Relative atomic and molecular masses

No chemist has ever placed a single atom on a weighing scale — atoms are far too light and far too small. Yet every textbook confidently states that an oxygen atom is "16 times as heavy as" one-twelfth of a carbon-12 atom, or that sulphuric acid has a molecular mass of 98. That confidence comes from a comparison trick: instead of measuring atomic mass in grams, chemists measure it relative to a fixed reference atom. This article builds the ICSE Class 9 picture of Relative Atomic Mass (RAM) and Relative Molecular Mass (RMM) from that one idea — a ratio with no unit — through to calculating the percentage composition of a compound, the exam-ready skill that follows directly from it. Every worked number here traces back to just a handful of RAM values you are given or must recall: H = 1, C = 12, O = 16, S = 32, Ca = 40.

The core insight

Relative atomic mass compares one atom's mass to one-twelfth the mass of a carbon-12 atom (a unitless ratio), relative molecular mass sums those ratios over a whole formula, and dividing each element's contribution by the total gives the percentage composition.

The core idea

The standard is carbon-12. Chemists needed one fixed atom to compare every other atom against, and modern chemistry settled on carbon-12: one-twelfth of its mass is the unit against which every other atom is measured. Historically, hydrogen (the lightest element) served as an even simpler standard, and both give almost the same numbers because $\tfrac{1}{12}$ of a carbon-12 atom happens to be very close to the mass of one hydrogen atom.

\text{RAM} = \frac{\text{mass of one atom of the element}}{\tfrac{1}{12}\times\text{mass of one atom of }^{12}\text{C}}

where: the numerator is the actual mass of one atom of the element in question, and the denominator is the fixed reference unit, one-twelfth the mass of a carbon-12 atom. Because both sides of this fraction are masses, the units cancel — RAM is a pure number, never written with "g" or "amu" in a Class 9 answer. Familiar values follow directly: RAM of H = 1, C = 12, O = 16, Na = 23, S = 32, Cl = 35.5, Ca = 40.

Molecules are built from atoms, so their mass adds up the same way. The Relative Molecular Mass (RMM) — called relative formula mass for ionic compounds like salts — is simply the sum of every atom's RAM, counted as many times as that atom appears in the formula.

\text{RMM} = \sum \left(\text{RAM of each atom} \times \text{number of such atoms in the formula}\right)

where: the sum runs over every distinct element in the chemical formula, and "number of such atoms" is the subscript attached to that element (multiplying through a bracket where needed, as in $Ca(OH)_2$ ). Like RAM, RMM is unitless — it is a count of "how many times heavier than the reference unit," never a mass in grams.

Percentage composition turns RMM into a share of the whole. Once you know how much each element contributes to the total RMM, dividing that contribution by the RMM and multiplying by 100 tells you what fraction of the compound's mass belongs to that element:

\%\,\text{element} = \frac{\text{RAM of the element}\times\text{number of its atoms in the formula}}{\text{RMM of the compound}} \times 100

where: the numerator is exactly one term from the RMM sum above — the mass contribution of a single element — and the denominator is the compound's total RMM. Summed over every element present, the percentages must always total 100%; this is the standard check used to catch arithmetic slips.

Figure

Bar chart of percentage composition by mass of calcium carbon and oxygen in calcium carbonate summing to one hundred per cent

Derivation ABuilding percentage composition from the RMM formula

The goal is to show, using only the definitions of RAM and RMM already stated above, exactly why the percentage composition formula divides an element's contribution by the total RMM and multiplies by 100 — so that the formula is something you can rebuild from first principles rather than recall by rote if you forget it under exam pressure.

Step 1. Write the RMM as a sum of individual element contributions. For any compound with elements $A, B, C, \dots$ present in quantities $a, b, c, \dots$ atoms per formula unit, $\text{RMM} = (\text{RAM}_A \times a) + (\text{RAM}_B \times b) + (\text{RAM}_C \times c) + \dots$ . Each bracketed term is that one element's own share of the total, sitting side by side in a sum.

Step 2. Isolate the share belonging to a single element, say $A$ . Its contribution to the total is exactly the term $\text{RAM}_A \times a$ — nothing more, nothing less — because RMM was built precisely by adding up such terms, one per element.

Step 3. Convert that share into a fraction of the whole. Dividing element $A$ 's contribution by the compound's total RMM gives the fraction of the total mass that belongs to $A$ : $\dfrac{\text{RAM}_A \times a}{\text{RMM}}$ . This is a plain fraction between 0 and 1, since the part cannot exceed the whole.

