Last updated: 17 August 2026
A gas can expand to fill an entire room, be compressed into a cylinder or exert enough pressure to inflate a tyre. Behind all of these observations is the rapid, continuous motion of enormous numbers of particles.
Describing every collision between every particle would be impossible. Chemists therefore use a simplified model called the ideal gas. By making a few carefully chosen assumptions about the particles, we can connect pressure, volume, temperature and amount using one remarkably useful equation: pV = nRT.
The model is deliberately idealised. Real molecules do occupy space and do attract one another. Understanding exactly what has been simplified is therefore just as important as knowing the equation itself, because those assumptions explain when real gases behave ideally and why they eventually deviate.
Diagnostic Quiz
Try these five questions before reading the chapter. They check the unit conversions, particle ideas and gas relationships that will make the rest of the topic much easier to follow.
- 5 quick starting-point questions
- Focus on common gas-law misconceptions
- Every answer option is explained
What is an ideal gas?
An ideal gas is a hypothetical gas that obeys the general gas equation exactly under all conditions:
No real gas behaves perfectly ideally under every possible condition. The ideal gas is therefore best thought of as a model. The model removes some of the complications of real molecules so that their overall behaviour can be described mathematically.
A real gas may nevertheless behave extremely close to the ideal model. When its molecules are far apart and moving with sufficiently high kinetic energy, the features neglected by the model have relatively little effect.
| Feature | Ideal-gas model | Real gas |
|---|---|---|
| Particle volume | Treated as negligible | Molecules occupy a finite volume |
| Intermolecular forces | Assumed to be absent | Attractive and repulsive interactions exist |
| Gas equation | Obeys pV = nRT exactly | Approaches pV = nRT under suitable conditions |
| Condensation | Would not occur because attractions are absent | Can occur when intermolecular attractions become sufficiently important |
Saying that a real gas behaves ideally means that the effects of molecular size and intermolecular forces are small enough for the ideal-gas assumptions to give a good approximation.
The kinetic theory of an ideal gas
The kinetic theory explains the large-scale behaviour of gases by considering what their particles are doing microscopically. For an ideal gas, several simplifying assumptions are made.
| Assumption | What it means |
|---|---|
| Negligible particle volume | The particles themselves occupy a negligible volume compared with the total volume occupied by the gas. |
| No intermolecular forces | The particles are assumed not to attract or repel one another except during the instant of collision. |
| Continuous random motion | Particles move continuously and randomly in straight lines between collisions. |
| Perfectly elastic collisions | Collisions between particles and collisions with the container walls cause no net loss of kinetic energy. |
| Kinetic energy depends on temperature | The average translational kinetic energy of the particles is directly proportional to the absolute temperature. |
Negligible particle volume
Imagine a gas inside a large container. Most of the space between the molecules is empty. The ideal gas model takes this idea to the limit and treats the actual volume occupied by the molecules as negligible compared with the volume of the container.
This does not mean that real molecules literally have zero size. It means that their own volume can sometimes be ignored without significantly affecting the result.
No intermolecular forces
Ideal-gas particles are assumed to move independently. One particle is not pulled towards or pushed away from another while they are separated.
Real molecules are different. They experience intermolecular attractions, including instantaneous dipole–induced dipole attractions and, where appropriate, permanent dipole–permanent dipole attractions or hydrogen bonding.
If the molecules are very far apart or have sufficiently high kinetic energy, these attractions may have only a small effect on the overall behaviour of the gas.
Continuous random motion
Gas particles are in continuous motion. Between collisions they travel in straight lines, but repeated collisions continually alter their directions, producing an overall random pattern of motion.
Perfectly elastic collisions
During a collision, individual molecules may gain or lose kinetic energy because energy is transferred between them. However, the total kinetic energy of the colliding particles is conserved.
The same idealisation applies when particles collide with the walls of the container.
Average kinetic energy and absolute temperature
The average translational kinetic energy of gas particles depends only on the absolute temperature:
The temperature must therefore be measured in kelvin.
At a higher temperature, the particles possess greater average kinetic energy and move faster on average.
Two different gases at the same temperature have the same average translational kinetic energy per molecule. This does not mean that they have the same average speed. Lighter particles move faster on average than heavier particles at the same temperature.
