Molarity Calculator

What molarity measures

Molarity is moles of solute per litre of solution, written M or mol/L. A 1 M solution contains one mole of the dissolved substance in every litre of the finished liquid. The two steps are always the same: convert mass to moles by dividing by molar mass, then divide moles by volume in litres.

So M = (mass ÷ molar mass) ÷ litres. Rearranged for the practical direction — you know what you want and need to know what to weigh — it becomes mass = M × litres × molar mass.

A worked example

To make one litre of 0.1 M sodium chloride: NaCl has a molar mass of 58.44 g/mol, so you need 0.1 × 1 × 58.44 = 5.844 g. Weigh that out, dissolve it, and make the solution up to exactly one litre.

Going the other way: if you dissolved 5.844 g of NaCl and made it up to 500 mL instead, the concentration would be 0.1 mol ÷ 0.5 L = 0.2 M. Same mass, half the volume, double the concentration.

The mistake that matters: solution volume, not solvent volume

Molarity is defined against the volume of the finished solution, not the volume of solvent you started with. Adding a solid to one litre of water gives you slightly more than one litre of solution, because the solute occupies space too. For dilute solutions the difference is negligible; for concentrated ones it is not.

The correct technique is to dissolve the solute in a smaller volume first, then top up to the mark on a volumetric flask. "Dissolve in 800 mL, then make up to 1 L" is the standard phrasing, and it is not fussiness — it is what makes the number on the bottle true.

Dilution

Once you have a stock solution, the relationship for diluting it is C₁V₁ = C₂V₂. To make 250 mL of 0.1 M from a 1 M stock: V₁ = (0.1 × 250) ÷ 1 = 25 mL of stock, topped up to 250 mL. The moles of solute are unchanged; only the volume they are spread through has grown.

Always add concentrated acid to water and never the reverse. The dilution of strong acids is strongly exothermic, and adding water to acid can boil it and spatter.

Molarity, molality and the others

Molality is worth knowing about specifically because it uses mass rather than volume, and mass does not change with temperature. A molar solution prepared at 20 °C is slightly less concentrated at 80 °C because the liquid has expanded — a molal one is not affected.

Do I add the solute to a litre of water, or make it up to a litre?

Make it up to a litre. Molarity is defined per litre of finished solution, and the solute takes up volume of its own, so dissolving a solid into a full litre of water gives you slightly more than a litre and therefore a slightly weaker solution than intended. Dissolve in a smaller volume, then top up to the graduation mark. For dilute solutions the error is small; for concentrated ones it is significant.

How do I dilute a stock solution to a lower concentration?

Use C₁V₁ = C₂V₂. To make 250 mL of 0.1 M from a 1 M stock, you need (0.1 × 250) ÷ 1 = 25 mL of stock, made up to 250 mL. The number of moles does not change during a dilution — only the volume they are distributed through. With acids, always add the acid to the water rather than the other way round.

What is the difference between molarity and molality?

Molarity is moles per litre of solution; molality is moles per kilogram of solvent. The practical difference is temperature: volume expands when heated but mass does not, so a molar solution’s concentration drifts slightly with temperature while a molal one is fixed. Molarity is more convenient for everyday work because measuring volume is easier than weighing solvent; molality is used where temperature changes matter, such as freezing point depression.

Does this work for solutions that are not water-based?

Yes — molarity is defined without reference to any particular solvent, so the arithmetic is identical whether you are working in water, ethanol or DMSO. What changes is practical: solubility limits differ enormously between solvents, and a mass that dissolves easily in one may not dissolve at all in another. The calculator will happily give you a number for a solution that cannot physically be made.

How do I convert molarity to parts per million?

For dilute aqueous solutions, ppm is approximately milligrams of solute per litre of solution. Multiply molarity by molar mass to get grams per litre, then by 1000 for mg/L. A 0.001 M solution of sodium chloride is 0.001 × 58.44 × 1000 = about 58 ppm. The approximation relies on the solution having roughly the density of water, which holds for dilute aqueous work and not much else.