Maths and data skills for chemistry — Edexcel GCSE Chemistry revision

Moles and concentration

• The number of moles of a substance is calculated using moles = mass ÷ Mr (relative formula mass), with mass in grams.
• For solutions, concentration in g/dm³ = mass of solute (g) ÷ volume of solution (dm³); concentration in mol/dm³ = moles of solute ÷ volume of solution (dm³).
• Remember to convert cm³ to dm³ by dividing by 1000 before using the concentration formulae.
• In titration calculations, use moles = concentration × volume (in dm³) for each solution, then use the balanced equation ratio to find the unknown quantity.

Percentage yield and atom economy

• Percentage yield = (actual yield ÷ theoretical yield) × 100; it is always less than 100% due to practical losses, incomplete reactions or side reactions.
• Theoretical yield is calculated from the balanced equation using moles, assuming the reaction goes to completion with no losses.
• Atom economy = (relative formula mass of desired product ÷ sum of relative formula masses of all reactants) × 100, showing what proportion of reactant mass ends up as useful product.
• A high atom economy reaction is more sustainable because it produces less waste; percentage yield and atom economy are different measures and should not be confused.

Key terms

Mole

The amount of substance containing 6.02 × 10²³ particles (Avogadro's constant), linked to mass via Mr.

Relative formula mass (Mr)

The sum of the relative atomic masses of all atoms in a formula.

Percentage yield

Actual yield divided by theoretical yield, multiplied by 100; measures reaction efficiency in practice.

Atom economy

The percentage of total reactant mass converted into the desired product, showing efficiency of resource use.

Molar gas volume

The volume occupied by one mole of any gas at room temperature and pressure, approximately 24 dm³.

Standard form

A way of writing numbers as A × 10ⁿ where 1 ≤ A < 10, useful for very large or small values.

Common exam traps

• Percentage yield and atom economy are calculated differently and mean different things — don't mix up the formulae.
• Always convert cm³ to dm³ (divide by 1000) before using mol/dm³ concentration or the 24 dm³ molar gas volume rule.
• Percentage yield can never be above 100%; if your answer is, you've made an arithmetic or setup error.

Practice questions with answers

1. 1. Calculate the number of moles in 8.0 g of NaOH (Mr = 40).

   Answer: 0.2 mol

   moles = mass ÷ Mr = 8.0 ÷ 40 = 0.2 mol.

2. 2. Which formula correctly links moles, mass and Mr?

   • • moles = mass × Mr
   • • moles = mass ÷ Mr
   • • moles = Mr ÷ mass
   • • moles = mass + Mr

   Answer: moles = mass ÷ Mr

   Rearranging mass = moles × Mr gives moles = mass ÷ Mr.

3. 3. A solution has 0.5 mol of solute dissolved in 250 cm³ of water. Calculate the concentration in mol/dm³.

   Answer: 2 mol/dm³

   Convert 250 cm³ to dm³: 250 ÷ 1000 = 0.25 dm³. Concentration = moles ÷ volume = 0.5 ÷ 0.25 = 2 mol/dm³.

4. 4. To convert cm³ to dm³, you should:

   • • Multiply by 1000
   • • Divide by 1000
   • • Multiply by 100
   • • Divide by 10

   Answer: Divide by 1000

   There are 1000 cm³ in 1 dm³, so dividing cm³ by 1000 gives dm³.

5. 5. The theoretical yield of a reaction is 20 g, but only 15 g is actually obtained. Calculate the percentage yield.

   Answer: 75%

   Percentage yield = (actual ÷ theoretical) × 100 = (15 ÷ 20) × 100 = 75%.

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