Relative atomic mass and relative molecular mass

This page covers a single Form 4 content standard: relative atomic mass and relative molecular mass. These two quantities are the starting point for the whole of the mole concept, every calculation in this chapter, and much of the stoichiometry you will meet in later chapters of SPM Chemistry, begins by reading an Ar value or adding up an Mr. Getting them exactly right here saves marks everywhere later.

Why chemists use “relative” masses

The actual mass of a single atom is far too small to weigh directly, a hydrogen atom has a mass of roughly 1.67 × 10⁻²⁴ g. Numbers like that are awkward in every calculation, so chemists compare masses instead of measuring them in grams. They choose one atom as a reference standard and describe every other atom relative to it. The agreed standard is the carbon-12 atom, whose mass is defined as exactly 12 units. Everything is then measured against one-twelfth of that atom.

Relative atomic mass (Ar)

The relative atomic mass of an element is the average mass of one atom of that element compared with one-twelfth of the mass of one carbon-12 atom. Written as a formula:

Ar = (average mass of one atom of the element) ÷ (1/12 × mass of one carbon-12 atom)

Because it is a ratio of two masses, relative atomic mass has no units. The word average matters: most elements exist as a mixture of isotopes, atoms with the same number of protons but different numbers of neutrons, so the Ar you read from the Periodic Table is a weighted average of the isotope masses, weighted by how abundant each isotope is. That is why chlorine has an Ar of 35.5 rather than a whole number: it is a mixture of chlorine-35 and chlorine-37.

In the SPM examination the Ar values you need are provided (for example H = 1, C = 12, N = 14, O = 16, Na = 23, Mg = 24, S = 32, Cl = 35.5, Ca = 40, Cu = 64). You are not expected to memorise them, but you must read them correctly and use them without rounding away the decimals.

Relative molecular mass (Mr)

The relative molecular mass of a substance is the sum of the relative atomic masses of all the atoms shown in its molecular formula, again compared with one-twelfth of a carbon-12 atom. Like Ar, it has no units. To find Mr you simply count how many of each atom the formula contains, multiply each count by that element’s Ar, and add the results.

For substances made of ions rather than molecules, such as sodium chloride, NaCl, or calcium carbonate, CaCO₃, chemists use the term relative formula mass, but it is calculated in exactly the same way from the formula unit. The exam accepts the same method.

Worked example

Question. Calculate the relative molecular mass of calcium hydroxide, Ca(OH)₂. [Ar: Ca = 40, O = 16, H = 1]

Step 1, Read the formula carefully. The subscript 2 outside the bracket multiplies everything inside the bracket. So Ca(OH)₂ contains 1 calcium atom, 2 oxygen atoms and 2 hydrogen atoms.

Step 2, Multiply each count by its Ar.

• Calcium: 1 × 40 = 40
• Oxygen: 2 × 16 = 32
• Hydrogen: 2 × 1 = 2

Step 3, Add the contributions. Mr = 40 + 32 + 2 = 74

Answer. The relative molecular mass (relative formula mass) of Ca(OH)₂ is 74. No unit is written, because Mr is a ratio.

Practice question

Question. Chlorine exists as two isotopes: chlorine-35, which makes up 75% of a natural sample, and chlorine-37, which makes up the remaining 25%. Calculate the relative atomic mass of chlorine, correct to one decimal place.

Answer. Ar = [(35 × 75) + (37 × 25)] ÷ 100 = [2625 + 925] ÷ 100 = 3550 ÷ 100 = 35.5. Because the Ar is a weighted average of the two isotope masses, it is not a whole number.

Exam tip

Three points are marked precisely on this standard. First, never write a unit after Ar or Mr, they are ratios, and adding “g” or “g/mol” loses the mark (molar mass, which does have the unit g mol⁻¹, comes in the next standard). Second, when a formula has brackets, multiply every atom inside the bracket by the subscript outside it, Ca(OH)₂ is the classic trap. Third, keep the decimal in Ar values such as Cl = 35.5 and Cu = 63.5; rounding them early is a common way to lose an accuracy mark in a longer calculation.

Reading formulae with confidence

Many mistakes on this standard are really reading mistakes, so slow down on the formula before you calculate. In (NH₄)₂SO₄, ammonium sulfate, the subscript 2 applies to the whole ammonium group, giving 2 nitrogen atoms and 8 hydrogen atoms, then 1 sulfur and 4 oxygen atoms from the sulfate. In a hydrated salt such as CuSO₄·5H₂O the dot notation means five separate water molecules are attached, adding 10 hydrogen and 5 oxygen atoms to the count. If you can dissect a formula into “how many of each atom” without hesitating, the arithmetic that follows is straightforward, and you will carry that same skill into molar mass, empirical formula and stoichiometry.

The carbon-12 standard in one sentence

If you are asked to define relative atomic mass or relative molecular mass, the marking scheme wants the comparison spelled out: it is the (average) mass of an atom, or of a molecule, compared with one-twelfth of the mass of a carbon-12 atom. Leaving out the “one-twelfth of carbon-12” reference is the most common reason a definition scores zero, so learn that phrase word for word. Carbon-12 was chosen because it is a stable, easily available isotope, and fixing its mass at exactly 12 makes the Ar of most common elements come out close to whole numbers.

Where this fits

This is content standard 3.1, the foundation of the The Mole Concept, Chemical Formula and Equation chapter, and it feeds straight into the mole, molar mass and every stoichiometry calculation that follows. Revise the definitions with the revision notes, and drill the arithmetic with the worked examples. In our online 1-to-1 SPM Chemistry lessons, taught in English, from RM50/hr, our teachers make sure you can read any formula, including bracketed and hydrated ones, and produce a clean Mr every time before you move on to the mole.

Quick recap

• Ar = average mass of one atom compared with 1/12 the mass of a carbon-12 atom; no units.
• Mr = sum of the Ar values of every atom in the formula; no units.
• Ar values are weighted averages over isotopes, so some (Cl = 35.5) are not whole numbers.
• Multiply everything inside a bracket by the subscript outside it; keep the decimals.