Calculations from chemical equations

Use the coefficients as a recipe

A balanced equation gives the mole ratio of every reactant and product. Multiply each mole by its molar mass and you get the mass ratio too.

CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂ means 1 mol + 2 mol → 1 mol + 1 mol + 1 mol. In grams: 100 g + 73 g → 111 g + 18 g + 44 g. Both sides total 173 g.

Method: write the balanced equation, read the ratio between the two substances you need, scale it to the amount given, then convert to grams or particles if asked.

Only the two substances in the question matter; the rest of the equation can be ignored for that step.

Key terms

Coefficient

Giving moles in the equation.

Mole ratio

Scaling from one substance to another.

Mass ratio

Scaling grams directly.

Excess

Telling which reactant does not limit the product.

Short questions with model answers

1. Q1. 25 g of limestone (CaCO₃) reacts with excess HCl. How much CaCl₂ forms? (Example 1, p. 62)

   • 100 g CaCO₃ → 111 g CaCl₂
   • 111 ÷ 100 × 25
   • = 27.75 g

   27.75 g CaCl₂

2. Q2. How many grams of O₂ react with 0.3 mol of Al? 4Al + 3O₂ → 2Al₂O₃ (Example 3, p. 63)

   • 4 mol Al : 3 mol O₂
   • 3 ÷ 4 × 0.3 = 0.225 mol O₂
   • 0.225 × 32 = 7.2 g

   7.2 g O₂

Common mistakes

• ✗ 1 mol CaCO₃ reacts with 1 mol HCl.

  ✓ The coefficient 2 means 2 mol HCl (73 g).

• ✗ 4 g of H₂ gives 2 g of water because the ratio is 2 : 2.

  ✓ The ratio is in moles; 2 mol H₂O is 36 g.

• ✗ 0.3 mol Al needs 4 ÷ 3 × 0.3 = 0.4 mol O₂.

  ✓ Put the wanted substance on top: 3 ÷ 4 × 0.3 = 0.225 mol.

MCQs

1. 1. 1.80 mol ethanol burns: C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O. Moles of O₂ used?

   1. (a) 1.8
   2. (b) 3.6
   3. (c) 5.4
   4. (d) 0.6
   Show answer

   (c) 3 × 1.8 = 5.4 (Example 2, p. 62).

2. 2. In the same reaction, moles of CO₂ formed?

   1. (a) 3.6
   2. (b) 1.8
   3. (c) 5.4
   4. (d) 0.9
   Show answer

   (a) 2 × 1.8 = 3.6 (p. 62).

3. 3. 5 g of H₂ reacts with excess O₂ (2H₂ + O₂ → 2H₂O). Mass of water?

   1. (a) 10 g
   2. (b) 36 g
   3. (c) 40 g
   4. (d) 45 g
   Show answer

   (d) 4 g H₂ → 36 g H₂O, so 5 g → 45 g (Example 4, p. 63).

4. 4. How many grams of HCl react with 100 g of CaCO₃?

   1. (a) 36.5 g
   2. (b) 73 g
   3. (c) 100 g
   4. (d) 111 g
   Show answer

   (b) 2 mol × 36.5 g mol⁻¹ = 73 g (p. 61).

5. 5. 0.3 mol Al needs how many moles of O₂ (4Al + 3O₂ → 2Al₂O₃)?

   1. (a) 0.4
   2. (b) 0.3
   3. (c) 0.225
   4. (d) 0.15
   Show answer

   (c) 3 ÷ 4 × 0.3 = 0.225 (p. 63).

Quick revision

• Coefficients give the mole ratio; × molar mass gives the mass ratio.
• Scale with the wanted substance on top: 3 ÷ 4 × 0.3 mol Al = 0.225 mol O₂.
• Convert at the end: moles × molar mass = grams; moles × N_A = particles.