2.1.3(a) - The mole and chemical amount | OCR A-Level Chemistry

Chemists need a way to count particles that are far too small to count one by one. The amount of substance, measured in moles, is the counting quantity that connects particles, mass and gas volume. In this lesson you will learn the exact language and one-step conversions that later mole calculations depend on.

Amount of substance and specified entities

Amount of substance is a chemical quantity. It tells you how many specified elementary entities are present, where the entities might be atoms, molecules, ions, electrons or formula units.

The symbol for amount of substance is usually n. The unit is the mole, with symbol mol.

Amount of substance

Amount of substance is the quantity that counts specified chemical entities. It is measured in mol.

The word specified is important. A statement such as "amount of oxygen" can be ambiguous, because oxygen might mean O atoms or O₂ molecules. Use the formula or named entity:

n(O₂) means amount of oxygen molecules.
n(O) means amount of oxygen atoms.
n(NaCl) means amount of sodium chloride formula units.
n(H⁺) means amount of hydrogen ions.

For ionic compounds, chemists often use the formula unit as the counted entity. One mole of NaCl means one mole of NaCl formula units, not one mole of separate NaCl molecules.

Always attach amount of substance to a formula or named entity: n(CO₂), n(Mg²⁺), n(NaCl). The formula tells you what is being counted.

Worked example: choosing the counted entity

A question refers to 0.200 mol of O₂.

This means:

the amount is 0.200 mol;
the specified entity is O₂ molecules;
it is not the same as 0.200 mol of O atoms.

Each O₂ molecule contains two O atoms. Therefore 0.200 mol of O₂ contains 0.400 mol of O atoms: changing the specified entity changes the amount. Similarly, 0.100 mol of MgCl₂ contains 0.100 mol of Mg²⁺ ions and 0.200 mol of Cl⁻ ions, or 0.300 mol of ions in total. Count the species named in the question before choosing a conversion.

The mole and the Avogadro constant

The mole is the SI unit for amount of substance. One mole contains exactly $6.02214076\times10^{23}$ specified elementary entities. Calculations here use the OCR data-sheet approximation $6.02\times10^{23}$ .

Mole

The mole, symbol mol, is the unit for amount of substance. One mole contains the Avogadro constant number of specified elementary entities.

Avogadro constant

The Avogadro constant, $N_A$ , is the number of specified particles per mole. Use $N_A$ = 6.02 × 10²³ mol⁻¹.

The value of the Avogadro constant is provided on the data sheet. You should know how to use it and how to keep the unit attached to the quantity. Some older resources define the mole using carbon-12; that wording and the modern Avogadro-constant definition are both acceptable routes to the same practical idea here.

Particles and amount

N = nN_A

where N is the number of particles, n is amount in mol, and $N_A$ is the Avogadro constant.

Rearranging gives:

n = \frac{N}{N_A}

Worked example: amount to number of particles

Calculate the number of CO₂ molecules in 0.250 mol of CO₂.

The specified entity is CO₂ molecules, so:

N(\text{CO}_2) = n(\text{CO}_2) \times N_A

N(\text{CO}_2) = 0.250 \times 6.02 \times 10^{23}

N(\text{CO}_2) = 1.505 \times 10^{23}

To three significant figures:

N(\text{CO}_2) = 1.51 \times 10^{23}\ \text{molecules}

The answer is a number of molecules, so it has no mol unit.

Worked example: particles to amount

A sample contains 3.01 × 10²² chlorine molecules, Cl₂. Calculate the amount of Cl₂.

n(\text{Cl}_2) = \frac{N(\text{Cl}_2)}{N_A}

n(\text{Cl}_2) = \frac{3.01 \times 10^{22}}{6.02 \times 10^{23}}

n(\text{Cl}_2) = 5.00 \times 10^{-2}\ \text{mol}

This is also 0.0500 mol.

Molar mass connects mass and amount

Molar mass is the mass per mole of a substance. Its unit is g mol⁻¹.

Molar mass

Molar mass, M, is the mass per mole of a substance, with units g mol⁻¹.

For a substance with relative formula mass or relative molecular mass of 44.0, the molar mass is 44.0 g mol⁻¹. The number is the same, but the meaning is different: relative mass has no unit, while molar mass is a mass per mole.

For example:

substance	relative mass, $M_r$	molar mass
CO₂	44.0	44.0 g mol⁻¹
NaCl	58.5	58.5 g mol⁻¹
MgO	40.3	40.3 g mol⁻¹

Mass and amount

n = \frac{m}{M}

where n is amount in mol, m is mass in g, and M is molar mass in g mol⁻¹.

Rearranging gives:

m = nM

Worked example: mass to amount

Calculate the amount of sodium chloride formula units in 5.85 g of NaCl. Use M(NaCl) = 58.5 g mol⁻¹.

n(\text{NaCl}) = \frac{m}{M}

n(\text{NaCl}) = \frac{5.85}{58.5}

n(\text{NaCl}) = 0.100\ \text{mol}

The entity is NaCl formula units because the formula is NaCl.

