How Do You Calculate Molarity/Molar Concentration?

At both SL and HL, calculate molar concentration by dividing the amount of solute in moles by the total volume of solution in cubic decimetres:

$$c = \frac{n}{V}$$

Here, $c$ is molar concentration in $\text{mol dm}^{-3}$, $n$ is amount in moles, and $V$ is solution volume in $\text{dm}^3$.

Concentration therefore describes how much solute is present per unit volume of solution. A larger amount of solute at the same volume gives a higher concentration, while dilution increases volume and lowers concentration without changing the amount of solute.

The Method

This calculation belongs to Structure 1.4: Counting particles by mass: the mole. Use these steps:

1. Calculate the amount of solute using $n = \frac{m}{M}$, if it is not already given.
2. Convert the solution volume to $\text{dm}^3$: $$$$

If concentration and volume are known, rearrange the same relationship to $n = cV$. This is especially useful before applying a mole ratio from a balanced equation.

Worked Example

Calculate the molar concentration when $5.85\text{ g}$ of sodium chloride, $\text{NaCl}$, is dissolved to make $500.0\text{ cm}^3$ of solution. The molar mass of $\text{NaCl}$ is $58.44\text{ g mol}^{-1}$.

First, calculate moles:

$$n = \frac{5.85}{58.44} = 0.100\text{ mol}$$

Convert the volume:

$$V = \frac{500.0}{1000} = 0.5000\text{ dm}^3$$

Then calculate concentration:

$$c = \frac{0.100}{0.5000} = 0.200\text{ mol dm}^{-3}$$

A quick dimensional check confirms the result: mol divided by $\text{dm}^3$ gives $\text{mol dm}^{-3}$. Since $0.100\text{ mol}$ occupies only $0.5000\text{ dm}^3$, the numerical concentration should be greater than 0.100, so 0.200 is reasonable. This check can expose conversion errors immediately.

A common misconception is to use the volume in $\text{cm}^3$ directly. This produces an answer that is 1000 times too small. Also use the final volume of the solution, not the volume of solvent added.

Exam Technique

For a calculate question, show the formula, volume conversion, substitution, and final unit. Keep units throughout your working and give the answer to an appropriate number of significant figures.