Concentration of Solutions
What Is Concentration?
Concentration tells you how much solute is dissolved in a given volume of solution. A concentrated solution has a lot of solute in a small volume; a dilute solution has little solute in a large volume.
Calculating Concentration
There are two ways to express concentration at GCSE:
1. Concentration in g/dm³
concentration (g/dm³) = mass of solute (g) ÷ volume of solution (dm³)
This tells you how many grams of solute are dissolved per cubic decimetre (litre) of solution.
2. Concentration in mol/dm³ (Higher Tier)
concentration (mol/dm³) = moles of solute ÷ volume of solution (dm³)
This is also called molarity and the unit is sometimes written as M.
Converting Between the Two
concentration (g/dm³) = concentration (mol/dm³) × Mr
concentration (mol/dm³) = concentration (g/dm³) ÷ Mr
Unit Conversions
Volume must be in dm³ for these formulae. To convert:
- 1 dm³ = 1000 cm³
- To convert cm³ to dm³: divide by 1000
- To convert dm³ to cm³: multiply by 1000
Always convert volumes before putting them into equations.
Worked Examples
Example 1: g/dm³
A solution contains 4 g of NaOH dissolved in 500 cm³ of water. What is the concentration?
Volume in dm³ = 500 ÷ 1000 = 0.5 dm³
Concentration = 4 ÷ 0.5 = 8 g/dm³
Example 2: mol/dm³
What is the concentration in mol/dm³ of a solution containing 0.4 mol of HCl in 250 cm³?
Volume in dm³ = 250 ÷ 1000 = 0.25 dm³
Concentration = 0.4 ÷ 0.25 = 1.6 mol/dm³
Example 3: Finding Mass of Solute
What mass of sodium chloride is needed to make 2 dm³ of a 5 g/dm³ solution?
Mass = concentration × volume = 5 × 2 = 10 g
Example 4: Converting Units
A solution has a concentration of 2 mol/dm³. Mr of the solute is 40. What is the concentration in g/dm³?
Concentration = 2 × 40 = 80 g/dm³
Required Practical: Titration
Titration is a technique used to find the concentration of an unknown solution using a solution of known concentration.
Equipment
- Burette — measures the volume of one solution added (accurate to ±0.05 cm³)
- Pipette — measures a precise volume of the other solution (e.g. 25.0 cm³)
- Conical flask — where the reaction takes place
- Indicator — shows when the reaction is complete (the end point)
Method
1. Rinse the burette with the solution it will contain; rinse the pipette with the solution it will measure
2. Fill the burette with acid (or alkali) and record the starting volume
3. Use the pipette to transfer exactly 25.0 cm³ of alkali (or acid) into a conical flask
4. Add 2-3 drops of a suitable indicator (e.g. methyl orange or phenolphthalein)
5. Add the acid from the burette slowly, swirling the flask
6. When the indicator permanently changes colour, record the burette reading
7. Calculate the titre (volume added = end reading − start reading)
8. Repeat until you get concordant results — two titres within 0.10 cm³ of each other
9. Calculate the mean of concordant results only (ignore any anomalous titres)
Indicators
| Indicator | In acid | At end point | In alkali |
|---|---|---|---|
| Methyl orange | Red | Orange | Yellow |
| Phenolphthalein | Colourless | Pale pink | Pink |
Universal indicator is NOT used in titrations because its colour change is gradual, not sharp.
Titration Calculations
Use the titre and known concentration to find the unknown concentration.
Example: 25.0 cm³ of NaOH was neutralised by 20.0 cm³ of 0.1 mol/dm³ HCl.
NaOH + HCl → NaCl + H₂O (1:1 ratio)
Moles of HCl = 0.1 × (20.0 ÷ 1000) = 0.002 mol
Moles of NaOH = 0.002 mol (1:1 ratio)
Concentration of NaOH = 0.002 ÷ (25.0 ÷ 1000) = 0.002 ÷ 0.025 = 0.08 mol/dm³
Exam Tips
- Always convert cm³ to dm³ before calculating (÷ 1000)
- Show the unit conversion clearly in your working
- In titration questions, always find moles first, then use the equation ratio
- Learn which indicator is suitable and why universal indicator is not used
- Concordant results are within 0.10 cm³ — discard outliers before averaging