You are viewing a free preview of this lesson.
Subscribe to unlock all 10 lessons in this course and every other course on LearningBro.
Spec Mapping — OCR H432 Module 2.1.2 — Compounds, formulae and equations / relative masses, content statements covering the definitions of relative isotopic mass, relative atomic mass (Ar), relative molecular mass (Mr) and relative formula mass, all referenced to the 12C scale; and the calculation of Ar from isotopic abundance data (refer to the official OCR H432 specification document for exact wording). This lesson sits between Module 2.1.1 (atomic structure) and Module 2.1.3 (the mole) and is the conceptual bridge to every quantitative chemistry calculation in the course.
Relative masses are the language in which all of A-Level Chemistry's quantitative work is conducted. The mole calculations of the next four lessons, the empirical-formula determinations, the percentage-yield problems, the titration arithmetic and even the Born–Haber and equilibrium thermodynamics of later modules all rest on knowing exactly what Ar and Mr mean and how to compute them. The lesson develops three threads in parallel: (i) the historical evolution of mass standards from Dalton through Ostwald to the modern 12C reference; (ii) the four formal OCR definitions of relative mass and the dimensionless-ratio property they all share; and (iii) the weighted-mean arithmetic that turns a list of isotopic abundances into a published Ar. We finish with the inverse problem — solving algebraically for unknown abundances given Ar — and with practical Mr calculation, including the bracket-handling discipline that catches many candidates out at Module 5 (pH and acids).
Key Definition: The relative atomic mass Ar of an element is the weighted mean mass of an atom of that element compared with one-twelfth of the mass of an atom of 12C.
Key Equation: Ar=∑abundances∑(isotopic mass×abundance)
Individual atoms are fantastically small — a single 12C atom has a mass of about 1.993×10−23 g. Working in kilograms is cumbersome, so chemists use relative masses: the mass of an atom or molecule expressed as a dimensionless ratio against a standard reference.
Since 1961, that standard has been carbon-12 (12C). One atom of 12C is defined as having a mass of exactly 12 atomic mass units (12 u). Every other atom or molecule is measured against this. Because the standard is itself an atom, the resulting numbers are conveniently scaled — a hydrogen atom is roughly 1, a chlorine atom roughly 35.5 — and the dimensionless ratio is the same regardless of the unit (kg, g, u) used in the underlying mass measurement.
The earliest atomic weights, measured by Dalton in 1803, used hydrogen =1 as the reference. In 1898 Wilhelm Ostwald proposed oxygen =16, convenient because oxygen combines with so many elements and so could anchor many compounds at once. From 1929 to 1961 chemists and physicists actually used different oxygen scales: chemists used "natural" oxygen (a weighted mean of 16O, 17O and 18O) while physicists used pure 16O. This caused small but persistent discrepancies between the two communities. In 1961 IUPAC and IUPAP agreed on 12C=12 exactly, resolving the conflict. Carbon-12 was chosen because: it is the most abundant carbon isotope (close to mono-isotopic in practical terms); carbon underpins organic chemistry; the new scale gives atomic masses within ≈1% of the old oxygen scale (minimising disruption); and 12C atoms can be counted very precisely in mass spectrometry, anchoring the standard to a measurable benchmark.
You must learn these definitions to the letter. OCR's mark schemes reward the 12C reference explicitly; mark-loss for vague wording such as "mass compared to carbon" is routine.
The mass of an atom of an isotope compared with one-twelfth of the mass of an atom of 12C.
Relative isotopic masses are effectively whole numbers (within 0.1%) because the dominant contribution to atomic mass comes from whole nucleons. For example, the relative isotopic mass of 35Cl≈35 and of 37Cl≈37.
In precise experimental work, exact relative isotopic masses differ very slightly from whole numbers because of the mass defect — when nucleons bind together in a nucleus a tiny fraction of mass is converted into binding energy E=mc2. For example, the relative isotopic mass of 35Cl is actually 34.9689 — very close to but not exactly 35. For A-Level calculations the whole number is usually sufficient, but if OCR gives a decimal value you must use it.
The weighted mean mass of an atom of an element compared with one-twelfth of the mass of an atom of 12C.
The word weighted is critical: Ar accounts for natural abundance. Because most elements exist as a mixture of isotopes, Ar values are rarely whole numbers. For chlorine, Ar=35.5 because of the natural ≈75:25 mix of 35Cl:37Cl.
The weighted mean mass of a molecule compared with one-twelfth of the mass of an atom of 12C.
For molecular compounds, Mr(H2O)=2(1.0)+16.0=18.0.
Used for ionic compounds, which do not exist as discrete molecules. The definition is analogous but uses "formula unit" rather than "molecule". For example, the relative formula mass of NaCl =23.0+35.5=58.5.
Note: In OCR exams the symbol Mr is used for both relative molecular and relative formula mass, with no distinction made at A-Level unless the question explicitly draws one.
The Ar values you use day-to-day come from a long history of refinement. The 2007 IUPAC review tabulated atomic weights for every element, and OCR's data booklet rounds these to 1 d.p. for use in A-Level calculations. The rounding is justified because the experimental precision of typical lab-bench measurements (titrations, gravimetric analysis) is rarely better than 3 s.f., so 1 d.p. on Ar does not limit the calculation precision.
A counter-example arises in modern mass-spectrometry: high-resolution Orbitrap and FT-ICR instruments measure isotopic masses to better than 10−5u, allowing the resolution of isobaric ions like N2 and CO (both Mr≈28 at A-Level precision, but 28.0061 and 27.9949 at high resolution). For such work the integer-mass approximation breaks down and exact isotopic masses are essential. This is why analytical chemists working in pharmaceutical R&D use the precise Ar values from the IUPAC tables, not the rounded periodic-table figures.
