The Mole: The Start of Chemical Calculations
 
The creation of formulas and the finding of their molecular masses is only partially complete.
What exactly does that number you have found for the molecular mass mean?  Is it the mass of one molecule, or a million, or ten billlion?  What unit is it measured in?

The Carbon-12 Based Atomic Mass Scale
In the years following Dalton's presentation of his atomic theory, chemists worked very hard at determining a complete set of relative masses for all the elements that were known.  By knowing these relative masses the chemists were able to select amounts of elements in grams needed for any desired atom ratio.    In establishing a table of atomic amsses, it is necessary to have a reference point against which to compare the relative masses. Currently, the agreed-upon reference is the most abundant isotope of carbon, which is carbon-12. By definition, an atom of this isotope is defined as having the mass of exactly 12.000 amu. (atomic mass units)  In other words, an amu is defined as 1/12th of the mass of one atom of carbon-12.

The definition of the size of the atomic mass unit was quite arbitrary.  It could just as easily have been selected to be 1/24th of the mass of one atom of a carbon atom, or 1/10th the mass of a calcium atom, or any other value. Why 1/12th the mass of carbon-12?  Carbon is a very common element, available to any scientist  and by choosing the amu to be of this size, the atomic masses of nearly all the other elements are almost whole numbers, with the lightest atom having a mass of approximately 1. (hydrogen-1 has a mass of 1.007825 amu when carbon-12 is assigned a mass of exactly 12 amu.)

The Mole
Suppose we want to make molecules of carbon dioxide, CO2, in such as way that there would be no extra carbon and oxygen atoms left. If we took ten atoms of carbon and twenty atoms of oxygen we would make 10 molecules of carbon dioxide.  Suppose we wanted to make more, lets say 40,000 molecules of carbon dioxide.  Once again, we could count out 40,000 atoms of carbon and 80,000 atoms of oxygen, let them react and we'd have 40,000 molecules of carbon dioxide.  This sounds all very nice and neat unless you realize the trap.  Have you ever seen an atom?  Atoms are too tiny to count individually.  Saying they are tiny is even wrong because tiny can be seen.   Even with the best scanning tunneling electron microscope ever invented the largest atoms known, look just like fuzzy cloud tops.  We have never seen individual atoms.  There are no lenses with the resolving power or balances fine enough to measure an individual atom.

We get around this problem because each element has its own characteristic atomic mass and each formula has its own unique molecular mass.    We know, that oxygen weighs in at 1.33 times that of carbon, because of this we get a ratio of their masses:

                   16.0 amu (for one atom of O) = 1.33
                   12.0 amu (for one atom of C)       1


If we take a sample of oxygen and carbon in a ratio of 1.33 to 1, we must obtain equal numbers of their atoms.  That is, if we actually had a balance that could measure amu directly we could mass out  32 amu of oxygen and 12 amu's of carbon - a mass ratio of 2.66 to 1 - we would have exactly 2 atoms of oxygen for every atom of carbon and a 2 to 1 ratio by atoms.

When we mass out a sample of an element such that its mass in grams is numerically equal to the element's atomic weight, we always obtain the same number of atoms no matter what element we choose.  Thus 12.0 g of carbon has the same number of atoms as 16.0 grams of oxygen, or 32.1 g of sulphur, or 55.8 g or iron.

This relationship also extends to compounds. The formula mass of water, H2O, is 18.0 amu. If we take 18.0 grams of water then it should have the same number of molecules as there were atoms in 12.0 grams of carbon.  The carbon-12 isotope, which makes up 98.89% of all naturally occuring carbon, is the reference used by SI Metric in its definition of the base unit for a chemical substance, the mole, abbreviated mol. 

This mole concept is the most important in all of chemistry. Once this concept is grasped all the rest of chemistry will appear easy.

Avogadro's Number
The mole is defined as 6.02 x 1023 units.  It is called Avogadro's number in honour of Italian scientist, Amadeo Avogadro (1776-1856). It is a pure number with a special name, just like so many others.  For example:
                                                 2 = pair
                                               12 = dozen
                                             144 = gross
                                             500 = ream
                                6.02 X 1023 = Avogadro's number
 
This number is not an odd number at all. It became inevitable once the amu was defined.   The relationships needed are:

                                          1 mole = 6.02 X 1023 particles     (General expression)
                                                         or
                                         12 amu = 1 atom of  C      (Specific example)
                                    1 mol of C = 6.02 X 1023 atoms of C
                                    1 mol of C = 12 g of  C
 

Another useful relationship is that 1 amu = 1.66 X 10-24 g

SO                            1  amu               =  6.0 X 1023 particles
                      1.66 X 10-24  grams
 

The mass in grams of a substance, that equals one mole is often called its molar mass, and the units are grams/mole or g/mol.   For example, aspirin has a molecular mass of 180 grams. Therefore if we massed out exactly 180 grams of aspirin we would have Avogadro's number of aspirin molecules.
          Atoms and Moles Exercise Sheet