# What is the Molarity of a Solution

A solution such as salt water is a uniform mixture of one or more solutes (e.g., salt) in a solvent (water).  For this article we will assume the solvent is a liquid, but there are solid solutions as well.  The solute (the substance dissolved in the solvent) can be gas, liquid, or solid, but once dissolved in the solvent the solute exists as individual molecules or ions which are usually mixed randomly among the molecules of the solvent.

The concentration of a solute in a solvent can be described in a number of ways.  The usual description in chemistry is in terms of the molarity of the solution.  Molarity is the number of gram-moles of the solute per liter of the solution.  A gram-mole of a chemical substance having a molecular weight of M is M grams of the substance.  Other descriptions include concentration as, for example, the number of solute atoms for every million solvent atoms (parts-per-million atomic), the weight of solute per weight of solvent (mass percentage), the initial volume of solute per initial volume of solvent (volume percentage), and so on.  We will use molarity for this article, but the techniques used will work for most other measures of concentration.

One day Joe comes in and gives you a bottle of fluid, and tells you that it is a solution.  Your approach toward determining the concentration of the solution depends on what additional information you are also given.  If there is only one solute, there are three main cases:

1.  Joe tells you what the solvent and solute are, and how much solvent and solute went into the bottle;

2.  Joe tells you what the solvent and solute are, but not their quantities;

3.  Joe just smiles and walks away.

In the first case, the concentration can nearly be worked out on paper.  Joe tells you that he dissolved 100 grams of salt in a liter of water to make the solution.  Salt is sodium chloride, which has a molecular weight of 58.443, so one mole would weigh 58.443 grams.  100 grams of salt is thus 100/58.443 moles, or 1.711 moles.  There is a liter of water, so the molarity must be 1.711 moles per liter, yes?

No.  If we dissolve 100 grams of salt in a liter of water, the resulting solution has a volume of 1.023 liters – adding the salt makes the water expand a bit.  We determine this be measuring the volume of the fluid from Joe’s bottle.  His solution has 1.771 moles of salt in 1.023 liters of water, so that the salt water has a molarity of 1.672.

Let’s look at the second case.  Joe tells you that he dissolved salt in water, but not how much of each.  There are quite a few approaches to use for this class of problems.  The easiest approach works when you know the density of salt water as a function of concentration.  In that case, simply weigh a known volume of the solution, weigh it, calculate the density, and look up the concentration of salt water at that density.  Other approaches:

For salt in water, simply measure the volume of the solution in the bottle, boil away the water, and weigh the salt.  This gives us the data to follow the calculation used for the first case;

Weigh the solution, distill the water out of the solution and condense it into another container, then measure the weight of the water.  The difference is the weight of the salt.  This technique is useful when the solute decomposes when heated, but still does not react with the solvent.

Compare some physical or chemical parameter with solutions of known concentration.  One example is light absorption, but others include refractive index, density, viscosity, boiling point, melting point, and many others.

Now for the third case – this is the tricky bit.  You don’t know either the solvent or solute that Joe used to make up his solution.  Still, if the solute doesn’t degrade on heating, you can boil off the solvent and determine the weight concentration of the solution, even though you don’t know the chemical composition of the solvent.  To do better, you have to import a range of techniques from fields of chemistry called qualitative and quantitative analysis, which goes far beyond the scope of this article.

Although determining the concentration of a diluted solution seems far from our everyday experience, it should now be clear that in most situations the answer to such questions is within your grasp.  As usual, for more complicated problems, the aid of specialists is called for.  Having read this article, you will at least understand what they are saying!