In simple terms
A friendly intro before the formal notes — no formulas yet.
The Rules of Gas Behaviour
An ideal gas is a simplified model of a gas made of tiny particles in constant, random motion that don't attract each other. One equation, PV = nRT, ties together how much gas you have, how much space it fills, how hard it pushes, and how hot it is.
Imagine a bouncy castle. The pressure (P) is how hard the kids push against the inside walls. The volume (V) is the size of the castle. The number of moles (n) is the number of kids inside. The temperature (T) is how energetically they are all bouncing. The ideal gas law, PV = nRT, is the 'rulebook' connecting them: add more kids (increase n) or make them bounce faster (increase T) and the pressure on the walls rises, if the castle size stays the same.
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Identify all known variables (P, V, n, T) and the one you must find.
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Convert every value into SI units: pressure in pascals (Pa), volume in cubic metres (m³), temperature in kelvin (K).
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Rearrange PV = nRT to make the unknown the subject.
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Substitute, solve, then convert the answer to the units the question asks for and quote the correct significant figures.
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step 1
Identify all known variables (P, V, n, T) and the one you must find.
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Full topic notes
Formal explanation with the rigour you need for the exam.
The kinetic molecular theory and the ideal gas
The kinetic molecular theory pictures a gas as a very large number of tiny particles in continuous, rapid, random motion. They collide with one another and with the container walls, and it is these wall collisions that we measure as pressure. The collisions are treated as perfectly elastic, meaning no kinetic energy is lost, and the average kinetic energy of the particles is directly proportional to the absolute (kelvin) temperature — hotter gas means faster particles.
An 'ideal' gas is an idealisation of this picture built on two assumptions that make the mathematics simple. These assumptions are the thing examiners most often ask you to state, so learn them precisely.
Assumption 1 — negligible particle volume: the volume of the particles themselves is negligible compared with the volume of the container. The gas is treated as mostly empty space.
Assumption 2 — no intermolecular forces: there are no forces of attraction or repulsion between the particles, so between collisions they travel in straight lines at constant speed.
Consequence: because average kinetic energy ∝ T(K), raising the temperature raises the speed of the particles and the force of their collisions with the walls.
Ideal gases vs. real gases
No real gas is truly ideal, because real particles do occupy space and do attract one another (through London dispersion and other intermolecular forces). Real gases behave most ideally at high temperature and low pressure: the particles are far apart and moving fast, so both their own volume and the weak forces between them are negligible. Deviations become significant under the opposite conditions.
High pressure → deviation: particles are forced close together, so their finite volume is no longer negligible relative to the container. Assumption 1 fails.
Low temperature → deviation: particles move slowly, so intermolecular attractions have time to act and pull particles together. Assumption 2 fails.
Most ideal behaviour: low pressure and high temperature — the conditions under which both assumptions hold best.
The individual gas laws and their graphs
Before the single combined equation, it helps to see the three pairwise relationships, each holding one pair of variables constant. Every temperature here is the absolute (kelvin) temperature.
Combining all three for a fixed amount of gas gives the combined gas law, which lets you follow one sample of gas between two sets of conditions without needing R.
Pressure–volume (Boyle's law) — constant n and T: P ∝ 1/V, so PV = constant. A graph of P against V is a curve (a hyperbola); a graph of P against 1/V is a straight line through the origin.
Volume–temperature (Charles's law) — constant n and P: V ∝ T, so V/T = constant. A graph of V against T(K) is a straight line through the origin.
Pressure–temperature (Gay-Lussac's law) — constant n and V: P ∝ T, so P/T = constant. A graph of P against T(K) is a straight line through the origin.
The ideal gas equation
When the amount of gas is allowed to vary, the individual laws and Avogadro's principle (equal volumes of gases at the same T and P contain equal numbers of particles) combine into a single relationship — the ideal gas equation. It is the central equation of this topic.
