GCSE · Chemistry · AQA · Spec 8462

Volumes of gases (chem HT)

A mole of carbon dioxide weighs 22 times as much as a mole of hydrogen. At room temperature and pressure, which fills more space? Neither. Exactly the same volume.

Chemistry · Moles and gas volume

One mole of any gas fills 24 dm³

the amount of gas in moles: 4/12. Amount of gas 1 mol. If it's hydrogen, H₂ 24 dm³. If it's carbon dioxide, CO₂ 24 dm³

Amount of gas1 molIf it's hydrogen, H₂24 dm³If it's carbon dioxide, CO₂24 dm³

Drag the amount of gas from 0 to 3 moles. One readout is for hydrogen, the other for carbon dioxide, both at room temperature and pressure. Do they ever split apart? Then run it backwards: find the amount of gas that fills 42 dm³.

Watch out: 24 dm³ per mole belongs to room temperature and pressure (RTP): 20 °C and 1 atmosphere. It's the number to use at RTP — don't carry it to other conditions.

Which idea is yours?

Two syringes, two very different gases

Two sealed gas syringes, both at room temperature and pressure. Syringe A holds 1 mole of hydrogen, H₂ — just 2 g of gas. Syringe B holds 1 mole of carbon dioxide, CO₂ — a hefty 44 g. How do the volumes of gas in the two syringes compare?

Which is closest to what you think right now?

B holds more. 44 g is way more stuff than 2 g, so it needs more room.B holds more, because each CO₂ molecule has three atoms and each H₂ molecule only has two.They'd only be the same if both syringes held the same mass of gas — say 10 g of each.They're the same — 24 dm³ each — because each syringe holds 1 mole of gas.

How sure are you?

I'm sureI think soI'm guessing

B holds more. 44 g is way more stuff than 2 g, so it needs more room.

This is a common misconception

A very natural thought — more stuff usually means more space. But a gas isn't packed like a solid. Its particles are very far apart, so almost all of a gas's volume is empty space between them. What sets the volume is how many particles there are, not how heavy each one is. Heavier particles make a gas denser (more grams in every dm³), not bigger. Both syringes read 24 dm³.

B holds more, because each CO₂ molecule has three atoms and each H₂ molecule only has two.

This is a common misconception

That's a good instinct for solids and liquids, where the particles touch. In a gas, the gaps between particles are huge compared with the particles themselves, so a slightly bigger molecule barely changes anything. A mole is always the same number of particles, so both syringes hold the same number of molecules — and the same number of widely spaced particles fills the same space. 24 dm³ each.

They'd only be the same if both syringes held the same mass of gas — say 10 g of each.

This is a common misconception

Try it and the idea falls apart. 10 g of hydrogen is 5 moles, which fills 120 dm³. 10 g of carbon dioxide is less than a quarter of a mole — under 6 dm³. Equal masses give wildly different volumes. It's equal MOLES that give equal volumes. (You'll see how to turn grams into moles in a moment.)

They're the same — 24 dm³ each — because each syringe holds 1 mole of gas.

This matches the evidence

Spot on. At the same temperature and pressure, equal amounts in moles of gases take up equal volumes. A mole is always the same number of particles, and gas particles are so spread out that their mass and size don't change the space they fill. So 2 g of hydrogen and 44 g of carbon dioxide both fill 24 dm³.

Same moles + same temperature and pressure = same volume. Which gas it is — how heavy or how big its molecules are — doesn't come into it.

From grams to dm³ — and back again

moles = mass ÷ Mr

Questions often hand you a mass, but gas volume follows moles — so count the moles first. Example: 3.4 g of ammonia, NH₃ (Mr = 17). 3.4 ÷ 17 = 0.20 mol.

1 / 5

Spot the slip

Where does this answer go wrong?

What mass of carbon dioxide, CO₂, has a volume of 6.0 dm³ at room temperature and pressure? (Mr of CO₂ = 44)

A student's answer — which line goes wrong?

Volume in dm³ = moles × 24
So moles = 24 ÷ 6.0 = 4.0 mol
Mass = moles × Mr
Mass = 4.0 × 44
Answer: 176 g

Reacting volumes: let the equation do the work

Problem

Carbon monoxide burns in oxygen: 2CO(g) + O₂(g) → 2CO₂(g). What volume of oxygen reacts with 60 cm³ of carbon monoxide, and what volume of carbon dioxide forms? All the volumes are measured at the same temperature and pressure.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Count the moles and you know the volume — whichever gas it is.

