Moles (HT only)

What you'll learn

What a mole is: a unit for measuring chemical amount.
How the Avogadro constant links moles to numbers of atoms, molecules or ions.
Why one mole has a mass in grams equal to the substance’s relative formula mass.
How to calculate moles from mass, and mass from moles.

Why chemists use moles

Atoms, molecules and ions are far too tiny to count one at a time in the lab. Even a small spatula of powder contains an enormous number of particles.

This Higher Tier idea lets you count particles by weighing substances. It is similar to using “a dozen” to mean 12 items, except a mole is much, much bigger.

Definition

Amount of substance

Amount of substance means how many particles of a substance you have. In chemistry, it is measured in moles, and the unit symbol is mol.

Know what particle you are counting

The word particle depends on the substance:

An atom is a single particle of an element, such as C or Mg.
A molecule is a group of atoms bonded together, such as O₂ or CO₂.
An ion is a charged particle, such as Na⁺ or Cl⁻.
A formula unit is the simplest whole-number ratio of ions in an ionic compound, such as NaCl.
An electron is a negatively charged subatomic particle; moles can be used for electrons too.

Key Idea

Stated particles matter

One mole always means the same number of stated particles. So 1 mol of carbon contains carbon atoms, while 1 mol of carbon dioxide contains CO₂ molecules.

Relative formula mass, $M_r$

Before you can link mass to moles, you need formula masses.

A relative atomic mass, $A_r$ , is the mass number for an element from the periodic table, compared with carbon-12. At GCSE, you normally use the rounded values given in the exam.

Definition

Relative formula mass

The relative formula mass, $M_r$ , is the total of the relative atomic masses, $A_r$ , of all the atoms shown in a formula. It has no units.

A subscript is the small lower number in a formula. For example, in CO₂, the ₂ means there are 2 oxygen atoms in each molecule.

Example

Finding relative formula mass

Calculate $M_r$ for calcium carbonate, CaCO₃. Use $A_r$ : Ca = 40, C = 12, O = 16.

Count the atoms in the formula: CaCO₃ contains 1 calcium atom, 1 carbon atom and 3 oxygen atoms.
Multiply each $A_r$ by the number of that atom and add them: $Mr=40+12+(3×16)M_r = 40 + 12 + (3 \times 16)$ .
Calculate the total: $M_r = 100$ , so calcium carbonate has relative formula mass 100.

Common Mistake

Forgetting the subscript

In CaCO₃, the ₃ applies only to oxygen, not to calcium or carbon. Always multiply only the element directly before the subscript.

One mole and the Avogadro constant

Definition

Avogadro constant

The Avogadro constant, $N_A$ , is the number of atoms, molecules or ions in one mole of a substance: $mol−1N_A = 6.02 \times 10^{23}\ \text{mol}^{-1}$ .

That means:

1 mol of carbon atoms contains $6.02 \times 10^{23}$ carbon atoms.
1 mol of CO₂ molecules contains $6.02 \times 10^{23}$ CO₂ molecules.
1 mol of NaCl formula units contains $6.02 \times 10^{23}$ NaCl formula units.

They contain the same number of stated particles, but their masses are different because their formula masses are different.

Schematic showing one mole of carbon atoms, carbon dioxide molecules and sodium chloride formula units all containing 6.02 × 10^23 particles but having different masses

Counting particles from moles

Use:

N = nN_A

where $N$ is the number of particles and $n$ is the amount in moles.

Example

Calculating molecules from moles

How many CO₂ molecules are in 0.250 mol of carbon dioxide?

Choose the particle type: the formula CO₂ represents molecules, so the answer should be in CO₂ molecules.
Substitute into $N = nN_A$ : $\times 6.02 \times 10^{23}$ .
Calculate and round suitably: $\times 10^{23} \approx 1.51 \times 10^{23}$ CO₂ molecules.

Common Mistake

Molecules are not the same as atoms

1 mol of CO₂ means $6.02 \times 10^{23}$ CO₂ molecules. Because each CO₂ molecule has 3 atoms, it contains 3 times as many atoms in total.

