Molarity Calculator

Per liter of solution, not of solvent

Molarity is defined as moles of solute divided by liters of final solution. That distinction is the source of most first-year laboratory errors. To make one liter of 1 M sodium chloride you do not add 58.44 g to a liter of water — you dissolve 58.44 g in less water, then make the total volume up to one liter in a volumetric flask. Dissolving a solid changes the volume, sometimes noticeably, so the two routes give different concentrations.

Moles are just a counting unit

One mole is exactly 6.02214076 × 10²³ entities — a defined number since the 2019 revision of the SI, no longer tied to a sample of carbon. Molar mass in grams per mole is numerically equal to the relative atomic or molecular mass, which is the convenience that makes the whole system work: weigh out the molar mass in grams and you have counted out Avogadro's number of molecules without having to see a single one.

Dilution keeps the moles constant

When you dilute a stock solution you add solvent, not solute, so the number of moles does not change. Concentration times volume is therefore the same before and after: C₁V₁ = C₂V₂. Any pair of units works as long as you are consistent on both sides. The practical order matters too — for concentrated acids, always add acid to water rather than water to acid, because the heat of mixing can boil the first drops and spit them back at you.

Molarity versus molality

Molality is moles of solute per kilogram of solvent, and it is not the same thing. Because it is based on mass rather than volume, molality does not change with temperature, whereas molarity does — a solution warmed up expands, so its molarity falls slightly even though nothing has been added or removed. Physical chemistry uses molality for exactly that reason when studying boiling point elevation and freezing point depression. For ordinary bench work at constant room temperature, molarity is more convenient and the difference is negligible.

Reading a percentage concentration

Reagent bottles often quote percentages instead, and there are three incompatible conventions: weight per weight, weight per volume, and volume per volume. A "5% solution" is ambiguous without knowing which. Converting to molarity needs the density of the solution and the molar mass of the solute, so always work from the figure printed on the bottle rather than assuming.

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