Atoms, molecules and stoichiometry

• Moles first, ratio second, answer last — and round only once.
• One twelfth of a carbon-12 atom. Moles first, ratio second. No spectators, no unsplit aqueous salts, and round once.

• 2.1.1 I can define — define the unified atomic mass unit as one twelfth of the mass of a carbon-12 atom
• 2.1.2 I can define — define relative atomic mass, Ar, relative isotopic mass, relative molecular mass and relative formula mass, both referred to as Mr, in terms of the unified atomic mass unit
• 2.2.1 I can define — define and use the term mole in terms of the Avogadro constant
• 2.3.1 I can — write formulas of ionic compounds from ionic charges and oxidation numbers (shown by a Roman numeral), including: (a) the prediction of ionic charge from the position of an element in the Periodic Table (b) recall of the names and formulas for the following ions: NO₃⁻, CO₃²⁻, SO₄²⁻, OH⁻, NH₄⁺, Zn²⁺, Ag⁺, HCO₃⁻, PO₄³⁻
• 2.3.2 I can — (a) write and construct equations (which should be balanced), including ionic equations (which should not include spectator ions) (b) use appropriate state symbols in equations
• 2.3.3 I can define — define and use the terms empirical and molecular formula
• 2.3.4 I can understand — understand and use the terms anhydrous, hydrated and water of crystallisation
• 2.3.5 I can calculate — calculate empirical and molecular formulas, using given data
• 2.4.1 I can — perform calculations including use of the mole concept, involving: (a) reacting masses (from formulas and equations) including percentage yield calculations (b) volumes of gases (e.g. in the burning of hydrocarbons) (c) volumes and concentrations of solutions (d) limiting reagent and excess reagent (When performing calculations, candidates' answers should reflect the number of significant figures given or asked for in the question. When rounding up or down, candidates should ensure that significant figures are neither lost unnecessarily nor used beyond what is justified (see also Mathematical requirements section).) (e) deduce stoichiometric relationships from calculations such as those in 2.4.1(a)-(d)

Units and significant figures are marked. The syllabus states that failure to quote units, the inclusion of units in quantities defined as ratios, and answers given to an inappropriate number of significant figures are all liable to be penalised. Give a calculated answer to the same number of significant figures as the least precise data, or one more; keep full precision in the working and round only at the end. A fifth of the qualification is experimental: Papers 3 and 5 test AO3 only, and their questions may be set in contexts outside the syllabus content, so the practical work in this chapter is set out as procedure, recording and evaluation rather than as theory.

• “Magnesium is the limiting reagent because there is less of it by mass.” Correct Moles first, ratio second. Convert both reactants to moles, then use the equation to see how much of one the other needs. The smaller mass, and even the smaller number of moles, is not the test: the equation ratio is (section M).
• “The relative atomic mass of carbon is 12 g mol⁻¹.” Correct Ar and Mr are ratios to one twelfth of the mass of a carbon-12 atom, so they have no unit. The molar mass M carries the unit g mol⁻¹ (sections B and C).
• “One mole of oxygen contains 6.022 × 10²³ atoms.” Correct Name the particle. One mole of O₂ molecules contains 6.022 × 10²³ molecules and 1.204 × 10²⁴ atoms (section C).
• “Ag⁺(aq) + NO₃⁻(aq) + Na⁺(aq) + Cl⁻(aq) → AgCl(s) + Na⁺(aq) + NO₃⁻(aq) is the ionic equation.” Correct An ionic equation must not include spectator ions. Cancel the ions that are the same on both sides: Ag⁺(aq) + Cl⁻(aq) → AgCl(s) (section E).
• “n = c × V = 0.100 × 22.50 = 2.25 mol.” Correct The volume goes into c = n/V in dm³. Divide cm³ by 1000 first: 0.100 × 0.02250 = 2.25 × 10⁻³ mol (section L).
• “The ratio came out as 1 : 1.5, so the formula is XY.” Correct 1.5 is a real 3 : 2. Multiply the whole set by 2. Round only a near-integer such as 2.98 (section H).
• “I rounded each step to three figures as I went.” Correct Carry the calculator value through the working and round once, at the end, to the same number of significant figures as the least precise datum, or one more (section I).
• “The unified atomic mass unit is the mass of a hydrogen atom.” Repair It is one twelfth of the mass of a carbon-12 atom. Hydrogen is only about 1 u.
• “Relative atomic mass has the unit g mol⁻¹.” Repair Ar and Mr are ratios and have no unit. The molar mass M has the unit g mol⁻¹.
• “Mr(CuCl₂) = 64 + 2(35) = 134.” Repair Use the Periodic Table values: 63.5 + 2(35.5) = 134.5. Chlorine and copper are weighted means of isotopic masses and are never whole numbers.
• “One mole of oxygen contains 6.022 × 10²³ atoms.” Repair Specify the particle: one mole of O₂ molecules contains 6.022 × 10²³ molecules and 1.204 × 10²⁴ atoms.
• “MgOH, AlSO₄, NH₄SO₄.” Repair Balance the charges and bracket repeated polyatomic ions: Mg(OH)₂, Al₂(SO₄)₃, (NH₄)₂SO₄.
• “Iron(III) sulfate is Fe₃SO₄.” Repair The numeral is the charge on the iron ion, not the number of iron atoms: Fe³⁺ with SO₄²⁻ gives Fe₂(SO₄)₃.
• “Ag⁺(aq) + NO₃⁻(aq) + Cl⁻(aq) → AgCl(s) + NO₃⁻(aq).” Repair Spectator ions are unchanged and must be cancelled: Ag⁺(aq) + Cl⁻(aq) → AgCl(s).
• “Ca²⁺ + CO₃²⁻ + 2H⁺ → Ca²⁺ + CO₂ + H₂O” for marble chips in acid. Repair CaCO₃ is a solid and is never split: CaCO₃(s) + 2H⁺(aq) → Ca²⁺(aq) + CO₂(g) + H₂O(l). And the state symbols are part of the answer.
• “The empirical formula tells you what the compound is.” Repair CH₂O is glucose, ethanoic acid and methanal. Mr is needed for the molecular formula, and even that may not distinguish isomers.
• “The ratio is 1 : 1.5, so I rounded it to 1 : 2.” Repair 1.5 is a real 3 : 2. Multiply the whole set by 2.
• “Oxygen in the compound = oxygen in the CO₂ + oxygen in the H₂O.” Repair Most of that oxygen came from the air. Find the compound's oxygen by subtracting the masses of C and H from the sample mass.
• “The reactant with the smaller mass is the limiting reagent.” Repair Convert both to moles and compare with the equation ratio. 5.00 g of Mg is limiting against 4.00 g of O₂.
• “n = 0.100 × 22.50 = 2.25 mol.” / “24.0 dm³ of water is one mole.” Repair Convert cm³ to dm³ first: 0.02250 dm³, so 2.25 × 10⁻³ mol. The molar gas volume applies to gases only; for a liquid or solid use n = m/M.
• “c = 0.1799999 mol dm⁻³”, or “c = 0.18” from data given to three figures. Repair Round once, at the end, to three (or at most four) significant figures: 0.180 mol dm⁻³. Too many figures claim a precision that was not measured; too few lose figures unnecessarily.

