Molarity is moles of solute per litre of solution: a mass divided by the molar mass gives moles, and moles divided by the volume in litres gives mol/L. For a dilution, M₁V₁ = M₂V₂, and any one of the four can be found from the other three.
The formula
Moles from mass
n = mass (g) ÷ molar mass (g/mol)Molarity
M = n ÷ V (litres)Dilution
M₁ × V₁ = M₂ × V₂Solvent to add
solvent = V₂ − V₁A dilution makes a solution weaker and bigger, so the starting volume cannot be more than the final one, and the starting concentration cannot be less than the final one.
Worked example
For a dilution, to make 500 mL of 1 M from 12 M stock: V₁ = 1 × 500 ÷ 12 = 41.67 mL, so add 458.33 mL of solvent. Or 10 mL of 10 M made up to 100 mL is 1 M, a 10× dilution.
When to use it, and the mistakes to avoid
Use it to make up a solution of a given strength, to find the concentration of one you have made, or to work out how much stock to dilute in the lab.
- Using the solvent volume. Molarity is per litre of the finished solution.
- Forgetting to convert millilitres to litres. The calculator does it if you pick the unit; by hand, divide by 1,000.
- Using the wrong molar mass. Include every atom, and the water in a hydrate such as CuSO₄·5H₂O.
- Mixing units in a dilution. Both volumes must be in the same unit, and both concentrations too.
- Swapping 1 and 2. M₁ and V₁ are the starting solution, M₂ and V₂ the finished one.
FAQ
What is molarity?
The concentration of a solution as moles of solute per litre of solution, written mol/L or M. A 1 M solution of sodium chloride has 1 mole (58.44 g) of salt in every litre of finished solution. Molarity is the most common way to give a concentration in chemistry.
How do I find molarity from grams?
Divide the mass by the molar mass to get moles, then divide the moles by the volume in litres. 5.844 g of sodium chloride (molar mass 58.44 g/mol) is 0.1 mol, and in 100 mL, which is 0.1 L, that is 1 mol/L. Look up the molar mass from the formula by adding up the atomic masses.
What does M₁V₁ = M₂V₂ mean?
When you add solvent to a solution, the amount of solute does not change, only the volume it is spread through. Concentration times volume is the amount of solute, so it is the same before (M₁V₁) and after (M₂V₂). Use it to find how much stock solution to dilute, or what concentration you end up with.
Do the units have to be litres?
Not for a dilution. The units on the two sides cancel, so the volumes can be in millilitres or microlitres and the concentrations in molar or millimolar, as long as the two volumes use the same unit and the two concentrations use the same unit. For a molarity, the volume is converted to litres for you.
Why is the solution volume and not the solvent volume used?
Because molarity is moles per litre of the finished solution. Dissolving a solute changes the volume a little, so adding it to a litre of water gives slightly more than a litre. For an exact solution, dissolve the solute, then make it up to the final volume in a volumetric flask. This calculator assumes the volume you enter is the final one.