Most tested C4.6

Reacting Masses and Limiting Reactants

This topic involves using balanced chemical equations to perform mass-to-mass calculations. It's a foundational skill for determining the theoretical yield of a product, especially when one reactant is used up completely before the others.

Part of the ESAT Chemistry syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.

Key points

  • A balanced chemical equation provides the molar ratio of reactants and products, which is essential for all calculations.
  • The standard calculation pathway is: mass of reactant A → moles of A → moles of product B (using ratio) → mass of B.
  • If the masses of multiple reactants are given, you must first identify the limiting reactant.
  • The limiting reactant is the one that produces the least amount of product, thereby dictating the maximum possible yield.
  • To find the limiting reactant, calculate the moles of each reactant and compare their ratio to the stoichiometric ratio in the balanced equation.
  • All calculations rely on the accurate determination of molar mass (Mr) from the relative atomic masses (Ar) provided.

Formulae

moles = mass / Mr

To convert a known mass of a substance into moles, or to find the mass from a known number of moles. Mr is the molar mass in g/mol.

Definitions

Limiting Reactant
The reactant in a chemical reaction that is completely consumed first. It determines the maximum amount of product that can be formed.
Stoichiometry
The quantitative relationship between reactants and products in a chemical reaction, as defined by the coefficients in the balanced equation.

Worked example

What is the maximum mass of iron (Fe) that can be produced when 32.0 g of iron(III) oxide (Fe₂O₃) is heated with 7.2 g of carbon (C)? The equation for the reaction is: 2Fe₂O₃ + 3C → 4Fe + 3CO₂. [Ar values: C=12, O=16, Fe=56]

  1. 1

    Step 1:

    Calculate the molar mass of the reactants.

    Mr(Fe₂O₃) = 2(56) + 3(16) = 112 + 48 = 160 g/mol
    Mr(C) = 12 g/mol
  2. 2

    Step 2:

    Convert the mass of each reactant to moles.

    Moles Fe₂O₃ = 32.0 g / 160 g/mol = 0.2 mol
    Moles C = 7.2 g / 12 g/mol = 0.6 mol
  3. 3

    Step 3:

    Identify the limiting reactant using the stoichiometric ratio (2 Fe₂O₃ :

    3 C).

    Based on the Fe₂O₃, we would need (3/2) × 0.2 = 0.3 mol of C.

    Since we have 0.6 mol of C, which is more than enough, the Fe₂O₃ is the limiting reactant.

  4. 4

    Step 4:

    Use the moles of the limiting reactant (Fe₂O₃) to find the moles of product (Fe) using the ratio (2 Fe₂O₃ :

    4 Fe, or 1:2).

    Moles Fe = 2 × Moles Fe₂O₃ = 2 × 0.2 = 0.4 mol
  5. 5

    Step 5:

    Convert the moles of product into mass.

    Mr(Fe) = 56 g/mol
    Mass Fe = moles × Mr = 0.4 × 56 = 22.4 g

Answer: 22.4 g

Common mistakes

  • ×Forgetting to use molar ratios from the balanced equation. A 2:3 ratio must be applied; assuming a 1:1 ratio will give an incorrect answer.
  • ×Failing to identify the limiting reactant when amounts for more than one reactant are given. You must perform the check; don't just use the first reactant you calculate moles for.
  • ×Arithmetic errors in multiplication or division, especially with decimals. For example, misplacing a decimal point when calculating 7.2 / 12 or 0.4 × 56.
  • ×Mixing up the 'mass = moles × Mr' formula, for example by dividing mass by moles to find Mr when you should be dividing mass by Mr to find moles.

No-calculator tips

  • ✓Simplify stoichiometric ratios before calculating. A ratio of 2:4 becomes 1:2, and 3:6 becomes 1:2, making the mental multiplication simpler.
  • ✓When doing divisions like 32/160, cancel common factors. 32/160 = 16/80 = 8/40 = 1/5 = 0.2. This is less error-prone than long division.
  • ✓To multiply decimals like 0.4 × 56, treat it as (4 × 56) / 10. Calculate 4 × 56 = 224, then divide by 10 to get 22.4.

Read this topic in the official UAT-UK ESAT guide →

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