Solutions

The behavior of solutions is a major topic in chemistry, particularly aqueous solutions. Since chemical reactions are governed by the law of definite proportions, it is important to characterize solutions in terms of the number of particular solute molecules or ions per unit volume. It is standard practice to state the concentration of a solution in terms of the number of moles of the solute (dissolved matter) per unit volume of the solution. This is called the molarity of the solution:

Note that a 1 Molar (1 M) solution is different from dumping a mole of solute into a liter of solvent. So in practice, you need to measure a mole of the solute and dissolve it in the solvent, then add enough solvent to increase the volume of the solution to 1 liter. For example, to make a 1 Molar solution of NaOH, you would put 40.01 grams of NaOH into a volume of water and then add water to reach 1 liter total volume.

Other ways of characterizing solutions include percent by volume (appropriate for liquid in liquid solutions) or percent by mass. These are often convenient as a way of labeling products, but for work with chemical reactions, you need to know how many reactant molecules there are per unit volume. If two solutions of reactants have the same molarity, then you know that if they are mixed with equal volumes, you have the same number of the two reactant species.

Another way of characterizing solutions is called molality. It is defined by

Note the difference from molarity: the denominator is the mass of solvent in molality whereas it is the volume of solution in molarity. So even when the solvent is water where 1 liter and 1 kilogram are equivalent, molality and molarity are never quite the same. A solution where 1 mole of solute is dissolved in 1 kilogram of solvent is denoted a 1 m solvent (lower case m) -- not enough difference in notation to avoid confusing the two, so care must be taken to distinguish between molarity and molality.