For OCR A-Level work, the data-sheet values are sufficient; OCR's mark schemes use the same values as inputs, so following the data sheet ensures consistency with the marking benchmark.
Before the 1961 carbon-12 standardisation, three different reference scales coexisted across chemistry and physics. Chemists used "naturally occurring oxygen" — a mixture of 16O, 17O and 18O in their terrestrial proportions — as the reference at 16.0000 exactly. Physicists used pure 16O as the reference. The two scales differed by about 1 part in 4000 — small, but enough to cause persistent inconsistencies when atomic masses measured by mass spectrometry (a physics technique) were compared with chemical-weighing measurements.
The choice of carbon-12 in 1961 was driven by several factors. First, carbon is the universal organic-chemistry element, and adopting carbon as the reference brought atomic-mass standards into closer alignment with the most-used element in chemistry. Second, 12C is a single isotope rather than a mixture, eliminating the abundance-dependence of natural oxygen. Third, the new standard gave atomic masses on the order of 1 % from the previously published oxygen-scale values — small enough that decades of accumulated tabulated data could be rescaled with minimal disruption. Fourth, 12C can be precisely isolated and weighed in mass spectrometers, providing a tangible experimental anchor for the abstract standard.
The 2019 SI redefinition further consolidated the framework by fixing Avogadro's constant L exactly (see the lesson on the mole). The mole now contains exactly 6.02214076×1023 entities; the relative atomic mass scale on 12C=12 continues unchanged because the dimensionless ratios are unaffected by the choice of base unit.
All four quantities are ratios of masses — they are dimensionless and have no units. Candidates who write "Ar=35.5 g" lose a mark. If you want to express mass per mole, use molar mass (e.g. 35.5 g mol−1), not relative atomic mass. The dimensional distinction matters again when you meet the ideal gas equation in the lesson on pV=nRT.
The formula above, restated for emphasis:
Ar=∑abundances∑(isotopic mass×abundance)
If abundances are given as percentages, the denominator is 100. If given as relative abundances (peak heights on a mass spectrum), divide by their actual total — never assume the total is 100.
Naturally occurring chlorine contains 75.78 % 35Cl and 24.22 % 37Cl. Calculate Ar(Cl) to 1 d.p.
Ar=100(35×75.78)+(37×24.22)=1002652.3+896.14=1003548.44=35.5
Copper exists as 69.2 % 63Cu and 30.8 % 65Cu.
Ar=100(63×69.2)+(65×30.8)=1004359.6+2002.0=63.6
| Isotope | Abundance / % |
|---|---|
| 24Mg | 78.99 |
| 25Mg | 10.00 |
| 26Mg | 11.01 |
Ar=100(24×78.99)+(25×10.00)+(26×11.01)=1001895.76+250.00+286.26=24.3
A sample of silicon contains 92.23 % 28Si (isotopic mass 27.977), 4.67 % 29Si (28.976) and 3.10 % 30Si (29.974).
Ar=100(27.977×92.23)+(28.976×4.67)+(29.974×3.10)=1002580.52+135.32+92.92=28.09
When OCR provides decimal isotopic masses, use them — the answer changes in the second decimal place and the difference is examinable.
When Ar is known and you must find abundances, the same equation rearranges into a linear algebra problem. The structure is always: let x = the percentage of one isotope, (100−x) = the percentage of the other, substitute into the weighted-mean expression, and solve.
Boron has Ar=10.8 and exists as 10B and 11B. Let x= % 10B.
10.8=10010x+11(100−x) 1080=10x+1100−11x −20=−x⇒x=20
Boron is 20 % 10B and 80 % 11B.
Ar(Ga)=69.7 with isotopes 69Ga and 71Ga. Let x= % 69Ga.
69.7=10069x+71(100−x) 6970=69x+7100−71x −130=−2x⇒x=65
Gallium is 65 % 69Ga and 35 % 71Ga.
Ar(Ag)=107.9, isotopes 107Ag and 109Ag.
107.9=100107x+109(100−x)⇒x=55
Silver is 55 % 107Ag and 45 % 109Ag.
Magnesium has three naturally occurring isotopes: 24Mg, 25Mg and 26Mg, with Ar(Mg)=24.31. If 25Mg has a fixed abundance of 10.00 %, find the abundances of 24Mg and 26Mg.
Let x = % 24Mg. Then % 26Mg=(100−10−x)=(90−x).
24.31=10024x+25(10)+26(90−x) 2431=24x+250+2340−26x=2590−2x 2x=159⇒x=79.5
So 24Mg=79.5% and 26Mg=10.5%. Compare with the published natural abundances (78.99 %, 10.00 %, 11.01 %) — close to within the precision of the Ar value used. This is the most demanding inverse problem OCR can set: three unknowns with two constraints (one fixed abundance, the weighted-mean equation, and the implicit "abundances sum to 100").
A pure sample of an unknown element X contains 4.50×1022 atoms and has a mass of 4.65 g. Determine Ar(X) and identify the element.
The reverse-mass workflow (N→n→Ar) is the same arithmetic as the forward direction but is procedurally less practised. Top candidates flag the limited precision of inputs as the source of the discrepancy rather than treating the mismatch as an arithmetic error.
Subscribe to continue reading
Get full access to this lesson and all 10 lessons in this course.