Solution Concentration Calculator: Molarity, Percent, Dilution

Which concentration unit to use

Molarity, moles of solute per litre of solution, dominates in the laboratory because reagents are taken by volume and reaction coefficients are ratios between moles. It has one flaw: the volume of a liquid changes with temperature, so a 1 M solution at 20 °C is not exactly 1 M at 60 °C. That is why thermodynamic calculations prefer molality, which divides by the mass of solvent and is unaffected by temperature.

Percentages are used where there is no need to know the substance at the molecular level. Percent by mass is what food labels and commercial reagents use; percent mass per volume, grams per hundred millilitres, is what 0.9% saline is; percent by volume is alcohol by volume. Parts per million come in when percentages would mean too many zeros, as in water analysis.

Dilution is by far the most frequent calculation, and it rests on a single observation: adding solvent does not change the moles of solute. From this follows M₁V₁ = M₂V₂, where the two products are the same moles before and after. The practical question is almost never what concentration you end up with, but how much solvent to add: that is the difference between the two volumes, reported under the result.

Common mistakes

Using the volume of solvent instead of the volume of solution in molarity: dissolving one mole in one litre of water does not give a 1 M solution, because the final volume exceeds a litre. You make up to volume, you do not add a litre.
Leaving the volume in millilitres: molarity needs litres. Two hundred and fifty millilitres is 0.25 L, and forgetting it throws the answer off by a thousand.
Confusing molarity with molality: the first divides by the volume of solution in litres, the second by the mass of solvent in kilograms. In dilute aqueous solutions the values are similar, which makes the mistake hard to spot.

Frequently asked questions

How do you calculate the molarity of a solution?

Divide the moles of solute by the litres of solution: M = n/V. If you have grams rather than moles, first divide the mass by the molar mass. Note: the volume is that of the finished solution, not of the solvent added.

How do you use the formula M₁V₁ = M₂V₂?

Multiply the initial concentration by the initial volume and divide by the final volume to get the concentration after dilution. The solvent to add is the difference V₂ − V₁.

What is the difference between % w/w and % w/v?

The first is grams of solute per hundred grams of solution, the second grams per hundred millilitres. They coincide only when the density of the solution is one gram per millilitre, that is for very dilute aqueous solutions.

How much is 1 ppm?

One part in a million, that is one milligram of solute per kilogram of solution, or equivalently one milligram per litre in dilute aqueous solutions. It corresponds to 0.0001%.

How this calculation works

Molarity: M = n/V, with n in moles and V in litres of solution. From grams: M = m/(M·V). Molality: b = n/kg of solvent. Percent by mass: % w/w = (mass of solute / mass of solution) × 100. Percent mass per volume: % w/v = (g solute / mL solution) × 100. Percent by volume: % v/v = (volume of solute / volume of solution) × 100. Parts per million: ppm = (mass of solute / mass of solution) × 10⁶, equal to % × 10⁴. Dilution: M₁V₁ = M₂V₂, so M₂ = M₁V₁/V₂; the solvent to add is V₂ − V₁ and the dilution factor is V₂/V₁.

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