Relative atomic mass (Ar): the C-12 average
Relative atomic mass () is the average mass of an atom of an element relative to the mass of a carbon-12 atom. The mark scheme needs two elements: average (weighted over the isotope abundances) and the carbon-12 reference — not hydrogen. As a ratio it has no units. On the 0620 Periodic Table every is whole except copper (63.5) and chlorine (35.5); the larger printed number is the , the smaller the proton number.
Relative formula mass (Mr) — add every Ar
Relative formula mass () is the sum of the of every atom in the formula, each counted as often as it appears. Multiply each by its atom count, add, and state one final number — never leave an unevaluated sum. Worked example, (: H = 1, S = 32, O = 16): . For molecules is also called the relative molecular mass; it is dimensionless, so add g/mol only when molar mass is asked for.
Expand brackets and hydrated-salt dots first
A formula with brackets or a dot (hydrated salt) must be expanded before adding values. A subscript outside a bracket multiplies everything inside: . The dot means "plus that many waters", so add them: . The classic slip is to ignore the bracket and count only one O and one H in .
Drawn from real examiner reports.
Atomic number used instead of Ar
Proton number and relative atomic mass () are both printed on the Periodic Table but are different quantities. Nitrogen has proton number 7 but ; confusing them gives instead of the correct . The larger of the two numbers shown is always — check which is which before calculating.
W22 Paper 31 Q8(d); S22 Paper 32 — atomic number used instead of relative atomic mass when calculating Mr.
Left as a sum, no final value
Examiners flagged answers left as a sum — writing and stopping, without evaluating to 40. The accuracy mark is for the final number, not the sum, so it is lost even when the method mark survives. Always finish: sum, equals, then the value, e.g. . Add a unit only where one is asked for.
W22 Paper 42 Q2(c)(iv) — answers left as sums (e.g. Mr = 23 + 16 + 1) without a final stated value; units omitted.
Vague Ar definition loses the mark
Defining needs two elements: that it is an average (weighted) mass of an atom, and that the reference is of a carbon-12 atom. "The mass of an atom" or "the mass compared with hydrogen" earns no full credit — both the word average and the carbon-12 reference must appear for the mark.
Bracketed group not multiplied out
A subscript outside a bracket multiplies every atom inside, not just the last one. In the 2 gives two O and two H: , not . In the outer 3 gives 3 S and 12 O — not 4 O. Expand the bracket in writing before adding, so no atom is undercounted.
W22 Paper 31 Q8(d); S22 Paper 32 — Mr miscalculated by using the wrong number of atoms.
Rounding Cl from 35.5 to 35 or 36
exactly: do not round it to 35 or 36, and never use chlorine's proton number 17. Copper is the other non-integer, . Rounding either changes every that contains it — , not 94 or 96. Carry the .5 through to the final answer.
Ar and Mr are not interchangeable
belongs to a single element; is the sum for a whole formula. Using where is needed under-counts badly — taking as instead of . If a question names a compound or molecule, you need (add every atom); alone answers only single-element questions.
Three-step method for every Mr
marks split into method (correct , multiplications) and accuracy. Collect both: list each element with its atom count (expand brackets first), write , then add and state. Example, : .
Show each multiplication separately
Write each element's contribution on its own line () rather than one long sum. If a slip happens on the final addition, the separate multiplications still earn the method mark — and a missed bracket or dot becomes obvious before you commit to a number.
Explain non-integer Ar via isotopes
For "why is not a whole number?" the chain is: the element is a mixture of isotopes of different mass, so is a weighted average and need not be whole. Chlorine is 75% , 25% : .
Mark-scheme two-element requirements:
| Term | Element 1 (must include) | Element 2 (must include) |
|---|---|---|
| "average mass of an atom of the element" | "relative to the mass of a carbon-12 atom" | |
| "sum of values" | "of all atoms in the formula" |
Key values from the 0620 Periodic Table (non-integer ones to remember):
| Element | Symbol | |
|---|---|---|
| Chlorine | Cl | 35.5 |
| Copper | Cu | 63.5 |
All other common elements have whole-number values (H = 1, C = 12, N = 14, O = 16, Na = 23, Mg = 24, Al = 27, S = 32, K = 39, Ca = 40, Fe = 56, Zn = 65).
Define relative atomic mass ().
Calculate the relative formula mass () of carbon dioxide, .
(: C = 12, O = 16)