What you need to know

Equal amounts in moles of gases take up the same volume when they're at the same temperature and pressure.
Room temperature and pressure (RTP) means 20 °C and 1 atmosphere. At RTP, one mole of any gas has a volume of 24 dm³.
Volume in dm³ = moles × 24. Change the subject and you get moles = volume in dm³ ÷ 24.
From a mass: moles = mass ÷ Mr, then multiply by 24 to get the volume at RTP.
1 dm³ = 1000 cm³, so convert a volume in cm³ to dm³ (divide by 1000) before you use 24.
For gases reacting at the same temperature and pressure, the balanced equation's mole ratio is also their volume ratio.

The big picture

At the same temperature and pressure, equal amounts in moles of gases take up the same volume, whichever gases they are. At room temperature and pressure (RTP: 20 °C and 1 atmosphere), one mole of any gas fills 24 dm³, so volume in dm³ = moles × 24, and moles = volume ÷ 24. To get from the mass of a gas to its volume, divide by the relative formula mass to find the moles, then multiply by 24. In a reaction between gases at the same conditions, the balanced equation's mole ratio is also the ratio of their volumes.

Key points

1Volume tracks moles: double the moles, double the volume. Half a mole fills 12 dm³ at RTP; three moles fill 72 dm³.

2A gas's mass and molecule size don't change the volume of a mole: 2 g of hydrogen and 44 g of carbon dioxide are each 1 mole, and each fills 24 dm³ at RTP.

3Rearranging means undoing what's done to the quantity you want. Moles × 24 gives volume, so volume ÷ 24 gives moles.

4The volume-ratio shortcut is for gases only. If a solid, liquid or solution is involved, work through moles.

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Worked example

Problem

Calcium carbonate reacts with excess hydrochloric acid: CaCO₃(s) + 2HCl(aq) → CaCl₂(aq) + H₂O(l) + CO₂(g). What volume of carbon dioxide, at room temperature and pressure, is made from 5.0 g of calcium carbonate? (Mr of CaCO₃ = 100)

⚠ Watch out

Forgetting to convert cm³ to dm³ before using 24. For 600 cm³ of gas, 600 ÷ 24 = 25 mol is wildly wrong. Convert first: 600 cm³ = 0.600 dm³, and 0.600 ÷ 24 = 0.025 mol. (Or divide the cm³ by 24 000 in one go.)

🧠

Memory hook

Count moles, not grams. One mole, any gas, 24 dm³ at RTP — and between gases, the equation's big numbers are the volume ratio.

✓

Check yourself

At RTP, what volume do 1.5 mol fill? How many moles fill 60 dm³? In N₂(g) + O₂(g) → 2NO(g), 10 cm³ of N₂ makes how much NO? (36 dm³; 2.5 mol; 20 cm³)

Flashcards

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What volume does one mole of any gas occupy at room temperature and pressure?

24 dm³ — whichever gas it is.

What conditions does room temperature and pressure (RTP) mean?

20 °C and 1 atmosphere pressure.

Two gas samples at the same temperature and pressure have the same volume. What else must be the same about them?

Their amount in moles.

Does a heavier gas take up more volume per mole?

No. At the same temperature and pressure every gas has the same volume per mole. A heavier gas is simply denser.

How do you find the amount in moles of a gas from its volume at RTP?

Divide the volume in dm³ by 24 — the volume by 24, never 24 by the volume.

What is the route from the mass of a gas to its volume at RTP?

Mass ÷ Mr gives moles; moles × 24 gives the volume in dm³.

How many cm³ are there in 1 dm³?

1000 cm³. Divide a volume in cm³ by 1000 to get dm³.

For gases reacting at the same temperature and pressure, what does the balanced equation tell you about their volumes?

The mole ratio from the equation is also the volume ratio.

When can't you use the equation's numbers directly as a volume ratio?

When a substance isn't a gas — a solid, liquid or solution. Work through moles instead.

Sense check: is 30 dm³ of gas at RTP more or less than 1 mole?

More: 30 ÷ 24 = 1.25 mol.

How do you change the subject of an equation?

Undo whatever is being done to the quantity you want, doing the same to both sides. If it's multiplied by 24, divide both sides by 24.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Two syringes, two very different gases

Where does this answer go wrong?

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