In any given chemical reaction, the equation that describes it is made up of numbers and symbols that represent the molecules that are combining. Any molecule is represented by the atomic symbols and subscripts telling how many of each type of atom make up a single molecule.
When the equation is balanced, coefficients are added to the molecules of the reactants and to the molecules of the products until the number of atoms of each type are equal on each side of the reaction. Thus, if a reaction begins with 4 atoms of "X" and 3 of "Y", it must end up with the same number of each atom.
To balance an equation, coefficients are added in front of the molecules. The coefficient tells how many of which molecule is needed in order to come up with the right number of atoms on each side. The coefficient is a multiplier for the numbers of each atom in each molecule of the equation.
As has been explained previously (for example), 3 C6H12O6 means 3 molecules of C6H12O6, which results in 18 C, 36 H, and 18 O atoms.
However, the coefficients also give more information. They serve additionally as a ratio of molecules that will react with each other. The coefficients can be seen as the how many of any numeric units are needed to properly react.
Using water as an example, the equation is this:
2H2 + O2 --> 2H2O
At the simplest level, this means 2 molecules of H2 reacted with 1 molecule of O2 results in 2 molecules of H2O.
HOWEVER, it ALSO means that any number of molecules can be combined, so long as the ration of 2:1 --> is preserved. Thus:
2 molecules of H2 reacted with 1 molecule of O2 results in 2 molecules of H2O
2 dozen molecules of H2 reacted with 1 dozen molecules of O2 results in 2 dozen molecules of H2O
2 score molecules of H2 reacted with 1 score molecules of O2 results in 2 score molecules of H2O
2 bazillion molecules of H2 reacted with 1 bazillion molecules of O2 results in 2 bazillion molecules of H2O
And for the most relevant example…
2 moles of H2 reacted with 1 mole of O2 results in 2 moles of H2O
It is when we relate the coefficients to moles that we tap a great deal of power! While we cannot count moles, we can use the atomic mass of the atoms to find the right amounts of elements or compounds to use in reactions.
For the reaction of sodium (Na) and Chlorine (Cl) we can use the balanced equation to determine the masses of the two elements that would be needed in a reaction. Here is the reaction:
2 Na + Cl2 → 2 NaCl
According the the formula above, we need molecules of Na and Cl2 in a ration of 2:1. Thus, if we have 2 moles of Na and 1 mole of Cl2 we will have the right ratio for a complete reaction with no left-overs.
From the atomic masses, we know that one mole of NA weighs 22.989 grams. Thus, we begin with 45.979 grams of sodium, we will have the right amount.
Because chlorine is always Cl2, one mole of it will weigh 70.90 grams. Finding the mass of a gas is not as easy as finding the mass of a solid, but it can be done, so starting with 70.90 grams of chlorine is the right amount as well.
It is the coefficients of the balanced equation that guide us to these masses. Understanding that coefficients give us the correct ratio of molecules allows us to use the relationship between atomic mass and numbers of moles to come up with the correct amounts of reactants for any reaction.