How does a gas produce pressure?
A gas molecule moving towards a container wall collides with the wall and changes momentum. The wall therefore experiences a force.
A macroscopic sample contains an enormous number of molecules undergoing collisions continuously. The combined force of these collisions per unit area produces the measurable gas pressure.
This particle picture helps explain several familiar observations:
- Adding more gas particles tends to increase the collision frequency.
- Compressing the gas makes the particles reach the walls more frequently.
- Heating the gas increases the average kinetic energy of the particles.
The general gas equation: pV = nRT
For an ideal gas, pressure, volume, amount and absolute temperature are related by:
| Symbol | Quantity | Standard unit |
|---|---|---|
| p | Pressure | Pa |
| V | Volume | m³ |
| n | Amount of gas | mol |
| R | Molar gas constant | 8.31 J K⁻¹ mol⁻¹ |
| T | Absolute temperature | K |
Temperature must be in kelvin
The gas equation uses absolute temperature. A Celsius temperature must therefore be converted before substitution:
For example:
Incorrect: substituting T = 25 for a gas at 25 °C.
Correct: convert the temperature first and substitute T = 298 K.
Converting gas volumes
Laboratory gas volumes are often given in cm³ or dm³, while the SI volume used with pressure in Pa is m³.
Therefore:
- dm³ → m³: divide by 1000;
- cm³ → m³: divide by 1 000 000;
- cm³ → dm³: divide by 1000.
For example:
Why can kPa and dm³ also be used?
The safest SI combination is Pa with m³. However, kPa and dm³ can also be used together with the numerical value R = 8.31 because:
| Pressure | Volume | R |
|---|---|---|
| Pa | m³ | 8.31 J K⁻¹ mol⁻¹ |
| kPa | dm³ | 8.31 J K⁻¹ mol⁻¹ |
Use Pa with m³ or kPa with dm³. A large fraction of gas-equation errors comes from inserting correct numbers expressed in incompatible units.
Worked example: calculating pressure
Calculate the pressure exerted by 0.250 mol of an ideal gas occupying 5.00 dm³ at 298 K.
Since volume is in dm³, pressure can conveniently be calculated in kPa.
Answer: The pressure is 124 kPa, to three significant figures.
Worked example: calculating amount
Calculate the amount of gas occupying 480 cm³ at 30 °C and 102 kPa.
First convert the temperature:
Since pressure is in kPa, convert the volume to dm³:
Rearrange pV = nRT:
Answer: n = 1.94 × 10⁻² mol, to three significant figures.
Using pV = nRT to determine Mᵣ
The amount of a molecular substance can be calculated from its mass and relative molecular mass:
More precisely, the numerical value of Mᵣ is equal to the numerical value of the molar mass in g mol⁻¹. Substituting n = m/Mᵣ into the gas equation gives:
Rearranging:
Worked example: finding the Mᵣ of an unknown gas
A 0.455 g sample of a gaseous compound occupies 240 cm³ at 298 K and 100 kPa. Determine its relative molecular mass.
Convert 240 cm³ to dm³:
Using kPa and dm³:
Answer: The relative molecular mass of the gas is 46.9.
Relative molecular mass is a relative quantity. The corresponding molar mass would have the same numerical value expressed in g mol⁻¹.
Why do real gases deviate from ideal behaviour?
The ideal gas model works only as long as its assumptions remain good approximations. Real gases deviate because two important assumptions are never completely true:
- real molecules experience intermolecular forces; and
- real molecules occupy a finite volume.
The extent to which these effects matter depends strongly on pressure and temperature.
Effect of attractive intermolecular forces
Consider a molecule travelling towards the wall of a container. In an ideal gas, nothing attracts it backwards, so it reaches the wall exactly as the ideal model predicts.
In a real gas, neighbouring molecules attract it. The molecule approaching the wall may therefore be pulled slightly back towards the rest of the gas.
Its collision with the wall contributes less pressure than would be expected for an ideal gas under the same conditions.
This effect is particularly important when the molecules possess relatively low kinetic energy, such as at low temperature.
Effect of finite molecular volume
The ideal gas equation effectively treats the molecules as point particles. Therefore, all of the measured container volume is assumed to be available for the particles to move through.
