Molarity Calculator

About molarity

Molarity, symbol M and often called molar concentration, is the number of moles of a dissolved substance (the solute) per litre of total solution. It is the workhorse concentration unit of chemistry: reaction stoichiometry, titration math, buffer recipes, and most published lab protocols are written in molarity. One mole is 6.022 x 10^23 particles (Avogadro's number), so a 1 M solution holds one Avogadro's number of solute formula units in every litre.

Because molarity is defined per litre of solution and not per litre of solvent, it changes slightly with temperature: water expands when heated, so a solution made at 20 C is marginally less concentrated at 80 C even though no solute left. That is why temperature-sensitive work uses molality (moles per kilogram of solvent), which is mass-based and temperature-independent. Normality (equivalents per litre) is a third relative that scales molarity by the number of reactive units per molecule, so 1 M sulfuric acid is 2 N in an acid-base reaction.

How it works

The calculator chains two textbook relationships. First it converts the solute mass you enter into moles by dividing by molar mass, then it divides those moles by the solution volume in litres:

moles  = mass (g) / molar mass (g/mol)
M      = moles / volume (L)

combined:  M = mass / (molar mass x volume_L)

Molar mass is the sum of the atomic masses of every atom in the formula, taken from the periodic table. Sodium chloride (NaCl) is 22.99 + 35.45 = 58.44 g/mol; glucose (C6H12O6) is 180.16 g/mol. Get the molar mass right and the rest is arithmetic. If you already know the moles, skip the first line. If you know the molarity and want a mass, rearrange to mass = M x molar mass x volume.

Worked example

You want the molarity of a solution made by dissolving 10 g of sodium chloride in enough water to make 1 litre of solution.

1. Molar mass of NaCl: 22.99 + 35.45 = 58.44 g/mol.
2. Moles of solute: 10 g / 58.44 g/mol = 0.1711 mol.
3. Volume in litres: 1 L (already in litres).
4. Molarity: 0.1711 mol / 1 L = 0.171 M.

Common solutions reference

Mass needed to make one litre of a 1 M solution equals the molar mass in grams. Scale linearly for other concentrations.

To make a fraction of 1 M, scale the gram figure by the same fraction: a 0.25 M KCl litre needs 0.25 x 74.55 = 18.64 g. To prepare a smaller volume, multiply by the volume in litres as well, so 500 mL of 0.5 M glucose needs 180.16 x 0.5 x 0.5 = 45.04 g. These two moves, scale by concentration and scale by volume, cover almost every bench recipe you will meet.

Common pitfalls

• Volume of solution, not solvent. Molarity uses the final solution volume. Dissolving solute in 1 L of water gives slightly more than 1 L of solution, so dilute to the mark in a volumetric flask rather than adding a litre of water.
• Wrong molar mass. Using the atomic mass of one element instead of the full formula mass, or forgetting water of crystallisation in a hydrate (CuSO4.5H2O is 249.69 g/mol, not 159.61), throws every downstream number off.
• Millilitres entered as litres. A volume of 250 mL is 0.25 L. Mixing the units inflates or deflates the result by a factor of 1000.
• Confusing molarity with molality. They are numerically close only for dilute aqueous solutions. For concentrated or non-aqueous solutions the two diverge sharply.
• Ignoring purity and hydration. Reagent-grade chemicals are rarely 100 percent. A 95 percent pure solid means you weigh more to hit the target moles.
• Temperature drift. Stocks calibrated at room temperature read low when warm. For exacting work, prepare and use solutions at the same stated temperature.

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