Hong Life CalculatorsUnderstanding the molarity calculator — concept and principle
Molarity is the most common way to express the concentration of a solution: moles of solute per litre of solution (mol/L, written M). This calculator answers the everyday lab question "how many grams do I weigh out to make this volume at this concentration?" Enter the formula, the target molarity and the final volume, and it returns the mass, the moles and the molar mass.
How it is calculated
m = c × V × M
- c: molarity in mol/L.
- V: final solution volume, entered in mL and divided by 1000 to give litres.
- M: molar mass in g/mol, calculated from the formula.
- Moles needed: n = c × V (in L).
The principle
Molarity is defined as n ÷ V, so the amount of solute you need is n = c × V. Converting that amount to mass uses the molar mass, m = n × M. The volume is the volume of the whole solution, not of the solvent you add, because dissolving a solid changes the total volume slightly. That is why solutions are made up to the mark in a volumetric flask.
Worked example
Defaults: NaCl, 0.5 mol/L, 250 mL.
- Molar mass of NaCl: 22.990 + 35.45 = 58.44 g/mol.
- Volume in litres: 250 ÷ 1000 = 0.25 L.
- Moles: 0.5 × 0.25 = 0.125 mol.
- Mass: 0.125 × 58.44 = 7.305 g.
| Concentration (mol/L) | Mass to weigh (g) |
|---|---|
| 0.125 | 1.82625 |
| 0.25 | 3.6525 |
| 0.375 | 5.47875 |
| 0.5 | 7.305 |
| 0.625 | 9.13125 |
| 0.75 | 10.9575 |
| 1 | 14.61 |
How to read the result
Weigh 7.305 g of NaCl, dissolve it in less than 250 mL of water, transfer to a 250 mL volumetric flask and fill to the mark. Physiological saline (0.9% w/v) is about 0.154 M NaCl, so 0.5 M is roughly three times more concentrated. Laboratory stock solutions are often 1 M or higher and are diluted later.
Common mistakes
- Adding 250 mL of water to the solid instead of making the final volume 250 mL.
- Forgetting to convert mL to L, which gives a mass 1000 times too large.
- Using the anhydrous molar mass when the bottle contains a hydrate, such as CuSO₄·5H₂O.
- Confusing molarity (per litre of solution) with molality (per kilogram of solvent).
Frequently asked questions
What does 1 M mean?
One mole of solute in a total of one litre of solution.
How do I make a solution in millimolar (mM)?
Divide the mM value by 1000 to get mol/L, for example 50 mM = 0.05 M, then use the same formula.
Can I use this for liquids such as concentrated acids?
Liquids are usually measured by volume using their percentage and density; use a concentrated acid molarity calculator for that case.
Sources: IUPAC Compendium of Chemical Terminology (Gold Book), "amount concentration" · Harris, D. C., Quantitative Chemical Analysis, W. H. Freeman