Relative Atomic and Molecular Mass (Ar and Mr)

Two Ar and Mr habits decide whole calculation chains in 0620: multiplying through brackets, and counting water of crystallisation. An Mr slip in line 1 of a Paper 4 calculation can bleed into three later answers, rescued only partially by error-carried-forward. The definitions are Core, asked directly for 1-2 marks, and built on the carbon-12 standard. This page nails both the words and the arithmetic that the stoichiometry topic depends on.

Relative atomic mass, Ar (Core)

Relative atomic mass is the average mass of the atoms of an element compared to 1/12 of the mass of an atom of carbon-12. Carbon-12 is the standard: one atom of it is defined as exactly 12 units, and everything else is measured against a twelfth of it. Hydrogen’s Ar of 1 means a hydrogen atom has the same mass as 1/12 of a carbon-12 atom.

“Average” is in the definition because most elements are isotope mixtures. Chlorine’s Ar of 35.5 is the weighted mean of Cl-35 (75%) and Cl-37 (25%); the calculation lives in the isotopes subtopic. No atom of chlorine has mass 35.5; the average does. In exams, every Ar you need is printed on the Periodic Table supplied with the paper. The skill is using them, not recalling them.

Relative molecular (formula) mass, Mr (Core)

Mr is the sum of the relative atomic masses of all the atoms in a formula. For covalent molecules it is called relative molecular mass; for ionic compounds, which have no molecules, the identical sum is the relative formula mass. Both are dimensionless.

Substance	Working	Mr
CO2	12 + 2(16)	44
Ca(OH)2	40 + 2(16 + 1)	74
(NH4)2SO4	2(14 + 4) + 32 + 4(16)	132
CuSO4·5H2O	64 + 32 + 4(16) + 5(18)	250

Two rules generate every hard case. Brackets multiply everything inside them: the 2 in Ca(OH)2 doubles both the O and the H. The dot in a hydrated salt means “plus”: CuSO4·5H2O contains five water molecules per formula unit, adding 5 × 18 = 90. Miss the water and the Mr is 160, and every downstream mole answer is wrong by the same factor.

Mr matters because it converts to molar mass: one mole of a substance has a mass in grams numerically equal to its Mr. That single link powers n = m/M and everything in the mole and the Avogadro constant, and the full calculation method is drilled in our mole calculations technique guide.

Worked exam question

(a) Define relative atomic mass. (2) (b) Calculate the relative formula mass of hydrated sodium carbonate, Na2CO3·10H2O. [Ar: Na 23, C 12, O 16, H 1] (2) (c) State why chlorine’s relative atomic mass, 35.5, is not a whole number. (1)

Model answer: (a) The average mass of the atoms of an element (1) compared to/measured against 1/12 of the mass of an atom of carbon-12 (1). (b) Na2CO3 = 2(23) + 12 + 3(16) = 106 (1); plus 10(18) = 180, giving 106 + 180 = 286 (1). (c) Chlorine exists as two isotopes (Cl-35 and Cl-37), and 35.5 is their weighted average (1).

Mark-by-mark: (a) splits into the “average mass of atoms” mark and the carbon-12 comparison mark. Students reliably earn the first and drop the second. (b) gives one mark for the anhydrous part and one for handling the 10H2O; an answer of 106 shows the dot was ignored. (c) needs isotopes named as the reason; “it’s an average” alone is half the story.

The mistakes that cost marks

1. Defining Ar against “a carbon atom” or “carbon” instead of 1/12 of a carbon-12 atom. The isotope and the fraction are both checked.
2. Bracket blindness: Mg(NO3)2 computed as 24 + 14 + 48 = 86 instead of 24 + 2(62) = 148. Expand the bracket before adding.
3. Dropping water of crystallisation, or adding it as 10 H atoms rather than 10 H2O units (180, not 10).
4. Units pinned on relative masses: “Mr = 44 g”. Relative masses are ratios with no units; only molar mass carries g/mol.

How examiners want it phrased

Typical student wording	Accepted mark-scheme wording
”Ar is how heavy an atom is"	"The average mass of the atoms of an element compared to 1/12 of the mass of a carbon-12 atom"
"Mr is everything added up"	"The sum of the relative atomic masses of all atoms in the formula"
"Chlorine is 35.5 because that’s what the table says"	"Chlorine is a mixture of isotopes; 35.5 is the weighted average of Cl-35 and Cl-37"
"Mr of CuSO4·5H2O = 160"	"Mr = 160 + 5(18) = 250, including the water of crystallisation”

The Malaysia note

Ar and Mr questions appear in the first half of Malaysian school mid-year exams and the students cruise. Then October mock papers embed the same Mr inside a four-step titration calculation and accuracy drops sharply. The content was never the problem; calculation stamina was. SPM uses the identical carbon-12 standard (“jisim atom relatif”), so dual-track students carry this over directly. If multi-step calculations are where marks vanish, a free 1-hour trial lesson will show whether the leak is Mr arithmetic or the mole logic layered on top.

Test yourself

Do all three without looking back at the tables. Click each answer to check your arithmetic.

Q1 (1 mark). Calculate the relative formula mass of magnesium nitrate, Mg(NO3)2. [Ar: Mg 24, N 14, O 16]

Show answer

• Mr = 24 + 2(14 + 3 × 16) = 24 + 2(62) = 148 [1]

Q2 (2 marks). Calculate the relative formula mass of hydrated magnesium sulfate, MgSO4·7H2O. [Ar: Mg 24, S 32, O 16, H 1]

Show answer

• MgSO4 = 24 + 32 + 4(16) = 120 [1] • + 7(18) = 126, giving 120 + 126 = 246 [1]

Q3 (2 marks). State what is meant by relative formula mass, and explain why this term (rather than relative molecular mass) is correct for sodium chloride.

Show answer

• The sum of the relative atomic masses of all the atoms (ions) in the formula [1] • Sodium chloride is ionic, so it contains no molecules; the formula NaCl is a ratio of ions, not a molecule [1]