Molarity to Percentage

About the Molarity to Percentage

Molarity is moles of solute per litre of solution. To convert it to mass concentration, multiply by molar mass: 0.1 mol/L of sodium chloride (58.44 g/mol) is 5.844 g/L. Percent weight/volume is grams per 100 mL, so that becomes 0.5844% w/v.

Percent weight/weight needs the solution density. Five grams of solute in 100 mL of a solution that weighs 105 g is 4.76% w/w, not 5%. This distinction matters for concentrated acids and bases, where the density is far from 1 g/mL.

How the calculation works

• g/L = molarity × molar mass.
• % w/v = g/L ÷ 10.
• % w/w = g/L ÷ (density g/mL × 1,000) × 100.
• ppm = g/L × 1,000.

Reference values

Worked example: sulfuric acid and sodium chloride

A 0.5 M sulfuric acid solution (98.08 g/mol) contains 49.04 g/L, which is 4.904% w/v. If the solution density is 1.03 g/mL, the same solution is 49.04 ÷ 1,030 × 100 = 4.76% w/w. A 1 M sodium chloride solution (58.44 g/mol) is 58.44 g/L, 5.844% w/v, and—at a density of 1.04 g/mL—5.62% w/w.

The difference between w/v and w/w grows as the solution becomes denser. For dilute aqueous solutions near 1 g/mL the two figures are close, which is why the distinction is easy to miss. For concentrated acids, brines and syrups, use the measured density and state which percentage you mean.

Temperature, volume and molality

Molarity is defined per litre of solution, and the volume of a liquid changes with temperature. A solution prepared at 20 °C and used at 30 °C is slightly less concentrated in molar terms because it has expanded, which matters for work near a tolerance limit. Volumetric glassware is calibrated at a stated temperature, usually 20 °C, and should be used close to it.

Molality, moles of solute per kilogram of solvent, avoids the problem because mass does not expand. It is preferred for colligative properties and for work over a wide temperature range. For routine preparation at room temperature the difference is small, but for precise analytical work the distinction should be recorded alongside the result.

Frequently asked questions

Sources and standards

Converting between molarity and percentage by mass needs two inputs beyond the concentration itself: the solute's molar mass and the density of the solution. Atomic weights follow IUPAC and the density is a required field, because at typical lab concentrations an assumed density of 1.000 g/mL can be wrong in the second decimal place.

• IUPAC - Periodic Table of Elements and standard atomic weights
• NIST - CODATA recommended values of the fundamental constants

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