Concentration tells you how many moles of solute are dissolved in one cubic decimetre of solution. The equation is: concentration (mol/dm³) = moles ÷ volume (dm³). To find concentration in g/dm³ instead, multiply by the relative formula mass of the solute.
What is concentration and what are its units?
Concentration measures how much solute is dissolved in a given volume of solution. At GCSE, it is expressed in two ways:
- mol/dm³ (moles per cubic decimetre): the number of moles of solute dissolved in 1 dm³ (1 litre) of solution. This is the standard chemical unit.
- g/dm³ (grams per cubic decimetre): the mass of solute dissolved in 1 dm³ of solution.
A solution is described as concentrated if a large amount of solute is dissolved in a small volume of solution. A dilute solution has a small amount of solute in a large volume. These are qualitative terms; mol/dm³ and g/dm³ give the precise, quantitative measure.
What is the concentration equation?
$$c = \frac{n}{V}$$
Where:
- c = concentration (mol/dm³)
- n = number of moles (mol)
- V = volume of solution (dm³)
Rearranged:
$$n = cV \qquad V = \frac{n}{c}$$
Important: volume must be in dm³, not cm³. To convert: divide cm³ by 1,000 (since 1 dm³ = 1,000 cm³).
How do you convert between mol/dm³ and g/dm³?
Multiply concentration in mol/dm³ by the relative formula mass (Mr) of the solute to get concentration in g/dm³:
$$\text{concentration (g/dm³)} = \text{concentration (mol/dm³)} \times M_r$$
Example: sodium hydroxide (NaOH) has Mr = 23 + 16 + 1 = 40.
A 2.0 mol/dm³ NaOH solution has a concentration of 2.0 × 40 = 80 g/dm³.
Conversely, to go from g/dm³ to mol/dm³, divide by Mr:
$$\text{concentration (mol/dm³)} = \frac{\text{concentration (g/dm³)}}{M_r}$$
How do you calculate concentration — worked examples?
Example 1 — finding concentration from moles and volume:
0.050 mol of sodium chloride (NaCl) is dissolved in 250 cm³ of water. Calculate the concentration in mol/dm³.
- Convert volume: 250 cm³ ÷ 1,000 = 0.250 dm³
- Apply the equation: c = n ÷ V = 0.050 ÷ 0.250
- c = 0.20 mol/dm³
Example 2 — finding moles from concentration and volume:
What amount, in moles, of hydrochloric acid is present in 35 cm³ of 0.50 mol/dm³ HCl solution?
- Convert volume: 35 cm³ ÷ 1,000 = 0.035 dm³
- n = c × V = 0.50 × 0.035
- n = 0.0175 mol
Example 3 — finding volume from concentration and moles:
How many cm³ of 2.0 mol/dm³ sulfuric acid contain 0.10 mol of H₂SO₄?
- V = n ÷ c = 0.10 ÷ 2.0 = 0.050 dm³
- Convert to cm³: 0.050 × 1,000 = 50 cm³
How do you convert volumes between cm³ and dm³?
This conversion is the most common source of errors in concentration calculations:
| Volume unit | Equivalent | Conversion |
|---|---|---|
| 1 dm³ | 1,000 cm³ | Divide cm³ by 1,000 to get dm³ |
| 1 cm³ | 0.001 dm³ | Multiply dm³ by 1,000 to get cm³ |
| 1 dm³ | 1 litre (L) | Same volume, different notation |
| 250 cm³ | 0.250 dm³ | ÷ 1,000 |
| 25 cm³ | 0.025 dm³ | ÷ 1,000 (typical titration volume) |
A useful quick check: if your volume in dm³ is greater than 1.0 for a laboratory-scale experiment, you have probably forgotten to divide by 1,000.
How is concentration used in titration calculations?
Titrations measure the concentration of an unknown solution by reacting it with a known volume of a standard solution (one whose concentration is accurately known). The steps for a titration calculation are:
- Record the titre (volume of standard solution added from the burette) in cm³, then convert to dm³.
- Calculate the moles of the standard solution: n = c × V.
- Use the mole ratio from the balanced equation to find the moles of the unknown solution.
- Divide by the volume of unknown solution (in dm³) to find its concentration.
Example: 25.0 cm³ of NaOH solution requires 20.0 cm³ of 0.100 mol/dm³ HCl to reach the end point. The equation is: NaOH + HCl → NaCl + H₂O (1:1 mole ratio).
- Moles of HCl: n = 0.100 × (20.0 ÷ 1,000) = 0.100 × 0.0200 = 0.00200 mol
- Moles of NaOH = moles of HCl = 0.00200 mol (1:1 ratio)
- Concentration of NaOH: c = 0.00200 ÷ (25.0 ÷ 1,000) = 0.00200 ÷ 0.0250 = 0.080 mol/dm³
Frequently asked questions
What is the formula for concentration in GCSE chemistry?
The formula is c = n ÷ V, where c is concentration in mol/dm³, n is the amount of solute in moles, and V is the volume of solution in dm³. The equation can be rearranged to n = c × V (to find moles) or V = n ÷ c (to find volume). Volume must always be converted to dm³ before substituting — divide any cm³ value by 1,000.
How do you convert cm³ to dm³?
Divide by 1,000, because 1 dm³ = 1,000 cm³. So 250 cm³ = 0.250 dm³, and 25 cm³ = 0.025 dm³. This step is easy to forget but critical: using cm³ instead of dm³ in the concentration equation gives an answer 1,000 times larger or smaller than the correct value. Checking that a final concentration is a sensible number (typically between 0.01 and 5 mol/dm³ for school-level solutions) can help catch this error.
What is the difference between mol/dm³ and g/dm³?
Both measure concentration but in different units. Mol/dm³ counts the number of moles of solute per dm³ of solution — a chemical quantity that is directly useful for stoichiometry calculations. G/dm³ measures mass per dm³ — more directly related to what you weigh out. To convert from mol/dm³ to g/dm³, multiply by the relative formula mass (Mr) of the solute. For example, 1 mol/dm³ CuSO₄ = 1 × 159.5 g/dm³ = 159.5 g/dm³ (Mr of CuSO₄ = 64 + 32 + 64 = 160).
Why does a titration give the concentration of an unknown solution?
A titration works because the neutralisation reaction has a known, exact mole ratio from the balanced equation (e.g. 1:1 for NaOH and HCl, or 1:2 for Na₂CO₃ and HCl). Once you know the moles of the standard solution added and you know the ratio, you can calculate the moles of the unknown substance. Dividing by the volume of unknown solution gives its concentration. The precision of a titration depends on accurately reading the burette and identifying the sharp colour change at the end point.
For Socratic GCSE chemistry with Professor Curie — building the particle picture of what a 0.1 mol/dm³ solution looks like at the scale of individual ions before any arithmetic — visit aitutors.me.