Define relative atomic mass and the mole, calculate relative formula mass, and find the number of moles from a given mass

What this dot point is asking

SEAB wants you to define relative atomic mass and the mole, to calculate the relative formula mass of a compound, and to find the number of moles from a given mass. The central idea is that the mole lets chemists count huge numbers of tiny atoms simply by weighing them.

The answer

Relative atomic mass

Atoms are far too small and light to weigh one at a time, so chemists compare their masses. The relative atomic mass ($A_r$) of an element tells you how heavy its atoms are compared with other atoms. You read these values from the periodic table, for example $\text{H} = 1$, $\text{C} = 12$, $\text{O} = 16$.

The mole

A mole is simply a fixed, very large number of particles, in the same way that a dozen is $12$ of something. The clever part is that one mole of any element has a mass in grams equal to its relative atomic mass. So one mole of carbon weighs $12\ \text{g}$, and one mole of oxygen atoms weighs $16\ \text{g}$. This lets us count atoms by weighing.

Relative formula mass

The relative formula mass ($M_r$) of a compound is found by adding up the relative atomic masses of all the atoms in its formula. Remember to multiply by the small numbers in the formula:

Finding moles from mass

The link between mass, moles and relative formula mass is:

This can be rearranged to find the mass from a number of moles, or the relative formula mass from mass and moles. A simple way to remember it is to picture the three quantities in a triangle, with mass on top and moles and $M_r$ below: cover the one you want and the triangle shows whether to divide or multiply.

Reading a chemical formula

The formula of a compound tells you exactly which atoms it contains and how many of each. The small numbers (subscripts) apply only to the symbol just before them:

• $\text{CO}_2$ means one carbon and two oxygen atoms,
• $\text{H}_2\text{SO}_4$ means two hydrogen, one sulfur and four oxygen atoms,
• $\text{CaCl}_2$ means one calcium and two chlorine atoms.

Getting these counts right is the first step in working out a relative formula mass, so always read the formula carefully before you add the masses.

Examples in context

Example 1. Scaling up a recipe. A reaction equation works in moles, just like a recipe works in numbers of eggs. Knowing the moles of each substance lets a factory scale a small lab reaction up to industrial amounts while keeping the proportions correct.

Example 2. Checking a label. A fertiliser bag states it contains a certain mass of a compound. Converting that mass to moles tells a farmer how much of the active element is actually present, because the mole links mass to the number of particles that take part in reactions.

Try this

• Cue. Find the relative formula mass of $\text{NaCl}$ ($\text{Na} = 23$, $\text{Cl} = 35.5$): $23 + 35.5 = 58.5$.
• Cue. Find the moles in $8\ \text{g}$ of oxygen gas $\text{O}_2$ ($M_r = 32$): $n = \dfrac{8}{32} = 0.25\ \text{mol}$.
• Cue. Find the mass of $3\ \text{mol}$ of water ($M_r = 18$): mass $= 3 \times 18 = 54\ \text{g}$.