Mass of one mole

The key GCSE fact is:

Key Idea

Mass of one mole

The mass of one mole of a substance in grams is numerically equal to its $M_r$ .

So if CO₂ has $M_r = 44$ , then 1 mol of CO₂ has a mass of 44 g.

Definition

Molar mass

Molar mass, $M$ , is the mass of 1 mol of a substance, measured in grams per mole (g/mol). Its number is the same as the substance’s $M_r$ .

For a known pure substance, use:

n=mMm=nMM=mn\begin{aligned} n &= \frac{m}{M} \\ m &= nM \\ M &= \frac{m}{n} \end{aligned}

where $n$ is amount in mol, $m$ is mass in g, and $M$ is molar mass in g/mol.

At GCSE, you will often see this written as:

gMr\text{moles} = \frac{\text{mass in g}}{M_r}

Tip

Unit check

Use mass in grams, not kilograms, when using $M_r$ directly. If the question gives kg, convert first: 1 kg = 1000 g.

Calculating moles from mass

Example

Calculating moles from mass

Calculate the amount, in moles, in 8.80 g of carbon dioxide, CO₂. Use $A_r$ : C = 12, O = 16.

Find the formula mass: $Mr=12+(2×16)=44M_r = 12 + (2 \times 16) = 44$ , so $44\ \text{g mol}^{-1}$ .
Use the moles equation: $\frac{m}{M}$ .
Substitute and calculate: $\frac{8.80\ \text{g}}{44\ \text{g mol}^{-1}} = 0.200\ \text{mol}$ .

Calculating mass from moles

Example

Calculating mass from moles

Calculate the mass of 0.150 mol of magnesium chloride, MgCl₂. Use $A_r$ : Mg = 24, Cl = 35.5.

Find the formula mass: $Mr=24+(2×35.5)=95M_r = 24 + (2 \times 35.5) = 95$ , so $95\ \text{g mol}^{-1}$ .
Rearrange the equation to make mass the subject: $m = n M$ .
Substitute and calculate: $0.150\ \text{mol} \times 95\ \text{g mol}^{-1} = 14.25\ \text{g}$ , which is 14.3 g to 3 significant figures.

Moles in chemical equations

Balanced chemical equations can be read in particles or in moles.

For example:

2Mg(s) + O₂(g) → 2MgO(s)

This means:

2 magnesium atoms react with 1 oxygen molecule to form 2 magnesium oxide formula units.
2 mol of magnesium react with 1 mol of oxygen to form 2 mol of magnesium oxide.

Example

Reading a mole ratio

For 2Mg(s) + O₂(g) → 2MgO(s), how many moles of O₂ are needed to react with 0.600 mol of Mg?

Use the coefficients in the equation: 2 mol Mg react with 1 mol O₂.
Scale the ratio down from 2 mol Mg to 0.600 mol Mg: $n(O2)=0.600÷2n(\text{O}_2) = 0.600 \div 2$ .
Calculate the amount of oxygen: $moln(\text{O}_2) = 0.300\ \text{mol}$ .

Exam technique

In the exam

Identify what the question asks for: mass, moles, or number of particles.
Calculate $M_r$ carefully from the formula before using the mass–moles equation.
Keep units with your working: g for mass, mol for amount, and standard form for huge particle numbers.

Self review

Check yourself

How many molecules are in 2.00 mol of oxygen, O₂?
Calculate the amount in moles in 5.00 g of calcium carbonate, CaCO₃.
What mass of sodium chloride, NaCl, is present in 0.250 mol?

Moles (HT only)

What you'll learn

What a mole is: a unit for measuring chemical amount.
How the Avogadro constant links moles to numbers of atoms, molecules or ions.
Why one mole has a mass in grams equal to the substance’s relative formula mass.
How to calculate moles from mass, and mass from moles.

Why chemists use moles

Atoms, molecules and ions are far too tiny to count one at a time in the lab. Even a small spatula of powder contains an enormous number of particles.

This Higher Tier idea lets you count particles by weighing substances. It is similar to using “a dozen” to mean 12 items, except a mole is much, much bigger.

Definition

Amount of substance

Amount of substance means how many particles of a substance you have. In chemistry, it is measured in moles, and the unit symbol is mol.

