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Molarity calculator

Work out how much solid to weigh for a solution of a given molarity, or find the molarity or the volume from what you have. Type a formula to fill in the molar mass, and correct for reagent purity in one step.

What do you want to find?
g/mol
Common
%

Leave at 100 for pure reagents. A 98 % reagent needs more mass for the same moles.

Mass to weigh

2.922g

That is 0.05 mol (50 mmol) of solute.

Working

m = c × V × M = 0.1 mol/L × 0.5 L × 58.44 g/mol = 2.922 g

Weigh the solid, dissolve it in less solvent than you need, then make up to the final volume in a volumetric flask. Molarity is per litre of finished solution, not per litre of solvent added.

How the calculation works

Molarity (amount concentration) is the number of moles of solute per litre of finished solution. The number of moles comes from the mass you weigh and the molar mass of the compound.

c = n ÷ V n = m ÷ M so m = c × V × M
Molarity, moles and mass
c
molarity in mol/L (M). 1 mM = 0.001 M, 1 µM = 0.000001 M
V
final volume of the solution in litres
n
amount of solute in moles
m
mass of solute in grams
M
molar mass in g/mol, from the formula or the label

When the reagent is not 100 % pure, divide the mass by the purity as a fraction: m(weigh) = c × V × M ÷ (purity ÷ 100). Use the assay from the certificate of analysis for the batch you have, and the molar mass of the exact form you have, for example the dihydrate rather than the anhydrous salt.

For liquids sold as a percentage, such as concentrated acids, the molarity of the bottle is c = density × 1000 × (w% ÷ 100) ÷ M, with density in g/mL. Then use the dilution calculator to go from the stock to your working strength.

Worked example

The same steps the calculator follows, done by hand

You need 500 mL of 0.1 M sodium chloride (NaCl, 58.44 g/mol) and your salt has an assay of 99.5 %.

  1. 1
    Convert the volume to litres: 500 mL = 0.500 L.
  2. 2
    Moles needed: n = 0.1 mol/L × 0.500 L = 0.0500 mol.
  3. 3
    Mass of pure NaCl: m = 0.0500 mol × 58.44 g/mol = 2.922 g.
  4. 4
    Correct for purity: 2.922 g ÷ 0.995 = 2.937 g. Weigh 2.937 g, dissolve it in about 400 mL of water and make up to 500 mL.

Frequently asked questions

What is the difference between molarity and molality?
Molarity (M) is moles of solute per litre of solution. Molality (m) is moles of solute per kilogram of solvent. Molality does not change with temperature, while molarity changes slightly as the solution expands or contracts.
How many grams of NaOH do I need for 1 litre of 1 M solution?
Sodium hydroxide has a molar mass of 40.00 g/mol, so 1 mol/L × 1 L × 40.00 g/mol = 40.0 g. Dissolve it carefully in less water, because it releases heat, cool and then make up to 1 litre.
What is the molarity of concentrated hydrochloric acid?
Using c = density × 1000 × w% ÷ 100 ÷ M: 37 % HCl with a density of about 1.19 g/mL gives 1.19 × 1000 × 0.37 ÷ 36.46 = about 12.1 mol/L. Check the density and assay on your supplier's certificate, because they vary by grade.
What is normality and how does it relate to molarity?
Normality (N) counts reacting equivalents per litre. For an acid it is molarity times the number of protons it gives up, so 1 M sulfuric acid is 2 N. Most modern methods use molarity instead.
Should I use the anhydrous or the hydrate molar mass?
Always the molar mass of the form you actually weigh. Copper sulfate pentahydrate (249.68 g/mol) needs about 56 % more mass than the anhydrous salt (159.60 g/mol) for the same number of moles.

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