Real molecules occupy space. At ordinary pressures, their combined volume may be tiny compared with the volume of the container and can be neglected.
At very high pressure, however, the gas is strongly compressed. The molecules are crowded together and their own volume becomes a significant fraction of the total container volume.
The volume actually available for molecular motion is therefore smaller than the measured container volume. Very short-range repulsive interactions also become important when molecules are forced very close together.
Intermolecular attractions: tend to reduce the pressure relative to the ideal prediction.
Finite molecular volume and short-range repulsion: become important when particles are crowded together and can make the pressure greater than the ideal prediction.
Real-gas behaviour reflects the competition between these effects.
How temperature and pressure affect ideal behaviour
The two conditions most useful for predicting ideality are pressure and temperature.
Low pressure favours ideal behaviour
At low pressure, the gas occupies a large volume relative to the number of molecules. The molecules are therefore widely separated.
Two consequences follow:
- the volume occupied by the molecules themselves is negligible compared with the container volume; and
- intermolecular attractions are weak because the molecules are far apart.
The real gas therefore approaches the assumptions of the ideal model.
High temperature favours ideal behaviour
Increasing the temperature increases the average kinetic energy of the gas molecules.
The molecules are moving more energetically, so attractive intermolecular forces have a smaller effect on their overall motion.
The attractions still exist. They simply become less significant compared with the much greater kinetic energy of the molecules.
When is a real gas most ideal?
The particles are far apart and possess high kinetic energy. Molecular volume and intermolecular attractions both have relatively little effect.
When is deviation greatest?
At very high pressure, particles are forced close together, so their own volume and intermolecular interactions become important.
At very low temperature, their average kinetic energy is reduced, so attractive intermolecular forces have a greater influence on their motion. If the attractions become sufficiently important, the gas may eventually condense.
Why do some gases behave more ideally than others?
Pressure and temperature are not the whole story. The chemical identity of the gas also matters because different particles have different sizes and different strengths of intermolecular attraction.
| Particle characteristic | Effect on ideality | Reason |
|---|---|---|
| Small particle | Tends to behave more ideally | Its own volume is relatively small |
| Weakly polarisable particle | Tends to behave more ideally | Dispersion forces are relatively weak |
| Large, highly polarisable particle | Tends to deviate more | Stronger instantaneous dipole–induced dipole attractions occur |
| Polar molecule | Tends to deviate more | Permanent dipole–permanent dipole attractions may be present |
| Molecule capable of hydrogen bonding | Tends to deviate more | Relatively strong intermolecular attractions occur |
For example, helium generally behaves more ideally than NH₃ under comparable conditions. Helium atoms are very small and experience only weak dispersion forces. NH₃ molecules are polar and can form hydrogen bonds with one another.
Weak explanation: Helium is more ideal because helium is smaller.
Better explanation: Helium atoms are small and experience weak intermolecular attractions, so the assumptions of negligible particle volume and negligible intermolecular forces are better approximations.
Dalton’s Law of Partial Pressures
A gas sample does not have to contain only one substance. Air, for example, is a mixture of several gases sharing the same volume.
For a mixture of non-reacting gases, Dalton’s Law states:
The total pressure is therefore the sum of the partial pressures of the individual gases.
What is partial pressure?
The partial pressure of one gas in a mixture is the pressure that the gas would exert if it alone occupied the entire container at the same temperature.
This does not mean that different gases occupy separate parts of the container. Each gas spreads throughout the available space.
Its molecules collide with the container walls and make their own contribution to the total pressure.
Partial pressure and mole fraction
Suppose gas A is one component of an ideal gas mixture. For gas A:
For the complete mixture:
Dividing the two equations:
The mole fraction of gas A is:
Therefore:
It is a ratio of amounts. The mole fractions of all gases present in a mixture must add up to 1.
Worked example: neon and argon
A mixture contains 2.00 mol of Ne and 3.00 mol of Ar. The total pressure is 250 kPa. Calculate the partial pressure of each gas.
Answer: p(Ne) = 100 kPa and p(Ar) = 150 kPa. Notice that 100 + 150 = 250 kPa, as required by Dalton’s Law.
Gas collected over water
A gas collected over water is not the only gas present in the collection vessel. Some water evaporates, so the collected sample contains both the required gas and water vapour.