Know what particle you are counting

The word particle depends on the substance:

An atom is a single particle of an element, such as C or Mg.
A molecule is a group of atoms bonded together, such as O₂ or CO₂.
An ion is a charged particle, such as Na⁺ or Cl⁻.
A formula unit is the simplest whole-number ratio of ions in an ionic compound, such as NaCl.
An electron is a negatively charged subatomic particle; moles can be used for electrons too.

Key Idea

Stated particles matter

One mole always means the same number of stated particles. So 1 mol of carbon contains carbon atoms, while 1 mol of carbon dioxide contains CO₂ molecules.

Relative formula mass, $M_r$

Before you can link mass to moles, you need formula masses.

A relative atomic mass, $A_r$ , is the mass number for an element from the periodic table, compared with carbon-12. At GCSE, you normally use the rounded values given in the exam.

Definition

Relative formula mass

The relative formula mass, $M_r$ , is the total of the relative atomic masses, $A_r$ , of all the atoms shown in a formula. It has no units.

A subscript is the small lower number in a formula. For example, in CO₂, the ₂ means there are 2 oxygen atoms in each molecule.

Example

Finding relative formula mass

Calculate $M_r$ for calcium carbonate, CaCO₃. Use $A_r$ : Ca = 40, C = 12, O = 16.

Count the atoms in the formula: CaCO₃ contains 1 calcium atom, 1 carbon atom and 3 oxygen atoms.
Multiply each $A_r$ by the number of that atom and add them: $Mr=40+12+(3×16)M_r = 40 + 12 + (3 \times 16)$ .
Calculate the total: $M_r = 100$ , so calcium carbonate has relative formula mass 100.

Common Mistake

Forgetting the subscript

In CaCO₃, the ₃ applies only to oxygen, not to calcium or carbon. Always multiply only the element directly before the subscript.

One mole and the Avogadro constant

Definition

Avogadro constant

The Avogadro constant, $N_A$ , is the number of atoms, molecules or ions in one mole of a substance: $mol−1N_A = 6.02 \times 10^{23}\ \text{mol}^{-1}$ .

That means:

1 mol of carbon atoms contains $6.02 \times 10^{23}$ carbon atoms.
1 mol of CO₂ molecules contains $6.02 \times 10^{23}$ CO₂ molecules.
1 mol of NaCl formula units contains $6.02 \times 10^{23}$ NaCl formula units.

They contain the same number of stated particles, but their masses are different because their formula masses are different.

Schematic showing one mole of carbon atoms, carbon dioxide molecules and sodium chloride formula units all containing 6.02 × 10^23 particles but having different masses

Counting particles from moles

Use:

N = nN_A

where $N$ is the number of particles and $n$ is the amount in moles.

Example

Calculating molecules from moles

How many CO₂ molecules are in 0.250 mol of carbon dioxide?

Choose the particle type: the formula CO₂ represents molecules, so the answer should be in CO₂ molecules.
Substitute into $N = nN_A$ : $\times 6.02 \times 10^{23}$ .
Calculate and round suitably: $\times 10^{23} \approx 1.51 \times 10^{23}$ CO₂ molecules.

Common Mistake

Molecules are not the same as atoms

1 mol of CO₂ means $6.02 \times 10^{23}$ CO₂ molecules. Because each CO₂ molecule has 3 atoms, it contains 3 times as many atoms in total.

Mass of one mole

The key GCSE fact is:

Key Idea

Mass of one mole

The mass of one mole of a substance in grams is numerically equal to its $M_r$ .

So if CO₂ has $M_r = 44$ , then 1 mol of CO₂ has a mass of 44 g.

Definition

Molar mass

Molar mass, $M$ , is the mass of 1 mol of a substance, measured in grams per mole (g/mol). Its number is the same as the substance’s $M_r$ .

For a known pure substance, use:

n=mMm=nMM=mn\begin{aligned} n &= \frac{m}{M} \\ m &= nM \\ M &= \frac{m}{n} \end{aligned}

where $n$ is amount in mol, $m$ is mass in g, and $M$ is molar mass in g/mol.

