Stoichiometric Calculations: Mole to Mole Calculations 
When we balance an equation it is important to think if it in terms of atoms of each element. For example, in a simple reaction between hydrogen and oxygen to make water, the equation we get is

                           2 H2   +   O2   ------->  2 H2O

which can mean

           2 molecules of H2   +  1 molecules of O2   -------->  2 molecules of H2O
 

However, when we use a balanced equaiton to plan how much of each reactant to use in an actual experiment, we have to shift our thinking to huge collections of molecules - to moles. The shift from molecules to moles is done by taking advantage of a simple rule from mathematics. Multiplying a set of numbers, such as the coefficients, by any constant number does not alter the ratios among the members of the set.  If we select Avogadro's number as the multiplier then we get lab-sized units of each chemical.

  2  X (6.02 X 1023 molecules) of  H2  +   1 X (6.02 X 1023 molecules) of O2   -------->
                                              2 X (6.02 X 1023 molecules) of H2O

The essential 2:1:2 ratio has not been changed by this multiplication. But the scale of the reaction has shifted to the mole level.

               2 moles of H2   + 1 moles of O2   --------> 2 moles of H2O


The ratio of moles of molecules is identical to the ratio of molecules - it has to be, since equal numbers of moles have equal numbers of molecules.

The ratio of the coefficients for any given chemical reaction is set by nature. You cannot change this ratio.  It is set when you write the formulae correctly and then balance the equation properly.  Once this is done the coefficient numbers can be used as the basis for chemical calculations.  The decision that is left for us is the scale of the reaction - how much do we want to use or make?  The number of options is infinite.  We could have
         0.02 moles of H2   +   0.01  moles of O2   -------->   0.02 moles of H2O
or
        1.36 moles of H2   +   0.68 moles of O2   -------->   1.36 moles of H2O
or
        88 moles of H2   +   44 moles of O2   -------->   88 moles of H2O

In every case, the relative mole quantities of H2 to O2 to H2O are 2:1:2.  We could say that 2 moles of H2, 1 mole of O2, and 2 moles of H2O are equivalent to each other in this reaction.  This does not mean that one chemical can actually substitute for any other chemical.  It does mean that a specific mole quantity of one substance requires the presence of a specific mole quantity of each of the other substance in accordance with the ratio of coefficients.

Below shows five different scales for the reaction of iron with sulphur to make iron sulphide, FeS.  Notice that the mole ratios are the same regardless of the scale.

                 1 atom  of Fe   +   1 atom  of S  ---->   1 molecule of FeS

                10 atoms of Fe  + 10 atoms of S ----> 10 molecules of FeS

                 55.8 mg of Fe  +      32.1 mg S  ---->   87.9 mg  FeS

                 5.58 g of Fe     +      3.21 g of S ----> 8.79 g of FeS

                 55.8 g of Fe     +      32.1 g of S  ----> 87.9 g of FeS
 
 


Mole to mole calculations:
This is an example of how to do mole to mole type problems:
Two atoms of sulphur react with three molecules of oxygen to form two molecules of sulphur trioxide, which is an air pollutant.

                            2 S  +  3 O2   ------->  2 SO3


How many moles of sulphur react in this way with 9 moles of O2?
Solution: From the balanced equation you can see that  2 S react with 3 O2
Set up your ratio like this:    2 S  =   3 O2
                                            x       9 moles

Cross multiply to get    2 * 9 moles = 3 * x

                                   x = (2 * 9 moles) / 3 = 6 moles
 

Therefore if 9 moles of oxygen are reacted then 6 moles of S must also be present.
Note that the unit "moles" was carried through the calculation.
Mole to Mole Calculations Worksheet

The following files are recommended reading.  Not mandatory, but highly recommended.
Eggsamples of Concrete Stoichiometry
Bridging the Stoichiometry Gap