Step 4. Convert the fraction to a percentage by multiplying by 100, giving $\%A = \dfrac{\text{RAM}_A \times a}{\text{RMM}} \times 100$ . Repeating Steps 2 to 4 for every element and adding the results reproduces the whole RMM divided by itself, times 100 — which is exactly 100%. That is why the percentages of every element in a compound must always sum to 100, and why a total noticeably off from 100 signals an arithmetic error, not a real property of the compound.

Worked example

Question. Slaked lime, $Ca(OH)_2$ , is used to whitewash walls and to reduce soil acidity. Find its RMM and the percentage composition of calcium, oxygen, and hydrogen in it. (Given: RAM of Ca = 40, O = 16, H = 1.)

Step 1. Read the number of atoms of each element from the formula, taking care with the bracket: the subscript 2 outside $(OH)_2$ multiplies both atoms inside it, giving 1 Ca, 2 O, and 2 H per formula unit — not 1 O and 1 H as a careless glance might suggest.

Step 2. Multiply each RAM by its number of atoms to get each element's contribution: Ca gives $40 \times 1 = 40$ ; O gives $16 \times 2 = 32$ ; H gives $1 \times 2 = 2$ .

Step 3. Add the contributions to get the RMM: $\text{RMM}\left(Ca(OH)_2\right) = 40 + 32 + 2 = 74$ .

Step 4. Apply the percentage composition formula to each element: $\%Ca = \dfrac{40}{74}\times 100 = 54.05\%$ ; $\%O = \dfrac{32}{74}\times 100 = 43.24\%$ ; $\%H = \dfrac{2}{74}\times 100 = 2.70\%$ .

Step 5. Check the sum: $54.05 + 43.24 + 2.70 = 99.99\%$ , which is 100% within rounding — confirming the working is consistent. Answer: the RMM of slaked lime is 74, made up of 54.05% calcium, 43.24% oxygen and 2.70% hydrogen.

Common traps

Writing a unit after RAM or RMM. Both are ratios of two masses, so they are pure numbers — never write "16 g" or "40 amu" for a RAM value in a Class 9 answer unless the question specifically asks for atomic mass in amu.
Ignoring a subscript outside a bracket. In $Ca(OH)_2$ , both the O and the H inside the bracket must be doubled — a common slip is to double only one of them or neither, giving a wrong RMM before any percentage calculation even starts.
Confusing RAM (per atom) with RMM (per molecule). RAM belongs to a single element's atom; RMM belongs to the whole compound's formula unit. Mixing the two definitions in a written answer costs marks even if the arithmetic is right.
Not checking that percentages sum to 100%. If your calculated percentages clearly do not add up close to 100% (allowing for rounding), an arithmetic error has crept in somewhere and every step should be rechecked before moving on.

Ask the tutor: Want to practise the RMM and percentage composition of a compound with a trickier bracket, like $Al_2(SO_4)_3$ , or check your working step by step? Ask the AI tutor.

Why is carbon-12 used as the standard instead of just weighing atoms in grams?

A single atom is far too light to place on any real balance — even the lightest atom has a mass of roughly $10^{-24}$ grams, an impossibly small number to work with in ordinary calculations. By comparing every atom's mass to a fixed reference, one-twelfth the mass of a carbon-12 atom, chemists get clean, small, unitless numbers like 1 for hydrogen and 16 for oxygen instead of clumsy numbers in grams. The comparison is exact and reproducible because carbon-12 atoms are all identical, making it a reliable universal yardstick.

Do RAM and RMM ever change for the same element or compound?

No. RAM is fixed for a given element because it is defined against the unchanging carbon-12 standard, and RMM is fixed for a given compound because it is built entirely from RAM values and the fixed atom count in that compound's formula. What can change is which compound you are asked about, or which set of RAM values a question supplies you with — but for one specific formula, the RMM calculated correctly will always come out the same.

Why do the percentages sometimes not add up to exactly 100, like 99.99% instead of 100%?

This is purely a rounding effect, not an error in the chemistry. Each percentage is rounded to two decimal places before adding, and those small roundings can leave the total a tiny fraction away from exactly 100, such as 99.99% or 100.01%. As long as the total lands very close to 100%, the calculation is correct; a total that is off by several whole percentage points, on the other hand, does point to a genuine arithmetic mistake worth rechecking.

Relative atomic and molecular masses

The core idea

Worked example

Common traps

Before this

Where this leads