Relative Masses and the Mole

Relative formula mass $M_r$ is the sum of the relative atomic masses in a formula. A mole is the amount of substance containing $6.02\times10^{23}$ particles (the Avogadro constant); one mole has a mass in grams equal to $M_r$ . So $n=\frac{m}{M_r}$ . The empirical formula is the simplest whole-number ratio of atoms, found by dividing each mass by $A_r$ and simplifying.

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Section 1 of 14

Learning objectives

Calculate $M_r$ and percentage composition.
Use $n=m/M_r$ and the Avogadro constant.
Calculate empirical and molecular formulae.

Pause and think

Why can't chemists just count atoms when they want "equal amounts" of two substances?

Section 2 of 14

Core idea

Start hereCounting by weighing

A bank doesn't count thousands of coins one by one; it weighs them. Chemists do the same with atoms, which are far too small and numerous to count. The mole is the chemist's "bag of coins".

The big idea

One mole is $6.02\times10^{23}$ particles, and its mass in grams equals $M_r$ . So $n=m/M_r$ turns any mass into a number of particles.

1. Relative formula mass

Worked examplePercentage of water in a hydrate

Find the percentage by mass of water in $\mathrm{CuSO_4\cdot5H_2O}$ . ( $A_r$ : Cu 64, S 32, O 16, H 1)

Goal: % water.
Strategy: Find $M_r$ of the whole formula and of $5\mathrm{H_2O}$ .

$M_r=64+32+64+5(18)=250$
Add every atom.
$\frac{90}{250}\times100=36\%$
Mass of water ÷ total.

Answer

36\%

✓ CheckHeating blue crystals loses about a third of the mass ✓.

2. The mole

n=\frac{m}{M_r}

n: amount in moles
m: mass in grams
M_r: relative formula mass (molar mass in g/mol)

Converting between quantities

Drawing diagram…

Moles are the hub of every calculation.

3. Empirical formulae

Worked exampleAn oxide of iron

$11.2$ g of iron combines with $4.8$ g of oxygen. ( $A_r$ : Fe 56, O 16)

Goal: Empirical formula.
Strategy: Moles of each, divide by the smallest, make whole numbers.

$\mathrm{Fe}:\ \frac{11.2}{56}=0.20\qquad\mathrm{O}:\ \frac{4.8}{16}=0.30$
Convert to moles.
$1:1.5$
Divide by $0.20$ .
$2:3$
Double to get whole numbers.

Answer

\mathrm{Fe_2O_3}

✓ CheckIron(III) oxide is a known compound ✓.

Common misconceptionDon't round 1.5 A ratio of

1:1.5

means multiply by 2, and

1:1.33

means multiply by 3. Rounding loses the answer.

Pause and think

Do 2 g of hydrogen gas and 32 g of oxygen gas contain the same number of molecules?

Summary

$M_r$ = sum of $A_r$ .
$n=m/M_r$ .
Empirical formula from a moles table.

Mole: Amount containing $6.02\times10^{23}$ particles.
Avogadro constant: $6.02\times10^{23}$ per mole.
Empirical formula: Simplest whole-number ratio of atoms.

HistoryAvogadro. In 1811 Amedeo Avogadro proposed that equal volumes of gases contain equal numbers of particles. The constant named after him was measured only decades after his death.

Fun factA mole of sand. A mole of grains of sand would cover the whole of the UK to a depth of several kilometres. Yet a mole of water is just 18 g, about one mouthful.

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