical equation, it means that we are adjusting the coefficients in front of every compound so that the number of atoms for every element will match how many will be on the other side of the arrow.
Initially, we must take "inventory" of how many atoms of each element we have on both sides of the arrow.
On the left side:
1 potassium, 5 oxygen, 4 hydrogen, 1 P
On the right side:
3 potassium, 5 oxygen, 2 hydrogen, 1 P
Since there are quite a few components in this example, all of which need balancing, we just need to choose one element to start with and continue from there. Let's look at potassium. Since there is only one potassium atom on the left side, and 3 on the right side, let's think about what the lowest common multiple between 1 and 3 is - we can quickly decide that it is 3. This means we may place a 3 coefficient in front of the 
Adding the 3 coefficient in front of 
This brings our total of oxygen atoms on the right side to 7 as well. So we have indirectly balanced the oxygen atoms. Since the only element left to balance is phosphorus, we realize that phosphorus on both sides is already balanced. We have balanced our equation.
Now let's do one last tally to make sure we've balanced everything.
On the left:
3 potassium, 7 oxygen, 6 hydrogen, 1 phosphorus
On the right:
3 potassium, 7 oxygen, 6 hydrogen, 1 phosphorus
The equation has been balanced.
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