The mole and the volume of gas

This page covers a single Form 4 content standard: the mole and the volume of a gas. It adds a third route into and out of the mole. In standard 3.3 you connected the mole to mass; here you connect it to the volume of a gas, using a single, memorable constant called the molar volume. For gases this is often the fastest way to find an amount, because measuring a volume is easier than weighing a gas, a skill you will use throughout the calculations of SPM Chemistry.

Why one mole of any gas has the same volume

A remarkable experimental fact underlies this standard: equal volumes of all gases, measured at the same temperature and pressure, contain the same number of molecules (Avogadro’s law). Turned around, this means one mole of any gas, light or heavy, element or compound, occupies the same volume under the same conditions. The identity of the gas does not matter; only the temperature and pressure do. This works because in a gas the molecules are so far apart that their own size is negligible, so what fills the space is the number of molecules, not how big or heavy each one is.

Molar volume

The molar volume is the volume occupied by one mole of any gas at a stated temperature and pressure. You must know two standard values:

• At room conditions (room temperature and pressure): Molar volume of a gas is 24 dm³ mol⁻¹ at room conditions.
• At STP (standard temperature and pressure): Molar volume of a gas is 22.4 dm³ mol⁻¹ at STP.

So at room conditions one mole of any gas occupies 24 dm³ mol⁻¹ dm³, and at STP one mole occupies 22.4 dm³ mol⁻¹ dm³. Always check which set of conditions the question specifies before you choose the number.

The key relationship

To convert between the amount of a gas in moles and its volume, use:

Number of moles of gas (n) = volume of gas ÷ molar volume

which rearranges to volume of gas = n × molar volume. This is the gas analogue of “moles = mass ÷ molar mass” from the previous standard, same shape, different constant.

A note on units

Molar volume is given in dm³ mol⁻¹, so volumes must be in dm³ before you divide. If a question gives a volume in cm³, convert first: 1 dm³ = 1000 cm³, so divide the number of cm³ by 1000. Forgetting this conversion is the single most common error on this standard.

Worked example

Question. Calculate the volume of 0.5 mol of carbon dioxide, CO₂, at room conditions. [Molar volume at room conditions = 24 dm³ mol⁻¹ dm³ mol⁻¹]

Step 1, Choose the correct molar volume. The question says room conditions, so use 24 dm³ mol⁻¹ dm³ mol⁻¹.

Step 2, Apply volume = n × molar volume. Volume = 0.5 × 24 dm³ mol⁻¹ = 12 dm³.

Answer. 0.5 mol of CO₂ occupies 12 dm³ at room conditions. (Note that the answer would be the same for 0.5 mol of any gas at room conditions, because molar volume does not depend on the identity of the gas.)

Practice question

Question. How many moles of oxygen gas, O₂, are present in 6 dm³ of oxygen at room conditions, and how many molecules is that? [Molar volume = 24 dm³ mol⁻¹ dm³ mol⁻¹; NA = 6.02 x 10²³ mol⁻¹ mol⁻¹]

Answer. Number of moles = volume ÷ molar volume = 6 ÷ 24 dm³ mol⁻¹ = 0.25 mol. Number of molecules = 0.25 × 6.02 x 10²³ mol⁻¹ = 1.505 × 10²³ molecules.

Exam tip

Two checks protect the marks. First, read the conditions: use 24 dm³ mol⁻¹ dm³ mol⁻¹ at room conditions and 22.4 dm³ mol⁻¹ dm³ mol⁻¹ at STP, using the wrong one gives the wrong answer even with perfect method. Second, get the volume into dm³ before dividing; convert cm³ to dm³ by dividing by 1000. Remember that molar volume applies only to gases, you cannot use it for a solid or a liquid. And because the molar volume is the same for every gas, a question that gives you the mass of a gas and asks for its volume is really a two-step problem: mass → moles (using molar mass) → volume (using molar volume).

Linking gas volume into the full map

This standard extends the conversion map from standard 3.3 by adding a fourth box for gases:

mass ⇄ moles ⇄ number of particles, and for a gas also moles ⇄ volume of gas

The mole remains the hub in the centre. To find the volume of a gas from its mass, first turn the mass into moles with the molar mass, then turn the moles into a volume with the molar volume. To find how many molecules are in a measured volume of gas, first turn the volume into moles with the molar volume, then multiply by the Avogadro constant. Every one of these journeys passes through the mole, which is exactly why the mole is the centre of the whole chapter.

When to use molar volume rather than molar mass

Students sometimes reach for the molar mass out of habit even when the quantity given is a gas volume. Use this simple rule: if the data you are given is a volume of a gas, start with the molar volume; if it is a mass, start with the molar mass. Both routes deliver an amount in moles, and once you have moles you can go anywhere else on the map. Recognising which constant to start with, molar mass in g mol⁻¹ or molar volume in dm³ mol⁻¹, is often the whole difficulty of a question, and it is a decision you can make just by looking at the units of the data.

Where this fits

This is content standard 3.4 of the The Mole Concept, Chemical Formula and Equation chapter. It builds on the mole and molar mass and is used heavily in the stoichiometry of reactions that produce or consume gases. Practise gas-volume conversions with the worked examples and check yourself with the practice questions. In our online 1-to-1 SPM Chemistry lessons, taught in English, from RM50/hr, our teachers make sure you always pick the right molar volume for the stated conditions and never forget the cm³-to-dm³ conversion.

Quick recap

• One mole of any gas occupies the same volume at the same temperature and pressure.
• Molar volume: Molar volume of a gas is 24 dm³ mol⁻¹ at room conditions; Molar volume of a gas is 22.4 dm³ mol⁻¹ at STP.
• Number of moles of gas = volume ÷ molar volume; volume = moles × molar volume.
• Volumes must be in dm³ (1 dm³ = 1000 cm³); molar volume applies to gases only.