Concentration of solutions
Concentration in g/dm³
is how much solute is dissolved in a volume of solution. The more solute in the same volume, the more concentrated the solution.
concentration (g/dm³) = mass of solute (g) ÷ volume (dm³)
Volume must be in . To convert: cm³ ÷ 1000 = dm³ (1 dm³ = 1000 cm³).
Example: 4.0 g of sodium hydroxide is dissolved to make 250 cm³ of solution.
- volume = 250 ÷ 1000 = 0.25 dm³
- concentration = 4.0 ÷ 0.25 = 16 g/dm³
Rearranged: mass = concentration × volume.
Key terms
Concentration in mol/dm³ (Higher tier only)
Concentration can also be measured in :
So moles = concentration × volume.
Example: the 4.0 g of NaOH above is 4.0 ÷ 40 = 0.1 mol, dissolved in 0.25 dm³.
concentration = 0.1 ÷ 0.25 =
To convert between the units, use the solute's Mᵣ:
- mol/dm³ × Mᵣ = g/dm³ (0.4 × 40 = 16 g/dm³)
- g/dm³ ÷ Mᵣ = mol/dm³
Titration calculations use these ideas (see Titrations in C4).
Key terms
Finding the mass to dissolve
The formulas also work backwards, to find how much solute you need.
Example: what mass of sodium chloride (Mᵣ 58.5) is needed to make 500 cm³ of a 0.2 mol/dm³ solution?
- volume = 500 ÷ 1000 = 0.5 dm³
- moles = concentration × volume = 0.2 × 0.5 = 0.1 mol
- mass = moles × Mᵣ = 0.1 × 58.5 = 5.85 g
Write each step on its own line, with its unit: you can earn marks for the method even if a later step goes wrong.
Concentrated and dilute
A solution becomes more concentrated if more solute is dissolved in the same volume, or the same solute is dissolved in less water.
It becomes if more water is added. The amount of solute stays the same, but it is spread through a bigger volume.
Example: 50 cm³ of 0.4 mol/dm³ acid contains 0.4 × 0.05 = 0.02 mol. Diluted with water to 100 cm³, the concentration is 0.02 ÷ 0.1 = : double the volume, half the concentration.
Common mistake
Dividing cm³ by 100 instead of 1000 is the commonest slip. 1 dm³ is 1000 cm³.