concentration heading

Higher tier


solution= solvent + solute

Many chemical reactions are carried out using solutions of substances. In order to calculate the masses of the reactants and products that take part in these chemical reactions we need to know the concentration of these solutions. Remember a solution is made by dissolving a substance, the solute in a solvent. The solvent is usually water and these solutions would then be called aqueous solutions. When we talk about the concentration of a solution we mean how much solute has been dissolved in a certain volume of water (the solvent).

As an example consider the solution made by dissolving the salt sodium chloride in water.
Now the salt sodium chloride has the chemical formula NaCl. The relative atomic mass (Ar) of sodium is 23 and the Ar of chlorine is 35.5.
So the relative formula mass (Mr) of sodium chloride (NaCl)
= 23 + 35.5 = 58.5
So 1 mole of sodium chloride = 58.5 grams.
Most people in everyday life measure volumes in litres but this is not the SI unit used in science. The unit used for measuring volumes in science is the decimetre cube (dm3). A dm3 is the same as 1 litre or 1000cm3 or 1000ml, they all have the same volume, so don't get confused!

Calculating concentration

The units of concentration will vary and will depend upon the units used to measure the mass or amount of the solute; the substance which is dissolved and the volume of the solvent. You need to be confident in using different units for concentrations e.g.

1 mole or 58.5g of sodium chloride sitting on an electronic balance

Concentration and units

The concentration of a solution is often expressed in 2 ways e.g.

Example 1

If one mole or 58.5g of sodium chloride (NaCl) is added to a measuring cylinder with a volume of 1 dm3 or 1 litre and enough water is then added to completely dissolve the sodium chloride to form a solution with a volume of 1 decimetre cubed (1dm3) you can work out the concentration of this solution using the formula shown in methods 1 and 2 below.

Formula used to calculate the concentration of a solution

Concentration and common units

A bottle of sulfuric acid sitting on the bench in the lab. The only difference between the two concentrations of the sodium chloride solution above are the units. In method 1 the concentration is measured in units of grams per decimetre cubed (gdm-3 or g/dm3). Here the mass of the solute is measured in grams and the volume of the solution formed is measured in decimetres cubed while in method 2 the concentration of the sodium chloride solution is measured in units of moles per decimetre cubed (mol/dm3 or moldm-3) simply because this time rather than measuring the amount of the solute which was dissolved in grams the number of moles of the solute dissolved is used instead.

Measuring the concentration of solutions in moles per decimetre cubed is perhaps a more common unit and is the one you are most likely to see on bottles in the science lab; for example you may see bottles of acids or alkalis such as hydrochloric acid or sodium hydroxide; as shown in the image; with labels that say for example-"hydrochloric acid 2M"- The 2M refers to the concentration of the acid, its concentration is 2 moles per decimetre cubed.


1 mole of glucose sugar being weighed out on an electronic balance.

Let's look at some examples of the units that can be used to measure the concentration of a glucose solution. Now glucose is a simple sugar molecule which has the molecular formula C6H1206, its relative formula mass or relative molecular mass (Mr) is 180.

Problem 1

a. What is the concentration in g per dm3 of a glucose solution made by dissolving 30g of glucose to give a solution with a total volume of 500 ml?
To work out the concentration of this solution you will use the formula below to solve this problem since the mass of glucose dissolved is in grams:
Concentration = mass of solute ÷ volume of solution
The unit for volume asked for in the question is decimetres cubed (dm3) so we need to divide the 500ml volume by 1000 to convert it into dm3. This gives us:
Concentration = 30g ÷ volume of 0.5 dm3 = 60g/dm3
So the concentration of this glucose solution is 60g/dm3, that is 60g per decimetre cubed.

Problem 2

b. What is the concentration in mol per dm3 of a glucose solution made by dissolving 30g of glucose to give a solution with a volume of 500 ml?
This time it’s the same problem as above but the units are different, the units of concentration this time needs to be in mol (short for moles) per dm3. First thing to do here to answer this question is to calculate how many moles of glucose we have by using the formula below:
Number of moles = mass given ÷ mass of 1 mole
= 30g÷ 180g
= 0.167 moles
So simply substitute the number of moles into the formula below, remembering that the volume must be in dm3
concentration = number of moles ÷ volume of solution
= 0.167 mol÷ 0.5dm3
= 0.03 mol/dm3

Calculating the number of moles, volumes and concentrations

In the worked examples above the mass or the number of moles of solute dissolved in a given volume were used to calculate the concentrations of solutions; however the formulae used above can obviously be arranged to calculate an unknown volume or the mass of a solute which dissolves. All that is needed is to simply rearrange the formula as shown below to calculate an unknown volumes (v) or the number of moles (n) of a solute that dissolves:

concentration formulae

You should be able to use these formula to calculate either concentrations, volumes or the number of moles of a particular solute that dissolves, you should take care that you use the correct units. Questions in your exam may have volumes in ml or cm3 but you should remember to change these into dm3. The only way to ensure you can successfully answer this type of question is to complete a few practice problems- so what are you waiting for; click the link below!

Key Points

Practice questions

Check your understanding - questions on how to work out concentrations