Molarity Calculator
Molarity Calculator
Calculate the molar concentration of a solution from the mass weighed out, the formula weight on the bottle and the final volume.
Molarity
Mass + MW + volume → mol/L5.844 g of sodium chloride, formula weight 58.44 g/mol, made up to 1 L
Formula
- mass
- grams of solute actually weighed out
- formula weight
- g/mol, taken from the bottle rather than a periodic table calculation, so that water of crystallisation and any salt form are included
- final volume
- litres of FINAL SOLUTION, not litres of solvent added
- mol/L
- also written M; 1 mol/L = 1,000 mmol/L = 1,000,000 µmol/L
Worked example
5.844 g of sodium chloride, formula weight 58.44 g/mol, made up to 1 L
5.844 ÷ (58.44 × 1) = 0.1000 mol/L
= 100 mmol/L
Dissolve the 5.844 g in roughly 800 mL, then make up to the 1 L mark
Mass required for 1 L at formula weight 58.44 g/mol
| Target concentration | Same value in mmol/L | Mass to weigh out |
|---|---|---|
| 0.001 mol/L | 1 mmol/L | 0.058 g |
| 0.01 mol/L | 10 mmol/L | 0.584 g |
| 0.1 mol/L | 100 mmol/L | 5.844 g |
| 0.15 mol/L | 150 mmol/L | 8.766 g |
| 1 mol/L | 1,000 mmol/L | 58.44 g |
Concentration units on the same scale
| mol/L | mmol/L | µmol/L | nmol/L |
|---|---|---|---|
| 1 | 1,000 | 1,000,000 | 1,000,000,000 |
| 0.1 | 100 | 100,000 | 100,000,000 |
| 0.001 | 1 | 1,000 | 1,000,000 |
| 0.000001 | 0.001 | 1 | 1,000 |
Weighing out and making up to volume
Molarity is moles of solute per litre of final solution, and the phrase final solution carries the most frequently ignored instruction in solution preparation. The solute occupies volume of its own, so adding one litre of water to the weighed powder gives more than one litre of solution and a concentration below the one intended. The error is negligible for a millimolar buffer and substantial for a molar stock. Dissolve the solid in perhaps 80% of the final volume, then make up to the mark in a volumetric flask.
Use the formula weight printed on the bottle, not one calculated from the anhydrous formula. Many laboratory salts are supplied as hydrates, and the water of crystallisation is part of the formula weight: a hydrated salt therefore weighs more per mole than the anhydrous form, and weighing according to the anhydrous figure delivers fewer moles than intended and a solution that is too dilute. The same applies to salt forms of drugs and to reagents supplied at a stated purity or assay value, where the certificate of analysis rather than the label may carry the number you need.
Molarity is temperature-dependent, because it is defined per unit volume and volume expands with temperature. A solution made up at 4°C and used at 37°C is slightly more dilute than its label says. The effect is small enough to ignore for most bench work and is exactly why molality — moles per kilogram of solvent — is preferred where precision matters, since mass does not change with temperature. Make solutions up at, and record, the temperature at which the flask is calibrated.
The default here is a familiar sanity check: sodium chloride has a formula weight of 58.44, so 5.844 g made up to 1 L is 0.1 mol/L, or 100 mmol/L. Carrying one such example in mind catches the large errors — a factor of a thousand from confusing millimolar with molar, or a factor of ten from a misplaced decimal in the weighing — far more reliably than rechecking the arithmetic does. For very dilute solutions, weighing a few milligrams is less accurate than diluting a stronger stock, so prepare those by dilution instead.
Frequently asked questions
How do I calculate molarity?
Divide the mass of solute in grams by the formula weight in g/mol and by the final volume in litres. For example, 5.844 g of sodium chloride with a formula weight of 58.44 made up to 1 L gives 0.1 mol/L.
Which molecular weight should I use for a hydrated salt?
The formula weight printed on the bottle, which includes the water of crystallisation. A hydrate weighs more per mole than the anhydrous form, so using the anhydrous weight delivers fewer moles than intended and makes the solution too dilute.
Do I add the volume of solvent or make up to the volume?
Make up to the volume. Molarity is per litre of final solution, so the solute’s own volume counts. Dissolve the solid in about 80% of the final volume, then make up to the mark.
Why is molality used instead of molarity in physical chemistry?
Because molarity is defined per unit volume and volume changes with temperature, so a molar concentration drifts as the solution warms. Molality is moles per kilogram of solvent, and mass does not change with temperature.
How do I convert mol/L to mmol/L?
Multiply by 1,000. A 0.1 mol/L solution is 100 mmol/L and 100,000 µmol/L. Reagent bottles are usually labelled in mol/L while clinical results are reported in mmol/L or µmol/L.
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References
- Cohen ER, Cvitaš T, Frey JG, et al., eds. Quantities, Units and Symbols in Physical Chemistry (the IUPAC Green Book). 3rd ed. RSC Publishing.
- Bureau International des Poids et Mesures. The International System of Units (SI Brochure) — definition of the mole.
- Rifai N, Horvath AR, Wittwer CT, eds. Tietz Textbook of Clinical Chemistry and Molecular Diagnostics. Elsevier — solution preparation and volumetric technique.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.