Problem Solving with Atoms and Molecules

Introduction

Exam questions rarely test one idea in isolation. A single question might ask you to count atoms in a formula, identify whether a substance is an element or compound, find its relative formula mass and then work out a percentage. This page brings together the skills of the unit and shows a clear strategy for solving mixed problems confidently and accurately.

Core explanation

A general strategy. 1. Read the question twice and underline what is being asked. 2. Identify the substances and write correct formulae, remembering diatomic elements. 3. Plan the steps: which quantity leads to which? 4. Calculate step by step, labelling each line. 5. Check with an estimate or a second method.

Skill 1 — classifying particles. Ask: is it one kind of atom (element) or more than one (compound)? Is it made of molecules or of ions? For example, O₃ is an element made of molecules with atomicity 3; NaCl is a compound made of ions, so it has formula units rather than molecules.

Skill 2 — atomicity. Atomicity is the number of atoms in a molecule of an element: He is monatomic (1), Cl₂ diatomic (2), O₃ triatomic (3), P₄ tetratomic (4) and S₈ polyatomic (8).

Skill 3 — counting atoms. Expand brackets and multiply by coefficients. In 3(NH₄)₂SO₄ each formula unit has 2 N, 8 H, 1 S and 4 O (15 atoms), so three units contain 45 atoms.

Skill 4 — Mr. Multiply each Ar by the number of atoms and add. For (NH₄)₂SO₄: 28 + 8 + 32 + 64 = 132.

Skill 5 — percentage by mass. % N in (NH₄)₂SO₄ = 28 ÷ 132 × 100 = 21.2%.

Skill 6 — comparing substances. Use Mr to compare molecules: the heavier molecule in a similar family has the higher boiling point; the heavier gas is the denser.

Estimation as a check. Before calculating, estimate. Mg(NO₃)₂ has six oxygen atoms (about 96) plus magnesium and nitrogen, so an answer near 150 is expected; the exact value is 148. An answer of 86 would immediately signal a missed bracket.

Step-by-step reasoning

Solving: "Which contains the greater percentage of nitrogen, NH₄Cl or (NH₄)₂SO₄?" (N = 14, H = 1, Cl = 35.5, S = 32, O = 16)

1. Mr of NH₄Cl = 14 + 4 + 35.5 = 53.5. 2. % N = 14 ÷ 53.5 × 100 = 26.2%. 3. Mr of (NH₄)₂SO₄ = 132; % N = 21.2%. 4. Compare: 26.2% is larger. 5. Conclusion: NH₄Cl has the greater percentage of nitrogen.

Visual explanation

A flow chart helps: "Formula → count atoms → Ar values → Mr → percentage or comparison". Each arrow is one step. Writing the chain at the start of a long question keeps you on track and shows the examiner your plan.

Real-world analogy

Planning a journey with several connections works better with a route map than by guessing at each station. A multi-step chemistry problem is a journey from the data given to the answer asked for; plan the connections first.

Real-world example

Quality-control chemists in a fertiliser plant check whether a batch meets its label. They confirm the formula of the product, calculate its expected nitrogen percentage from Mr and compare this with the measured value to spot impurities.

Why?

Why check answers with a second method? Because a single slip, such as missing a subscript, can produce a believable-looking number. An independent route, such as counting all atoms rather than using group masses, rarely repeats the same mistake.

Common misconception

"Ionic compounds such as NaCl have molecules, and their atomicity is 2." Atomicity applies to molecules of elements. Sodium chloride is a giant lattice of ions; NaCl is its formula unit, showing a 1 : 1 ratio of ions, not a two-atom molecule.

Worked example

Question: For white phosphorus, P₄ (P = 31), state its atomicity and whether it is an element or a compound, then find its Mr and the number of atoms in 5 molecules.

Reasoning: P₄ contains only phosphorus, so it is an element. Each molecule has 4 atoms, so its atomicity is 4. Mr = 4 × 31 = 124. Five molecules contain 5 × 4 = 20 atoms.

Answer: Atomicity 4; element; Mr 124; 20 atoms.

Quick check

1. How many atoms are shown in 2Ca(OH)₂? Answer: Ten: each formula unit has 1 Ca, 2 O and 2 H (5 atoms), and there are two units.

Exam focus

Label every step with what it calculates, for example "Mr of CO₂ =". In multi-step questions, a mistake early on is only penalised once if later steps are correctly carried through, so clear working protects your marks.

Advanced insight

Problems can also run in reverse. If an oxide of sulfur has Mr = 80 and contains one sulfur atom, the oxygen accounts for 80 − 32 = 48, which is 48 ÷ 16 = 3 oxygen atoms, giving SO₃. Working backwards from Mr is how chemists confirm the formulae of unknown substances.

Summary

Mixed problems combine classifying particles, atomicity, counting atoms, Mr and percentages. A reliable strategy is read, identify, plan, calculate and check. Estimation and a second method catch common errors. Remember that ionic compounds have formula units rather than molecules, and that atomicity refers to molecules of elements.

Practice questions

1. State the atomicity of ozone, O₃, and calculate its Mr (O = 16). Answer: Atomicity 3; Mr = 48. 2. How many hydrogen atoms are in 3H₂SO₄, and what is the Mr of H₂SO₄ (H = 1, S = 32, O = 16)? Answer: 6 hydrogen atoms; Mr = 2 + 32 + 64 = 98. 3. Calculate the percentage by mass of calcium in calcium hydroxide, Ca(OH)₂ (Ca = 40). Answer: 40 ÷ 74 × 100 = 54.1%. 4. An oxide of nitrogen has Mr = 44 and contains two nitrogen atoms (N = 14). Find its formula. Answer: Oxygen = 44 − 28 = 16, one oxygen atom, so the formula is N₂O. 5. Is CO₂ an element or a compound, and is it made of molecules or ions? Answer: A compound made of molecules, each containing one carbon and two oxygen atoms.