A solution is a homogeneous mixture of a solute (the dissolved substance) and a solvent (the dissolving medium). Its concentration expresses how much solute is present in a given amount of solution or solvent. Chemists use several measures, each suited to a particular purpose.
- Mass percent $= \dfrac{\text{mass of solute}}{\text{mass of solution}}\times100$. Simple and temperature-independent.
- Mole fraction $x_A = \dfrac{n_A}{n_A + n_B}$; the sum of all mole fractions in a solution is $1$. Used in thermodynamics and gas laws.
- Molarity $M = \dfrac{\text{moles of solute}}{\text{volume of solution in litres}}$, in $mol\,L^{-1}$. The most common lab measure, but it changes slightly with temperature because volume expands on heating.
- Molality $m = \dfrac{\text{moles of solute}}{\text{mass of solvent in kg}}$, in $mol\,kg^{-1}$. Independent of temperature because it uses mass, so it is preferred for studying colligative properties.
- Parts per million (ppm) $= \dfrac{\text{mass of solute}}{\text{mass of solution}}\times10^{6}$. Used for very dilute solutions such as pollutants in water.
Dilution adds solvent without changing the moles of solute, so molarity falls while moles stay constant. This gives the dilution equation $M_1V_1 = M_2V_2$, where subscripts $1$ and $2$ denote the concentrated and diluted states. It is the basis of preparing standard solutions from a stock.
The concentration terms are interconvertible if the density of the solution is known. For instance, molality can be obtained from molarity using the solution density and the molar mass of the solute. Note that molarity always uses the volume of the whole solution, whereas molality uses the mass of solvent only — a frequent source of error. Because volume depends on temperature but mass does not, molality is the more reliable measure when temperature varies.