PV = nRT
The proportionality constant R is the ideal (universal) gas constant. Its value comes from the IB Data Booklet, so you never memorise it — but its units dictate the units of everything else, so all variables must be in SI units before substitution.
Pressure (P): pascals (Pa). Questions often give kPa or atm. .
Volume (V): cubic metres (m³). Lab data are usually cm³ or dm³. .
Amount (n): moles (mol) — you may have to find this from mass ÷ molar mass first.
Temperature (T): kelvin (K). (adding 273 is accepted in IB working).
Gas constant (R): . 'J K⁻¹ mol⁻¹' is the reminder that you need Pa, m³ and K.
Unit conversion is the most common source of lost marks in this whole topic. Before rearranging anything, write out P, V, n, T in a column and convert each to SI units (Pa, m³, K, mol). This one habit protects the answer mark on almost every gas calculation.
Molar volume of a gas
A direct consequence of PV = nRT is that, at a fixed temperature and pressure, V/n is the same for every ideal gas — one mole always occupies the same volume regardless of identity. This is the molar volume. From the Data Booklet, at STP (0 °C = 273 K and 100 kPa) the molar volume is 22.7 dm³ mol⁻¹. So for a gas at STP you can shortcut between moles and volume without R: n = V(in dm³) ÷ 22.7. Away from STP, go back to PV = nRT.
Common mistakes examiners penalise
Leaving temperature in °C — every gas law needs kelvin. This is the most heavily penalised slip in the topic; add 273 before you do anything else.
Mismatched units in PV = nRT — using kPa with cm³, or forgetting to convert dm³/cm³ to m³. R = 8.31 demands Pa, m³ and K together, or none of them.
Confusing direct and inverse relationships — P ∝ 1/V (inverse) but V ∝ T and P ∝ T (direct). Halving V doubles P; doubling T(K) doubles V.
Assuming molar volume applies at any conditions — 22.7 dm³ mol⁻¹ only holds at STP. Away from STP, use PV = nRT.
Rounding n too early in a molar-mass calculation, then quoting a molar mass that is out by several units.
Not showing the rearrangement — write V = nRT/P (or the relevant form) explicitly; the method mark depends on it, and it protects you under error-carried-forward marking.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
Calculate the pressure, in kPa, exerted by 0.250 mol of an ideal gas in a 5.00 dm³ flask at 22.0 °C. (R = 8.31 J mol⁻¹ K⁻¹)
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List variables and convert to SI units:
A sample of a volatile liquid was injected into a gas syringe. When vaporised at 98.0 °C and 101 kPa, 0.150 g of the substance occupied 65.0 cm³. Determine the molar mass of the substance. (R = 8.31 J mol⁻¹ K⁻¹)
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List variables and convert to SI units:
Calculate the volume, in dm³, occupied by 0.250 mol of an ideal gas at 300 K and 100 kPa. (R = 8.31 J mol⁻¹ K⁻¹) [3]
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List and convert to SI units:
How it all connects
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Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Try to recall each definition before you reveal it.
Quick check
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Revision flashcards
Flip the card. Test yourself before the exam.
State the kinetic molecular theory of an ideal gas.
A gas is a large number of tiny particles in continuous, rapid, random motion. Collisions between particles and with the walls are perfectly elastic (no kinetic energy is lost), and the average kinetic energy of the particles is proportional to the absolute (kelvin) temperature.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
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Assumption 1 — negligible particle volume: the volume of the particles themselves is negligible compared with the volume of the container. The gas is treated as mostly empty space.
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Assumption 2 — no intermolecular forces: there are no forces of attraction or repulsion between the particles, so between collisions they travel in straight lines at constant speed.
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Consequence: because average kinetic energy ∝ T(K), raising the temperature raises the speed of the particles and the force of their collisions with the walls.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Get a Paper 2 gas calculation marked: use PV = nRT with correct unit handling
Get a Paper 2 gas calculation marked: use PV = nRT with correct unit handling
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Checkpoint
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