How to Calculate Molar Concentration

Finds the molar concentration as the amount of solute ÷ the volume of the solution in litres. Enter the solute in grams and its molar mass converts it to moles.

Explanation

Molar concentration says how many moles of solute sit in one litre of solution. Its unit is mol/L, often written M.

c = \dfrac{n}{V} = \dfrac{m \div M}{V}

Here $c$ is the concentration, $n$ the amount of solute in moles and $V$ the volume of the solution in litres.

Example

Take 40 g of sodium hydroxide, $\mathrm{NaOH}$ , whose molar mass is 40 g/mol, and dissolve it to make 500 mL of solution.

n = \dfrac{40}{40} = 1\ \text{mol} \qquad c = \dfrac{1}{0.5} = 2\ \text{mol/L}

The result is a 2 mol/L solution of sodium hydroxide.

The classic mistake

The denominator is the volume of the solution, not the volume of the solvent.

Dissolving 40 g of $\mathrm{NaOH}$ in "500 mL of water" gives more than 500 mL of solution, because the solid takes up room too. The result is not 2 mol/L.

The right procedure is to put the solid in a volumetric flask and add water until the solution itself reaches the 500 mL mark. That is precisely what volumetric flasks are for.

Against mass percent

Molar concentration counts particles, which is what reactions care about, since they combine in whole-number ratios
Mass percent measures proportions by weight, which is convenient for labelling and preparation

Whenever a chemical reaction is involved, molar concentration is almost always the right choice.