Dalton’s Law therefore gives:
Hence:
For example, suppose a gas is collected over water at 25 °C. The measured total pressure is 101 kPa and the vapour pressure of water is 3.17 kPa.
If pV = nRT is then used to calculate the amount of the dry collected gas, 97.8 kPa is the appropriate gas pressure, not 101 kPa.
Bringing the gas ideas together
Example 1: comparing helium and ammonia
Helium and NH₃ are held at the same moderate temperature and pressure. Which gas would you expect to behave more ideally?
Helium atoms are very small and weakly polarisable. The intermolecular attractions between helium atoms are therefore weak.
NH₃ molecules are larger, polar and capable of hydrogen bonding. The assumption of no intermolecular forces is therefore much poorer for NH₃.
Conclusion: Helium is expected to behave more ideally than NH₃ under the same conditions.
Example 2: why cooling increases deviation
Suppose a gas is gradually cooled without immediately condensing.
Its average molecular kinetic energy decreases. The intermolecular attractive forces have not become newly created; they were already present.
However, those attractions now represent a larger influence compared with the molecules’ kinetic energy.
Conclusion: The gas generally deviates more from ideal behaviour as the temperature becomes sufficiently low.
Example 3: partial pressure from masses
A container holds 4.00 g of helium and 16.0 g of oxygen. The total pressure is 180 kPa. Calculate the partial pressure of helium.
Answer: The partial pressure of helium is 120 kPa.
Common mistakes with ideal gases
| Common mistake | Why it is wrong | Correct approach |
|---|---|---|
| Calling an ideal gas a real gas with very small molecules | An ideal gas is a theoretical model | Say that real gases may approach ideal behaviour under suitable conditions |
| Using °C directly in pV = nRT | The equation requires absolute temperature | Convert temperature to K before substitution |
| Using Pa with dm³ | The pressure and volume units are not matched | Use Pa with m³ or kPa with dm³ |
| Using cm³ directly with R = 8.31 | cm³ is not part of the usual matched unit pairs | Convert cm³ to dm³ or m³ first |
| Saying ideal-gas particles have zero volume | The model assumes their volume is negligible | Use the word negligible, not literally zero |
| Saying high temperature removes intermolecular forces | The forces still exist | State that their effect becomes less significant relative to kinetic energy |
| Explaining high-pressure deviation only using attractions | Finite molecular volume and short-range repulsion also become important | Consider both molecular interactions and molecular size |
| Writing units after Mᵣ | Relative molecular mass is dimensionless | Give Mᵣ without a unit |
| Using mass fraction to calculate partial pressure | Partial pressure is proportional to the amount in moles | Calculate mole fraction using n(component)/n(total) |
| Thinking each gas occupies only part of a mixed-gas container | Each gas spreads throughout the available volume | Think of each component contributing independently to the wall collisions |
| Using total pressure for a gas collected over water | The total includes the partial pressure of water vapour | Subtract the vapour pressure of water first |
| Saying lower temperature strengthens the intermolecular force itself | The important change is the lower molecular kinetic energy | Explain that the existing attractions become more significant relative to kinetic energy |
Ideal-gas checklist
Know the model
- Can I state the assumptions of an ideal gas?
- Can I explain what “negligible particle volume” means?
- Do I know that ideal collisions are perfectly elastic?
- Can I relate average kinetic energy to absolute temperature?
Use pV = nRT
- Have I converted the temperature to kelvin?
- Am I using Pa with m³ or kPa with dm³?
- Have I converted cm³ before substitution?
- Can I rearrange the equation to find p, V, n or T?
Explain real-gas behaviour
- Can I discuss intermolecular attractions?
- Can I discuss finite molecular volume?
- Can I explain why low pressure favours ideality?
- Can I explain why high temperature favours ideality?
Handle gas mixtures
- Can I state Dalton’s Law?
- Can I calculate a mole fraction?
- Can I use p(A) = x(A)p(total)?
- Can I correct for water vapour when a gas is collected over water?
Mastery Quiz
Now apply the chapter to calculations and unfamiliar particle-level situations. These questions test whether you can connect the equations to the assumptions behind the ideal gas model.
- 10 application-focused questions
- Calculations and explanation questions
- Every answer option is explained
Frequently asked questions
Questions students often ask about ideal gases
These questions connect the equations to the particle model and clear up several explanations that often sound correct at first but are incomplete.
