Example 1 — Relative atomic mass from a mass spectrum

A mass spectrum of element Q shows two peaks: at m/z 84 with a height of 5.6 units, and at m/z 86 with a height of 2.4 units. Calculate the relative atomic mass of Q to three significant figures.

The abundances are peak heights, not percentages, so they do not sum to 100. Divide by their total:

Total height = 5.6 + 2.4 = 8.0

Ar = (84 × 5.6 + 86 × 2.4) / 8.0
   = (470.4 + 206.4) / 8.0
   = 676.8 / 8.0
   = 84.6

Ar = 84.6.

The whole question is the denominator. Dividing by 100 out of habit gives 6.77, which is obviously absurd — and students still write it, because the method is automatic. Check that your answer lies between the two isotope masses, closer to the more abundant one. 84.6 sits between 84 and 86, nearer 84. That sanity check takes two seconds and catches almost every error here.

Example 2 — Deducing a group from successive ionisation energies

The first four ionisation energies of an element, in kJ mol⁻¹, are 738, 1451, 7733 and 10 540. Deduce the group of the element in the periodic table.

Look at the ratios between consecutive values, not the differences:

1451 / 738  = 1.97      a modest rise
7733 / 1451 = 5.33      a very large jump
10540 / 7733 = 1.36     a modest rise again

The large jump comes between the second and third ionisation energies. So two electrons are removed relatively easily, and the third requires far more energy because it is being removed from a new shell, closer to the nucleus and less shielded.

Two easily removed outer electrons means the element is in group 2.

Note what earned the marks: identifying where the jump is, explaining why a jump occurs in terms of shells and shielding, and only then stating the group. Deduce requires the reasoning on the page — "group 2" alone would score 1 of 3.

Example 3 — Limiting reagent and gas volume

0.240 g of magnesium is added to 50.0 cm³ of 0.500 mol dm⁻³ hydrochloric acid.

Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)

(a) Determine the limiting reagent. (b) Calculate the volume of hydrogen produced at 273 K and 1.00 × 10⁵ Pa.

(a) Convert both reactants to moles. Note the volume must go from cm³ to dm³:

n(Mg)  = m/M = 0.240 / 24.31 = 9.87 × 10⁻³ mol
n(HCl) = c × V = 0.500 × (50.0/1000) = 0.0250 mol

Now divide each by its coefficient in the balanced equation — this is the step students skip:

Mg :  9.87 × 10⁻³ ÷ 1 = 9.87 × 10⁻³
HCl:  0.0250        ÷ 2 = 0.0125

9.87 × 10⁻³ < 0.0125, so magnesium is limiting.

(b) The equation shows 1 mol Mg gives 1 mol H₂, so n(H₂) = 9.87 × 10⁻³ mol. Now pV = nRT, in base SI units:

V = nRT / p
  = (9.87 × 10⁻³ × 8.31 × 273) / (1.00 × 10⁵)
  = 22.40 / (1.00 × 10⁵)
  = 2.24 × 10⁻⁴ m³
  = 0.224 dm³

Mg is limiting; 0.224 dm³ (224 cm³) of hydrogen is produced.

Three separate unit traps in one question. cm³ to dm³ for the concentration; kelvin for the gas law (273 was already given in K — check, because it is often given in °C); and m³ back to dm³ at the end. Comparing raw mole values without dividing by the coefficients would have made HCl look limiting, which is wrong and would cost every subsequent mark.

Example 4 — Explaining deviation from ideal behaviour

Explain why a real gas deviates from ideal behaviour at high pressure. [3]

The ideal gas model assumes that particles have negligible volume and that there are no intermolecular forces between them. ✓ At high pressure the particles are forced close together, so the volume of the particles themselves is no longer negligible compared with the volume of the container. ✓ The particles are also close enough for intermolecular attractions to become significant, so they strike the walls with less force and the measured pressure is lower than the model predicts. ✓

3/3.

An answer must name the assumption it is breaking. "Because the particles are close together" describes the condition without explaining the deviation, and scores 1 at most. Note also the direction: attractions make the real pressure lower than ideal, while particle volume makes the real volume higher — a question asking which effect dominates is asking about temperature.

Educerie · original worked examples written against the published IB syllabus structure for Chemistry Structure 1, first assessment 2025. All data are our own. Constants are from the IB data booklet. Last reviewed 5 September 2026.