Relative formula mass, the mole as a counting unit, the relationship between moles, mass and relative formula mass, and calculating percentage composition by mass.

What this dot point is asking

CCEA wants you to calculate relative formula mass, understand the mole as a counting unit, use the equation linking moles, mass and relative formula mass, and find the percentage composition of a compound by mass.

Relative formula mass

To work it out, multiply each element's $A_r$ by the number of its atoms in the formula, then add. Remember to apply subscripts and brackets, so calcium hydroxide $\text{Ca(OH)}_2$ is $40 + 2 \times (16 + 1) = 74$.

The mole

The mole lets chemists count atoms by weighing, because atoms are far too small and numerous to count directly. This is the bridge between the mass we measure on a balance and the number of particles that react.

The moles, mass and Mr equation

A formula triangle with mass on top and moles and $M_r$ below helps you rearrange: cover the quantity you want to find. Always state units (mol for moles, g for mass).

Percentage composition

This tells you how much of a compound's mass comes from a given element, which is useful for comparing fertilisers by their nitrogen content, for example.

Worked example

Examples in context

Example 1. Choosing a fertiliser

Farmers compare fertilisers by their percentage of nitrogen by mass, calculated exactly as above. Ammonium nitrate's 35 percent nitrogen makes it a concentrated source, so the percentage composition directly informs a real purchasing decision.

Example 2. Weighing out a reaction

A chemist who needs 0.1 mol of a reactant simply multiplies 0.1 by the relative formula mass to find the mass to weigh out. The mole turns a particle count into a balance reading, which is how every quantitative experiment is set up.

Example 3. Counting particles

Because one mole contains Avogadro's number of particles, two moles of water contain twice as many molecules as one mole, even though they are different substances by mass. This is why the mole, not the gram, is the fair way to compare amounts in a reaction: equal moles mean equal numbers of particles.

Why relative masses have no units

Relative atomic mass and relative formula mass are ratios: they compare the mass of an atom or formula unit with one twelfth of a carbon-12 atom. Because they compare one mass with another, the units cancel and the values are just numbers. This is why you never write a unit after an $A_r$ or $M_r$ value. The mass in grams of one mole, however, does have units (grams), and equals the relative formula mass numerically. Keeping this distinction clear stops the common error of attaching grams to a relative mass, and it explains why the same number 18 describes both the relative formula mass of water and the mass in grams of one mole of it.

Try this

Q1. Calculate the relative formula mass of carbon dioxide, $\text{CO}_2$. (Ar: C = 12, O = 16) [1 mark]

• Cue. 12 plus (2 times 16) equals 44.

Q2. Calculate the number of moles in 36 g of water. (Mr = 18) [1 mark]

• Cue. 36 divided by 18 equals 2 mol.