At GCSE, you will often see this written as:

gMr\text{moles} = \frac{\text{mass in g}}{M_r}

Tip

Unit check

Use mass in grams, not kilograms, when using $M_r$ directly. If the question gives kg, convert first: 1 kg = 1000 g.

Calculating moles from mass

Example

Calculating moles from mass

Calculate the amount, in moles, in 8.80 g of carbon dioxide, CO₂. Use $A_r$ : C = 12, O = 16.

Find the formula mass: $Mr=12+(2×16)=44M_r = 12 + (2 \times 16) = 44$ , so $44\ \text{g mol}^{-1}$ .
Use the moles equation: $\frac{m}{M}$ .
Substitute and calculate: $\frac{8.80\ \text{g}}{44\ \text{g mol}^{-1}} = 0.200\ \text{mol}$ .

Calculating mass from moles

Example

Calculating mass from moles

Calculate the mass of 0.150 mol of magnesium chloride, MgCl₂. Use $A_r$ : Mg = 24, Cl = 35.5.

Find the formula mass: $Mr=24+(2×35.5)=95M_r = 24 + (2 \times 35.5) = 95$ , so $95\ \text{g mol}^{-1}$ .
Rearrange the equation to make mass the subject: $m = n M$ .
Substitute and calculate: $0.150\ \text{mol} \times 95\ \text{g mol}^{-1} = 14.25\ \text{g}$ , which is 14.3 g to 3 significant figures.

Moles in chemical equations

Balanced chemical equations can be read in particles or in moles.

For example:

2Mg(s) + O₂(g) → 2MgO(s)

This means:

2 magnesium atoms react with 1 oxygen molecule to form 2 magnesium oxide formula units.
2 mol of magnesium react with 1 mol of oxygen to form 2 mol of magnesium oxide.

Example

Reading a mole ratio

For 2Mg(s) + O₂(g) → 2MgO(s), how many moles of O₂ are needed to react with 0.600 mol of Mg?

Use the coefficients in the equation: 2 mol Mg react with 1 mol O₂.
Scale the ratio down from 2 mol Mg to 0.600 mol Mg: $n(O2)=0.600÷2n(\text{O}_2) = 0.600 \div 2$ .
Calculate the amount of oxygen: $moln(\text{O}_2) = 0.300\ \text{mol}$ .

Exam technique

In the exam

Identify what the question asks for: mass, moles, or number of particles.
Calculate $M_r$ carefully from the formula before using the mass–moles equation.
Keep units with your working: g for mass, mol for amount, and standard form for huge particle numbers.

Self review

Check yourself

How many molecules are in 2.00 mol of oxygen, O₂?
Calculate the amount in moles in 5.00 g of calcium carbonate, CaCO₃.
What mass of sodium chloride, NaCl, is present in 0.250 mol?

Moles (HT only)

What you'll learn

Why chemists use moles

Know what particle you are counting

Relative formula mass, $M_r$

One mole and the Avogadro constant

Counting particles from moles

Mass of one mole

Calculating moles from mass

Calculating mass from moles

Moles in chemical equations

You've reached the end

Moles (HT only)

What you'll learn

Why chemists use moles

Know what particle you are counting

Relative formula mass, $M_r$

One mole and the Avogadro constant

Counting particles from moles

Mass of one mole

Calculating moles from mass

Calculating mass from moles

Moles in chemical equations

You've reached the end

Moles (HT only)

What you'll learn

Why chemists use moles

Know what particle you are counting

Relative formula mass, MrM_rMr​

One mole and the Avogadro constant

Counting particles from moles

Mass of one mole

Calculating moles from mass

Calculating mass from moles

Moles in chemical equations

You've reached the end

Moles (HT only) Revision Guide

Moles (HT only)

What you'll learn

Why chemists use moles

Know what particle you are counting

Relative formula mass, MrM_rMr​

One mole and the Avogadro constant

Counting particles from moles

Mass of one mole

Calculating moles from mass

Calculating mass from moles

Moles in chemical equations

You've reached the end

Moles (HT only) Revision Guide

Relative formula mass, $M_r$

Relative formula mass, $M_r$