Molar Concentrations and Molarity 
Molarity is a way of specifing the amount of solute in one litre of solvent.   Molarity is also known as the concentration of a solution.  The concentration of a solution is the ratio of solute to a given quantity of solvent. We can use whatever units we wish but the most commonly used units are moles of solute per litre of solution.  The special name for this ratio is the molar concentration or molarity which is abbreviated 'M'.

       M =    mol solute    =        mol solute
                     L soln             1000 mL soln

Suppose we had a bottle with the label "0.5 M KBr".  This means that it contains a solution of potassium bromide with a concentration of 0.10 mol of potassium bromide per litre of solution (or per 1000 mL of solution).    It does not tell us the amount of solution in the bottle.
Solutions are considered to be homogenous substances once the solute has completely dissolved.
Sample Problem
A student requires 0.250 moles of NaCl for an experiment.  The only thing available to them is a bottle with a solution labeled "0.400 M NaCl."  What volume of the solution should be used?  Give the answer in millilitres.
Use the information on the bottle.  There is 0.400 moles of solute per litre.  We need 0.250 moles.

                0.400 moles = 0.400 moles = 0.250 moles
                         1 L             1000 mL              x

                   x = 625 mL.  Thus 625 mL of 0.400 M NaCl contains 0.250 mol of NaCl.

Practise Problem:
A glucose solution with a molar concentration of 0.200 M is available.  What volume of this solution must be measured to obtain 0.001 mol of glucose?
Preparation of Solutions
Another very common problem involving molar concentration is the calculation of the number of grams of solute needed to make a given volume of solution having a specific molarity.  The best way to see this is by example:
Problem:  How can 500 mL of 0.150 M Na2CO3 solution be prepared?
Solution: This is stated in a way that normally arises in the lab?  What we really want to know is how many grams of Na2CO3 that are going to be in 500 mL of 0.150 M Na2CO3 solution.
Although the label reads in M, the balance reads in grams.  Before we can calculate the number of grams we need to know the number of moles.

                   0.150 M  =  0.150 mol  = 0.150 mol  =         x
                                              L            1000 mL        500 mL

          x = 0.075 mol of solute.  Therefore we need to weigh out 0.075 mol of Na2CO3.

 The number of grams of Na2CO3 are therefore:

                                           g = n * mm
                                              = 0.075 mol * 105.99 g/mol
                                              =  7.95 grams

To answer the question:   Weigh out 7.95 grams of sodium carbonate.  Add it to 100 mL of water in a 500 mL volumetric flask.    Swirl to dissolve.  Top the flask up with 400 mL more water up to the 500 mL meniscus mark.
Practise problem:  How can we prepare 250 mL of 0.200 M NaHCO3?
Go to the Molarity and Solution Creation Worksheet
Go to the Stoichiometry of Solution Molarity Worksheet