Concentration is a measurement of the amount of substance per unit volume.

In Chemistry, concentration is measured in mol/dm^{3} (read as moles per cubic decimetre).

The following formula allows for the interconversion between a concentration (in mol/dm^{3}), the amount (in moles) of a substance in a solution, and the volume of the solution (in dm^{3}).

or

Note: 1 dm^{3} = 1000 cm^{3}

For example, to convert 250 cm^{3} into dm^{3}:

__Example 1__: 0.03 mol of sodium carbonate (Na_{2}CO_{3}) is dissolved in 300 cm^{3} of water. Calculate the concentration of the solution.

Step 1: Convert the volume of water from cm^{3} into dm^{3}.

Step 2: Use the molar concentration formula to calculate of the concentration of the solution.

__Example 2__: Calculate the amount, in moles, of 25cm^{3} of hydrochloric acid (HCl) with a concentration of 2 mol/dm^{3}.

Step 1: Convert the volume of HCl from cm^{3} into dm^{3}.

Step 2: Rearrange the molar concentration formula to calculate of the amount, in moles of HCl.

__Titration calculations, example 1__

The titration method that is used to prepare a soluble salt is also used to determine the concentration of an unknown solution.

For example, a titration problem will look like this:

*A pupil carried out a titration to find the concentration of a solution of hydrochloric acid (HCl). She found that 25.0 cm*^{3} of 0.100 mol/dm^{3} sodium hydroxide solution (NaOH) required 23.50 cm^{3} of dilute hydrochloric acid for neutralisation. Calculate the concentration, in mol/dm^{3} of the acid.

The chemical equation for this reaction is:

NaOH(aq) + HCl(aq) –> NaCl(aq) + H_{2}O(l)

volume 25.0cm^{3} 23.50cm^{3}

concentration 0.100mol/dm^{3}

It can be useful, as shown above, to write the values of the volumes & concentration underneath the equation.

Step 1: Calculate the amount, in moles, of the solution that you know the values for both volume and concentration. In this case sodium hydroxide (NaOH).

First convert the volume of NaOH from cm^{3} into dm^{3}.

Then rearrange the molar concentration formula to calculate of the amount, in moles of NaOH.

Step 2: Deduce the amount, in moles of the solution with the unknown concentration. In this case hydrochloric acid (HCl).

From the chemical equation the ratio of NaOH to HCl is 1:1

Therefore if you have 0.0025 mol of NaOH, this will react with 0.0025 mol of HCl.

Step 3: Calculate the concentration of the hydrochloric acid (HCl).

Convert the volume of HCl from cm^{3} into dm^{3}.

Use the molar concentration formula to calculate of the concentration of the HCl.

__Titration calculations, example 2__

*25.0 cm*^{3} of sodium carbonate solution (Na_{2}CO_{3}) of unknown concentration was neutralised by 30.0 cm^{3} of 0.100 mol/dm^{3} nitric acid (HNO_{3}).

Na_{2}CO_{3}(aq) + 2HNO_{3}(aq) –> 2NaNO_{3}(aq) + CO_{2}(g) + H_{2}O(l)

*Calculate the concentration, in mol/dm*^{3} of the sodium carbonate solution.

Step 1: Calculate the amount, in moles, of nitric acid (HNO_{3}).

Step 2: Deduce the amount, in moles of sodium carbonate (Na_{2}CO_{3}).

Using the equation:

Na_{2}CO_{3}(aq) + 2HNO_{3}(aq) –> 2NaNO_{3}(aq) + CO_{2}(g) + H_{2}O(l)

Ratio Na_{2}CO_{3}:HNO_{3} = 1:2

Step 3: Calculate the concentration of sodium carbonate (Na_{2}CO_{3}).

__Converting mol/dm__^{3} into g/dm^{3}

Concentration can also be expressed in g/dm^{3} (grams per cubic decimetre).

Therefore mol/dm^{3} can be converted into g/dm^{3}.

*Example: Convert 0.06 mol/dm*^{3} of sodium carbonate (Na_{2}CO_{3}) into g/dm^{3}

Step 1: calculate the relative formula mass (M_{r}) of sodium carbonate (Na_{2}CO_{3}).

Step 2: Recall the formula giving the relationship between mass, amount and formula mass.

therefore