Quantitative chemistry · GCSE Chemistry

Chemical calculations

Relative formula mass, conservation of mass, moles, concentration, limiting reactants, percentage yield and atom economy.

UNDERSTAND→RETRIEVE→REMEMBER
THE MEMORY HOOK
Mass is conserved because atoms are rearranged, not created. Moles = mass / Mᵣ. Concentration = moles / volume in dm³. Show the ratio from the balanced equation before you scale.

The important bits

What you need to know

  1. 1

    Relative formula mass, Mᵣ, is the sum of the relative atomic masses in the formula. CaCO₃ is 40 + 12 + (16 × 3) = 100.

  2. 2

    Mass is conserved in a closed system. If a gas escapes, the flask appears to lose mass; the atoms are still accounted for in the gas.

  3. 3

    On Higher tier, moles = mass (g) / Mᵣ. One mole of any substance contains the same number of particles (the Avogadro constant).

  4. 4

    The balanced equation gives the mole ratio. Convert the known mass to moles, use the ratio, convert the unknown moles back to mass.

  5. 5

    Concentration in mol/dm³ = moles ÷ volume in dm³. Convert cm³ to dm³ by dividing by 1000. Concentration in g/dm³ = mol/dm³ × Mᵣ.

  6. 6

    A limiting reactant is the one that is used up first. Extra of the other reactant cannot make more product.

  7. 7

    Percentage yield = (actual mass / theoretical mass) × 100. Atom economy = (Mᵣ of desired product / sum of Mᵣ of all products) × 100. High atom economy means less waste.

Go deeper

Every calculation is convert, ratio, convert

Write the balanced equation and underline the two substances in the question. Find Mᵣ for both. Change the given mass into moles. Multiply or divide using the big numbers in the equation. Change those moles into the mass you were asked for. If you skip the mole step and scale masses using Mᵣ values that do not match the ratio, you will be wrong whenever the equation is not 1:1. Check the order of magnitude: burning 4 g of hydrogen (Mᵣ = 2, so 2 moles) with oxygen cannot produce 4 g of water. Two moles of H₂ make two moles of H₂O, Mᵣ 18, so 36 g. Conservation of mass includes the oxygen that joined.

Go deeper

Yield and atom economy answer different questions

Percentage yield compares what you actually got with what the equation said you could get. Loss of product on filtering, incomplete reaction and side reactions all cut yield. Atom economy is theoretical: it asks what fraction of the atoms in the products are the atoms you wanted. An addition reaction can have 100% atom economy; a reaction that also makes a waste salt does not. Industry wants both a high yield and a high atom economy, plus a low energy cost. If a question gives actual and theoretical masses, it is yield. If it only gives formulae, it is atom economy. Do not mix the formulae.

WORKED EXAMPLE

See the idea in action

Calculate the mass of carbon dioxide from 10.0 g of calcium carbonate: CaCO₃ → CaO + CO₂. Mᵣ(CaCO₃) = 100, Mᵣ(CO₂) = 44. Moles of CaCO₃ = 10.0 / 100 = 0.100 mol. Ratio 1:1, so 0.100 mol of CO₂. Mass = 0.100 × 44 = 4.40 g. If only 3.96 g is collected, percentage yield = (3.96 / 4.40) × 100 = 90%. The missing mass is not destroyed; some carbon dioxide was lost to the air or the reaction did not finish.

Exam technique

Turn knowledge into marks

Write Mᵣ, moles, ratio, moles, mass as five short lines. Convert cm³ to dm³ before concentration. For limiting reactants, calculate how much product each reactant could make; the smaller answer wins. Give units and a sensible number of significant figures.

Common mistakes

Do not give these marks away

  1. 01

    Forgetting to convert cm³ to dm³, or using the wrong mole ratio from the equation.

  2. 02

    Treating percentage yield and atom economy as the same calculation.

  3. 03

    Ignoring a limiting reactant and assuming both reactants are fully used.

QUICK RETRIEVAL

What is the relative formula mass of CaCO₃? (Aᵣ: Ca = 40, C = 12, O = 16)

A68

B84

C100

D112

Show the answer

100. 40 + 12 + (3 × 16) = 40 + 12 + 48 = 100.

Quick questions

If this is the bit you searched

How do you calculate moles from mass?

Moles = mass in grams ÷ relative formula mass (Mᵣ).

What is atom economy?

The percentage of the total relative formula mass of all products that is the desired product. It measures how efficiently atoms are used.