Relative atomic mass (Ar) — an average of the isotopes
Relative atomic mass () is the average mass of the isotopes of an element, compared with 1/12 of the mass of an atom of carbon-12. Both ideas must be present: it is an average, weighted by how abundant each isotope is, and the scale is fixed against carbon-12. Because it is an average it need not be a whole number — a natural sample of chlorine is about 3 parts chlorine-35 to 1 part chlorine-37, so .
Relative molecular mass (Mr) — sum of the Ar values
Relative molecular mass () is the sum of the relative atomic masses of the atoms shown in a substance's molecular formula. Method: write the formula, list every element with its atom count (reading subscripts inside and outside brackets), multiply each count by its , then add. Water, : . Ionic compounds form a lattice rather than molecules, so the identical total is called the relative FORMULA mass.
Reacting masses — scale the equation's mass ratio
A balanced equation fixes the ratio of masses in which substances react, so an unknown mass follows by simple proportion — no mole concept needed. (1) Balance the equation. (2) Find the relative mass ( or ) of the substance given and of the one wanted. (3) Multiply each by its balancing number to get the mass ratio. (4) Scale the known mass in that ratio. For that is , so 6 g of Mg gives 10 g of MgO.
Drawn from real examiner reports.
Mass number is not relative atomic mass
The mass number of a single isotope counts its protons plus neutrons, so it is always a whole number. Relative atomic mass is the average over all the naturally occurring isotopes of an element, so it can be a decimal. Chlorine has isotopes of mass number 35 and 37, yet — no individual chlorine atom has that mass.
Diatomic elements: use Mr, not Ar
Several elements exist as diatomic molecules, and the question wants the molecule's , not the atom's . Oxygen gas is , so , not 16. Hydrogen gas is , so , not 1. Nitrogen gas is . The same slip shows up in equations, where candidates write O or N in place of the diatomic formula.
Flagged Jun 2022 P16 Q16, P42 Q8aii · Nov 2023 P11 Q15
Carbon dioxide is 44, not 28
Carbon dioxide, , contains one carbon and two oxygens: . The two classic wrong answers are 28 (only one oxygen counted) and 12 (the carbon quoted on its own, as though the compound were just carbon). A reacting-mass calculation built on 28 or 12 then carries that error straight through to a wrong final mass.
Flagged Jun 2022 P41 Q11c, P42 Q11e · Nov 2023 P41 Q5d, P42 Q8d, P42 Q11d
Dropped subscripts wreck the Mr total
Count every atom before doing any arithmetic. has 3 elements and 5 atoms (1 Ca, 1 C, 3 O); using 1 oxygen instead of 3 undercounts by 32 and gives 68 rather than 100. has 3 elements and 7 atoms (2 H, 1 S, 4 O) — the 2 and the 4 are both easy to miss. read as 1 H gives 15 instead of 17.
Flagged Jun 2023 P32 Q11c · Nov 2023 P31 Q11b
A bracket subscript hits everything inside
The number after a bracket multiplies every atom within it, not just the last one. In the 2 gives 2 O and 2 H, so ; applying it to oxygen alone gives 73. In the 3 gives 3 S and 12 O, so ; applying it to sulfur alone leaves only 4 oxygens and gives 214.
Ratio the masses, not the balancing numbers
Balancing numbers count particles, not grams, so they cannot scale a mass directly. Convert to relative masses first, then multiply by the balancing numbers. For that is — not 4 : 2 or 56 : 160. Note holds two irons, so , not 104.
Ar needs both halves of the definition
A partial definition scores at most one mark. Both clauses are required: is an average over the element's naturally occurring isotopes, weighted by abundance, and it is compared with 1/12 of the mass of an atom of carbon-12. Writing "the mass of an atom of the element", comparing to a hydrogen atom, or attaching a unit such as grams each lose the mark.
Ar and Mr carry no unit
Relative masses are ratios, so and never take a unit — writing "18 g" for the of water loses the mark. A mass answer is the opposite: give it in g, or the unit the question states. Omitting units is flagged across every sitting and science.
Write the proportion out in words
"Calculate" means show every line. Set the scaling out explicitly — "48 g of Mg gives 80 g of MgO, so 6 g gives 10 g" — because the method marks survive an arithmetic slip in the final number. A bare answer with no working scores nothing once it is wrong.
No mole language in a Core answer
0654 Core stoichiometry has no mole concept. Reacting-mass questions are answered by simple proportion on relative masses; "mol" and the Avogadro constant belong to the Extended leaf C3.3. Reaching for moles in a Core answer hides the proportion the mark scheme wants.
Name it by the type of substance
The arithmetic is identical, but the name is itself a mark-scheme point. Use relative molecular mass for a substance made of discrete molecules and relative formula mass for an ionic compound — and take the formula-mass name.
Cambridge 0654 spec reference: Section C3 "Stoichiometry", sub-topic C3.2 (Core -- the whole leaf is Core, with no Extended/Supplement content). This leaf covers relative atomic mass (), relative molecular/formula mass (), and calculating reacting masses by simple proportion.
Scope note: 0654 Core stoichiometry has NO mole concept. Every calculation below is done purely by proportional scaling of relative masses -- the mole, the Avogadro constant and the molar gas volume are Extended-only content, covered separately in C3.3.
| Term | Mark-scheme-precise meaning |
|---|---|
| Relative atomic mass () | The average mass of the isotopes of an element, compared with 1/12 of the mass of an atom of carbon-12 |
| Relative molecular mass () | The sum of the relative atomic masses of the atoms shown in the molecular formula of a molecular substance |
| Relative formula mass () | The same sum-of--values calculation, applied to an ionic compound (which has no molecules, only a lattice of ions) |
| Simple proportion (reacting masses) | Using the mass ratio implied by a balanced equation's relative masses and coefficients to scale a known mass to an unknown mass -- no mole concept used |
Core relationship (relative formula/molecular mass):
Core method (reacting mass by simple proportion), for a balanced equation :
Scale the known mass of A in this same ratio to find the mass of C (or vice versa).
Calculate the relative molecular mass of water, . (: H = 1, O = 16.)
Ammonia has the molecular formula . Calculate its relative molecular mass. (: N = 14, H = 1.) (2 marks)
