General Chemistry/Balancing equations

Chemical equations are useful because they give the relative amounts of the substances that react in a chemical equation. For example, from the chemical equation for the formation of ammonia, we can see that one mole of nitrogen gas will combine with three moles of hydrogen gas to form two moles of ammonia gas.

${\text{N}}_{2(g)}+3{\text{H}}_{2(g)}\to 2{\text{NH}}_{3(g)}$

In some cases, however, we may not know the relative amounts of each substance that reacts. Fortunately, we can always find the correct coefficients of an equation (the relative amounts of each reactant and product) by applying the law of conservation of matter. Because matter can neither be created nor destroyed, the total number of each atom on one side of the equation must be the same as the total on the other. This process of finding the coefficients is known as balancing the equation.

For example, assume in the above equation that we do not know how many moles of ammonia gas will be produced:

${\text{N}}_{2(g)}+3{\text{H}}_{2(g)}\to ?{\text{NH}}_{3(g)}$

From the left side of this equation, we see that there are 2 atoms of nitrogen gas in the molecule N₂ (2 atoms per molecule x 1 molecule), and 6 atoms of hydrogen gas in the 3 H₂ molecules (2 atoms per molecule x 3 molecules). Because of the law of conservation of matter, there must also be 2 atoms nitrogen gas and 6 atoms of hydrogen gas on the right side. Since each molecule of the the resultant ammonia gas (NH₃) contains 1 atom of nitrogen and 3 atoms of hydrogen, 2 molecules are needed to obtain 2 atoms of nitrogen and 6 atoms of hydrogen.

In a similar manner, you can use the law of conservation of matter to solve equations containing a greater number of unknown coefficients (the relative amounts of each reactant and product), or even subscripts (the number of each element in a molecule) on either side of the equation:

${\text{N}}_{?(g)}+3{\text{H}}_{2(g)}\to ?{\text{NH}}_{3(g)}$