Molarity is the amount concentration of a solute expressed as the number of moles of that solute present per unit volume of solution. It is commonly represented by the symbol M and is expressed in moles per litre, although the coherent SI expression is moles per cubic metre. In ordinary laboratory chemistry, molarity in moles per litre is extremely common because solutions are routinely prepared and measured using volumetric glassware calibrated in litres or millilitres.
The mathematical relationship is molarity equals amount of solute in moles divided by volume of solution in litres. Molarity therefore depends on the volume of the entire solution, not simply on the volume of solvent originally used. This distinction is important when preparing solutions because adding a specified mass of solute to a certain amount of solvent does not necessarily produce the desired molarity unless the final solution is brought to the required total volume. Molarity is widely used in stoichiometric calculations, acid base chemistry, equilibrium calculations, titrations, kinetics and laboratory solution preparation.
The word molarity is derived from mole, the chemical unit used to quantify amount of substance. A solution with a molarity of one mole per litre contains one mole of the specified solute in each litre of the final solution. A 0.1 molar solution therefore contains 0.1 mole per litre, while a 2 molar solution contains two moles per litre. The numerical value alone is incomplete unless the solute and volume basis are known.
Molarity is an intensive concentration measure because it does not depend directly on the total amount of solution. If two containers contain the same solution at the same molarity, a larger container contains more total solute even though the concentration is identical. This distinction between concentration and total amount is essential in laboratory calculations and explains why multiplying molarity by solution volume gives the amount of solute when the units are consistent.
Preparing a solution of known molarity usually involves accurately determining the required amount of solute and then adjusting the final solution volume to a calibrated value. For a solid reagent, the required mass can be calculated from the desired molarity, final volume and molar mass. The solid is weighed accurately, dissolved in an appropriate quantity of solvent, transferred to a volumetric flask, and the solvent is added carefully until the calibration mark is reached. The solution is then mixed thoroughly.
This procedure matters because simply adding the calculated mass to a measured volume of solvent can produce a final volume different from the intended volume due to volume changes on dissolution. For concentrated liquid reagents, an appropriate aliquot can be calculated and diluted to the desired final volume. Accurate preparation also requires attention to reagent purity, hydration state, temperature, glassware calibration and uncertainty in the measured quantities.
Molarity is particularly useful in reaction stoichiometry because chemical equations describe ratios of amounts of substances. If a reaction consumes two moles of one reactant for every one mole of another, their reacting amounts must satisfy that stoichiometric relationship regardless of the solution volumes. For example, if a reaction has a one to one stoichiometric ratio, the moles of the two reacting substances at equivalence are equal.
Since moles can be calculated as molarity multiplied by volume, the stoichiometric relationship can be converted into a relationship between solution concentrations and volumes. This principle forms the basis of many titration calculations. For a general reaction, coefficients in the balanced chemical equation determine how the molar quantities relate. The concentration alone does not determine whether a reaction is complete because the total amounts, stoichiometry, equilibrium and reaction conditions must also be considered.
Molarity has limitations because it is volume based and volume changes with temperature. A solution prepared at one temperature can have a slightly different molarity at another temperature if thermal expansion changes the solution volume. This is one reason molality is preferred in some thermodynamic applications, especially calculations involving boiling point elevation, freezing point depression and chemical potentials. Molality is defined using kilograms of solvent rather than litres of solution and is therefore substantially less affected by thermal expansion. Nevertheless, molarity remains highly convenient for laboratory work because volumes are easy to measure accurately with volumetric flasks, pipettes and burettes. The choice between molarity and other concentration measures depends on the physical situation, required accuracy and purpose of the calculation.
Molarity should also be distinguished from normality, a historical concentration measure still encountered in some older analytical chemistry contexts. Normality depends on equivalents and can vary according to the particular reaction being considered, whereas molarity is directly tied to the number of moles of chemical entities. Modern chemical education and many contemporary analytical practices favour molarity because it has a clearer connection with amount of substance and stoichiometric equations.
Molarity also differs from molality, mole fraction, mass concentration and percentage concentration. Converting between these measures requires additional information such as molar mass or solution density. For example, converting mass concentration in grams per litre into molarity requires dividing by the molar mass in grams per mole. Converting between molarity and molality generally requires the solution density and composition.
Molarity is used extensively in acid base chemistry, where hydrogen ion or hydroxide ion concentrations are important for describing aqueous systems. It is also used in solubility equilibria, complex formation, redox chemistry and reaction kinetics. However, for precise thermodynamic equilibrium calculations, concentrations are often replaced by activities because real solutions do not always behave ideally. An activity incorporates the effects of intermolecular and ionic interactions that cause the effective chemical behaviour of a species to differ from its numerical concentration. At sufficiently low concentrations, activity coefficients may approach one and concentration based approximations become more accurate. Thus molarity is both a practical laboratory quantity and an approximation to more fundamental thermodynamic quantities in situations where solution nonideality is negligible.
A common mistake is to confuse the volume of solvent with the final volume of solution. If one mole of solute is added to one litre of water, the resulting solution is not necessarily exactly one litre, so it should not automatically be called a one molar solution. To prepare one litre of a one molar solution, one mole of solute is dissolved and the final solution is made up to exactly one litre.
Another common mistake is failing to account for the chemical form of the reagent, such as a hydrate, or assuming that a commercial reagent is perfectly pure. Correct molarity calculations require a balanced understanding of moles, molar mass, volume, purity and stoichiometry. Once these ideas are established, molarity becomes one of the most useful quantitative tools in solution chemistry.
