mole per liter (molar)
Molar concentrationexact by definition
The mole per litre, symbol M and spoken as molar, is the everyday unit of solution concentration: moles of solute per litre of final solution. It equals exactly 1000 mol/m³, a factor that is exact by decimal prefix. A 1 M solution of sodium hydroxide contains 40 g of NaOH made up to one litre with water.
Watch out: Molarity is per litre of SOLUTION, not per litre of solvent. You dissolve the solute and then make up to the mark, rather than adding solute to a litre of water. And because liquids expand when heated, a molarity is only valid at the temperature it was prepared at. Molality, in moles per kilogram of solvent, avoids both problems.
| 1 M | 1 M |
About the mole per liter (molar)
Molarity is the concentration unit that fits how a solution is actually prepared. Weigh the solute, drop it into a volumetric flask, add solvent until the meniscus sits on the mark, and you have a known number of moles in a known volume. \(c = n/V\), moles per litre. The reason chemists prefer it to a mass percentage is that reactions consume moles, so a molarity lets you read off reacting quantities directly: 25 mL of 0.1 M HCl contains \(0.025 \times 0.1 = 0.0025\) mol of acid, and it will neutralise exactly that many moles of hydroxide.
The two things to keep straight are both about volume. First, it is per litre of finished solution, not per litre of solvent. Dissolving 58.44 g of salt in one litre of water gives you rather more than one litre of brine, so that is not a 1 M solution. Second, volume is a function of temperature. A solution made up at 20 °C and used at 60 °C has expanded, so its molarity has fallen by a fraction of a percent even though nothing was added or removed. For most bench work that is negligible, and for precise thermodynamic work it is why molality exists.
Dilution follows the simplest formula in the subject: \(c_1 V_1 = c_2 V_2\), because the number of moles does not change when you add water. Diluting 10 mL of 6 M acid to 250 mL gives \(6 \times 10/250 = 0.24\) M. The one habit worth building is to add concentrated acid to water and never the reverse, since the heat of mixing goes into whatever is at the bottom of the vessel.