Does a perfectly ideal gas actually exist?
An ideal gas is a theoretical model. Real gases contain particles with finite volume and intermolecular forces, so no real gas follows every ideal-gas assumption perfectly under all conditions.
However, many real gases behave closely enough to the ideal model at low pressure and high temperature that pV = nRT gives an excellent approximation.
Does negligible molecular volume mean that the molecules have zero size?
No. Real molecules occupy space. “Negligible” means that their combined volume is so small compared with the container volume that ignoring it has little effect on the predicted behaviour.
Why does high temperature make a gas behave more ideally?
Higher temperature gives the gas particles greater average kinetic energy. Attractive intermolecular forces therefore have a smaller effect on the particles’ overall motion.
The forces do not disappear; they simply become less significant relative to the kinetic energy.
Why does low pressure make a gas behave more ideally?
At low pressure, the molecules are widely separated. Their own volume is negligible compared with the total gas volume, and intermolecular attractions are weak at the larger separations.
Are attractive forces the only reason real gases deviate?
No. Real molecules also occupy a finite volume. This becomes especially important at very high pressure, when the molecules are crowded together and the amount of empty space is greatly reduced.
Short-range repulsive interactions also become important when particles are forced very close to one another.
Why can attractions make the pressure lower than the ideal value?
A molecule approaching the wall can be attracted backwards by neighbouring molecules. Its collision with the wall then contributes less momentum transfer than the ideal model predicts, reducing the measured pressure.
Why can finite molecular volume make the pressure higher than expected?
At very high pressure, the molecules occupy a significant fraction of the container volume. The actual space available for molecular motion is therefore smaller than the measured container volume.
Short-range repulsive interactions also become increasingly important when particles are forced very close together.
Can I use pV = nRT with pressure in kPa and volume in dm³?
Yes. kPa and dm³ form a convenient matched pair because 1 kPa dm³ = 1 J. You may therefore use R = 8.31 with p in kPa and V in dm³.
Alternatively, use the standard SI combination of Pa and m³.
Why can I not use Celsius temperature directly?
The kinetic theory and gas equation depend on absolute temperature. The kelvin scale has its zero at absolute zero, whereas 0 °C is simply the freezing point of water under standard conditions.
Temperature must therefore be converted to kelvin before it is used in pV = nRT.
Is Mᵣ the same thing as molar mass?
They have the same numerical value when molar mass is expressed in g mol⁻¹, but they are different quantities.
Relative molecular mass, Mᵣ, is a relative quantity and has no unit. Molar mass is the mass of one mole of substance and has units such as g mol⁻¹.
Does each gas in a mixture occupy only part of the container?
No. Gas particles spread throughout the available space. Each component of the mixture occupies the full container volume and contributes its own partial pressure through collisions with the walls.
Why is partial pressure based on mole fraction rather than mass fraction?
At the same temperature and volume, the ideal gas equation shows that pressure is proportional to the amount of gas in moles: p ∝ n.
The fraction of the total pressure contributed by a component therefore corresponds to its fraction of the total number of moles, not its fraction of the total mass.
Why must water vapour be considered when a gas is collected over water?
Water evaporates into the collected gas, so the measured pressure contains contributions from both the required gas and water vapour.
Dalton’s Law gives p(total) = p(gas) + p(H₂O), so the vapour pressure of water must be subtracted to obtain the pressure of the dry gas.
Which gas should I expect to behave most ideally in a comparison question?
Look for particles that are relatively small and experience weak intermolecular attractions. Such particles most closely satisfy the assumptions of negligible molecular volume and negligible intermolecular forces.
Do not rely on a memorised gas name alone. Use the particle size, polarity, polarisability and ability to form hydrogen bonds to justify the comparison.
The ideal gas model turns the apparently chaotic motion of gas particles into the simple relationship pV = nRT. The same assumptions that make the equation useful also explain its limitations: real molecules attract one another and occupy space. At low pressure and high temperature these effects become relatively unimportant, so real gases approach ideal behaviour. Once this particle picture is secure, calculations involving gas quantities, Mᵣ and partial pressures become much more than formula substitution — each equation becomes a description of what the particles are actually doing.