Worked example: amount to mass

Calculate the mass of 0.125 mol of CO₂. Use M(CO₂) = 44.0 g mol⁻¹.

m(\text{CO}_2) = nM

m(\text{CO}_2) = 0.125 \times 44.0

m(\text{CO}_2) = 5.50\ \text{g}

Molar gas volume at RTP

Molar gas volume is the gas volume per mole. Its unit is dm³ mol⁻¹.

Molar gas volume

Molar gas volume, $V_m$ , is the volume per mole of a gas, with units dm³ mol⁻¹.

At room temperature and pressure, RTP, the data sheet value is:

V_m = 24.0\ \text{dm}^3\ \text{mol}^{-1}

In this ideal-gas approximation, 1.00 mol of a gas at RTP occupies 24.0 dm³. Real gases may deviate from the approximation. This is a conversion factor for gases at RTP. Do not use it for solids, liquids, solutions, or gases under conditions where the ideal gas equation is being used.

Gas volume and amount at RTP

V = nV_m

At RTP, use $V_m$ = 24.0 dm³ mol⁻¹.

Rearranging gives:

n = \frac{V}{V_m}

When using 24.0 dm³ mol⁻¹, the volume must be in dm³. If a question gives cm³, convert first:

1000\ \text{cm}^3 = 1.000\ \text{dm}^3

Worked example: amount to gas volume

Calculate the volume of 0.150 mol of CO₂ at RTP.

V(\text{CO}_2) = n(\text{CO}_2)V_m

V(\text{CO}_2) = 0.150 \times 24.0

V(\text{CO}_2) = 3.60\ \text{dm}^3

Worked example: gas volume to amount

Calculate the amount of oxygen molecules, O₂, in 480 cm³ of O₂ at RTP.

First convert the volume:

480\ \text{cm}^3 = 0.480\ \text{dm}^3

Then use molar gas volume:

n(\text{O}_2) = \frac{V}{V_m}

n(\text{O}_2) = \frac{0.480}{24.0}

n(\text{O}_2) = 0.0200\ \text{mol}

Choosing the correct conversion route

Amount of substance is the central quantity. The information in the question tells you which conversion route to use.

[DIAGRAM: asset_name: Lesson 2.1.3a: The Mole and Chemical Amount - diagram 01; asset_slug: 02_01_03a_the_mole_and_chemical_amount__diagram_01; recommended_method: drawn_chem; description: A clean 16:9 conversion map with amount of substance n in mol at the centre, linked to particles N by Avogadro constant NA, mass m by molar mass M in g mol^-1, and gas volume V at RTP by molar gas volume Vm = 24.0 dm^3 mol^-1; includes formula-specific entity reminders.]
Diagram

Use this decision sequence:

Identify the specified entity: CO₂ molecules, NaCl formula units, Mg²⁺ ions, or another formula-named entity.
Identify the measured quantity: number of particles, mass, or gas volume at RTP.
Convert to amount in mol using the matching conversion factor.
Keep units visible in the working and round only at the end.

given information	route to amount
number of particles, N	n = N / $N_A$
mass in g, m	n = m / M
gas volume at RTP in dm³, V	n = V / $V_m$

Worked example: selecting the route

A student is given 1.20 dm³ of ammonia gas, NH₃, at RTP and asked for n(NH₃).

The measured quantity is a gas volume at RTP, so use molar gas volume:

n(\text{NH}_3) = \frac{V}{V_m}

n(\text{NH}_3) = \frac{1.20}{24.0} = 0.0500\ \text{mol}

The supplied molar gas volume gives the shortest route because the question gives a gas volume at RTP. Molar mass alone cannot convert a volume into an amount. The ideal gas equation is another valid gas model when a suitable pressure and temperature are available; it is developed in its own lesson.

Common traps

Use the precise quantity name amount of substance, with its value in mol.
Do not leave the entity unspecified. Write n(O₂) rather than just n(oxygen) when the formula matters.
Do not put mol on a particle count. A particle count such as 1.51 × 10²³ molecules is not an amount in mol.
Do not use 24.0 dm³ mol⁻¹ unless the substance is a gas at RTP.
Do not treat molar mass and relative mass as the same quantity. They can have the same numerical value, but molar mass has units g mol⁻¹.

The core skill in this lesson is choosing the correct bridge to n. Later calculations will use balanced equations and formula ratios, but those steps rely on this first idea: a chemical amount must name the entity and use the correct unit.

Quick Recap

Specify the entity before counting it. Convert particles with the Avogadro constant, mass with molar mass, or gas volume at RTP with molar gas volume. Amount has unit mol; particle number is a count. Match volume units to the conversion factor, and distinguish unitless relative mass from molar mass in g mol⁻¹.

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2.1.3(a) - The mole and chemical amount

Amount of substance and specified entities

The mole and the Avogadro constant

Molar mass connects mass and amount

Molar gas volume at RTP

Choosing the correct conversion route

Quick Recap

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