• Read the command word before you decide how much to write. This syllabus has twenty-two of them: analyse, calculate, compare, consider, contrast, deduce, define, demonstrate, describe, determine, discuss, evaluate, examine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Comment, estimate, name and outline are not among them: where a question wants something named it says identify, which the syllabus glosses as “name/select/recognise”. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Deduce and determine want a conclusion reached from the information given, with the reasoning visible.
• Interleave with the chapters that use this one. When you reach Topic 4, redo worked example 5 and ask why 24.0 dm³ mol⁻¹ only works at room conditions. In Topic 5, re-answer: how many moles of fuel were burned? In Topic 6, rewrite the metal-displacement and halogen-displacement ionic equations from section E as half-equations. In Topic 7, redo the titration in worked example 6 with a weak acid in mind. Recalling a topic inside a new context is worth more than another pass over this chapter on its own; at A Level, Paper 4 assumes the whole of the AS content, so nothing here is ever finished with.

• Cambridge International AS & A Level Chemistry 9701 has five components. Topic 2 is AS Level content, so it is examined in Papers 1, 2 and 3. AS Level content: examined in Paper 1 (multiple choice), Paper 2 (AS structured) and, as practical context, Paper 3. Assumed knowledge for Papers 4 and 5. AS Level candidates take Papers 1, 2 and 3; A Level candidates take all five, either staged over two years (Papers 1–3 in year one, Papers 4 and 5 in year two) or together in one series. Examinations are available in the June and November series, and in March in India.
• Across both the AS Level and the A Level the assessment objectives are weighted AO1 40% (knowledge and understanding), AO2 40% (handling, applying and evaluating information) and AO3 20% (experimental skills and investigations). AS candidates are graded a–e; A Level candidates A*–E.
• A multiple-choice item on this topic turns on one step done correctly: the right particle counted, the right formula for an ion, the right ratio from an equation, the limiting reagent chosen by ratio rather than by mass. A structured question asks you to define the unified atomic mass unit, a relative mass or the mole in full; to write a formula or an ionic equation with state symbols; and to calculate or deduce with every step shown.
• Amounts in moles, masses, gas volumes, concentrations, percentage yields, and empirical, molecular and hydrated-salt formulae. You are given the Avogadro constant (6.022 × 10²³ mol⁻¹), the molar gas volume (24.0 dm³ mol⁻¹ at room conditions, 22.4 dm³ mol⁻¹ at s.t.p.) and every relative atomic mass in the Periodic Table. You are expected to recall the definitions, the nine ions and the relationships n = m/M, N = nL and c = n/V.
• Topic 2 is the calculation behind three of the procedures the syllabus lists: the acid–alkali titration, gas collection over water, and heating a hydrated salt in a crucible to constant mass. Paper 3 asks you to record the readings to the right precision and finish the calculation; a Paper 5-style question asks you to plan one of them, draw the results table in advance, and name the largest error and its improvement.
• Read the command word before you decide how much to write. This syllabus has twenty-two of them: analyse, calculate, compare, consider, contrast, deduce, define, demonstrate, describe, determine, discuss, evaluate, examine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Comment, estimate, name and outline are not among them: where a question wants something named it says identify, which the syllabus glosses as “name/select/recognise”. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Deduce and determine want a conclusion reached from the information given, with the reasoning visible.