Solution concentration calculator

Concentration is one word for several different quantities, and the trouble starts when a method sheet assumes you know which one it means. Moles per litre answers "how many particles are in here", grams per litre answers "how much did I weigh out per litre", and mass percent answers "what fraction of the bottle is solute" — the same solution, three different numbers. This page reports all three from one weighing so you can quote whichever the method asks for without converting by hand.

How it is calculated

c = (m / M) / V · ρ(B) = m / V · w = m / (V × ρ) × 100 %

Dividing the mass you weighed by the molar mass gives the amount of substance in moles, and dividing that by the volume gives the amount-of-substance concentration — what everybody still calls molarity, though IUPAC retired the term. Mass concentration skips the molar mass entirely and stays in grams. Mass percent needs one more thing than the other two: the mass of the whole solution, which is its volume times its density, so a solution appreciably denser than water gives a lower percentage for the same weighing.

Source: NIST SP 811 (2008), Sec. 8.6, Amount of substance, concentration, molality, and the like — Sec. 8.6.5, amount-of-substance concentration c(B) = n(B)/V, with 1 mol/dm³ = 1 mol/L; Sec. 8.6.4, molar mass M = m/n

Questions people ask

Why does the page ask for a density?

Only the mass percent needs it. A percentage by mass is the mass of the solute divided by the mass of the whole solution, and the mass of the solution is not the volume unless the density happens to be 1.00 g/mL. Dilute aqueous solutions are close enough to water that leaving the default alone is fine; concentrated acids, brines and anything with a solvent other than water are not. The molarity and the grams per litre never use the density at all.

Is molarity the volume of solvent or of the finished solution?

The finished solution. Dissolve the solute, then make up to the mark — do not add a litre of water to the solid, because the solute takes up volume of its own and you will end up under strength. The quantity that uses the mass of the solvent instead is molality, in moles per kilogram, and it is a different number.

What if I do not know the molar mass?

Work it out from the formula with the molar mass calculator on this site and paste the figure in. Without it, the page still gives you grams per litre and the mass percent, which are often all a recipe needs — a 10 % w/v solution is defined by weight and volume alone.

Why is 1 M sodium chloride 58.44 g in a litre?

Because that is its molar mass in grams. One mole of anything is its molar mass weighed out in grams, so a one molar solution is that mass made up to one litre. The default on this page is exactly that case, which makes it easy to check the arithmetic against something you already know.

Does percent mean by mass or by volume?

This page reports percent by mass, which is why it asks for a density. The other conventions you will meet are % w/v — grams of solute per 100 mL of solution, which is the grams-per-litre figure divided by ten — and % v/v for two liquids mixed. They agree only when the density is 1.00 g/mL, so a label that says just "10 %" is worth querying.

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