The model, not the gas in the room

An ideal gas is a theoretical gas that follows a simplified particle model: its particles move randomly, take up no significant space, exert no intermolecular forces on one another, and collide without losing total kinetic energy. No real gas is perfectly ideal, but many gases get close enough to make useful predictions.

A scientific model is a simplified representation of a system that keeps the features needed for prediction and leaves out features judged to be less important. That last part is easy to forget. A model works best when we stay aware of what it leaves out.

Assumptions you should be able to recognize

The ideal gas model is built on a few assumptions:

• Gas particles are in continuous random motion. They move in straight lines between collisions.
• The particles are treated as points: their own volume is negligible compared with the volume of the container.
• There are no intermolecular forces between particles. In this model, particles neither attract nor repel one another except during collisions.
• Collisions between particles, and between particles and the container walls, are perfectly elastic.
• The average kinetic energy of the particles depends on absolute temperature, so hotter gas particles move faster on average.

An elastic collision is a collision in which the total kinetic energy of the colliding particles is unchanged. A single particle may speed up or slow down after a collision, but the total for the particles involved is conserved.

An intermolecular force is an attractive or repulsive interaction between molecules or particles. The ideal gas model deliberately ignores these forces; real gases do not.

How pressure arises in the model

Gas pressure is caused by particles striking the walls of the container. When collisions happen more often, or with greater force, the pressure is higher. In the ideal model, these collisions are clean rebounds: no energy is lost to attractions between particles or to deformation of the particles themselves.

That is what makes the assumptions useful. With particles that have negligible volume and no attractions, we can link the measurable properties of a gas — pressure, volume, temperature and amount — using simple mathematical relationships.

Why real gases are not perfectly ideal

A real gas is a gas whose particles have finite volume and may experience intermolecular forces. Many real gases behave almost ideally, especially when the particles are far apart and moving quickly, but the ideal gas assumptions start to break down in certain conditions.

Keep two main limitations in mind.

First, real particles occupy space. At high pressure, the gas is squeezed into a smaller volume, so the particles’ own volume becomes a noticeable fraction of the total volume. The “negligible volume” assumption is no longer safe.

Second, real particles attract each other. At low temperature, particles have lower kinetic energy, so intermolecular attractions affect their motion and collisions more strongly. The “no intermolecular forces” assumption becomes weak, and collisions can’t be treated as perfectly ideal rebounds.

Conditions for greatest deviation

Real gases deviate most from ideal behaviour at low temperature and high pressure.

At low temperature, particles move more slowly on average. Attractions between particles can noticeably change their paths and reduce the force or frequency of wall collisions compared with the ideal prediction.

At high pressure, particles are pushed close together. With less empty space between them, particle size and intermolecular attractions both matter more.

The opposite conditions — high temperature and low pressure — favour ideal behaviour. The particles are far apart, moving rapidly, and have little time to interact significantly.

Why some gases deviate more than others

Under comparable conditions, gases with stronger intermolecular forces deviate more from ideal behaviour. Polar molecules, molecules capable of hydrogen bonding, and molecules with large electron clouds tend to show greater attractions than small non-polar molecules.

Larger gas particles also deviate more, because their actual volume is less negligible. This links neatly to bonding and structure: the type and strength of intermolecular forces studied in Structure 2.2 help explain why different gases are not equally ideal.

No mathematical treatment of real-gas corrections is required here. Focus on the explanation: identify which ideal assumption breaks down, then connect it to temperature, pressure, particle size or intermolecular forces.

Avogadro’s law and molar volume

Avogadro’s law says that equal volumes of gases, at the same temperature and pressure, contain equal numbers of particles. For an ideal gas, the gas identity doesn’t change this: hydrogen, oxygen and carbon dioxide would each contain the same number of particles if their volumes, temperatures and pressures matched.

The main quantities used in gas measurements are P, where P is pressure (Pa), V, where V is volume (m³), T, where T is absolute temperature (K), and n, where n is amount of substance (mol). In this topic, use kelvin for temperature in gas calculations because gas volume and pressure depend on absolute temperature, not on the Celsius scale.

A molar volume is the volume occupied by one mole of a substance under specified conditions of temperature and pressure. For a gas, write it as Vₘ = V/n, where Vₘ is molar volume (m³ mol⁻¹). The data booklet gives the molar volume of an ideal gas at standard temperature and pressure.

At standard temperature and pressure (STP) for IB gas calculations, the temperature is 273.15 K and the pressure is 100 kPa. The molar volume of an ideal gas at STP is 22.7 dm³ mol⁻¹, which is the same as 2.27 × 10⁻² m³ mol⁻¹.

Students sometimes find this harder to trust than it looks: one mole of helium atoms and one mole of chlorine molecules take up the same volume at the same temperature and pressure, even though the particles have very different masses. Same n, same T, same P gives same V for an ideal gas.

Investigating gas relationships

For a fixed mass of ideal gas, n stays constant. That lets you change two variables and keep the others controlled.

• If T and n are constant, P is inversely proportional to V. Compressing the gas increases the frequency of wall collisions per unit area.
• If P and n are constant, V is directly proportional to T. Heating the gas makes particles move faster, so the gas must expand to keep pressure constant.
• If V and n are constant, P is directly proportional to T. Heating the gas increases the force and frequency of collisions with the container walls.

The individual names of the gas laws are not assessed. You need to recognise the relationships and interpret their graphs.

Ideal-gas graph relationships for a fixed amount of gas.

A good investigation controls variables on purpose. For example, if you use a simulation to vary temperature and record pressure, temperature is the independent variable, pressure is the dependent variable, and volume and amount of gas are controlled variables. A spreadsheet helps because you can add extra columns, such as reciprocal volume, and plot graphs quickly.

Sketches versus plotted data

A sketch graph helps when you want to show the shape of a relationship clearly: direct proportionality, inverse proportionality, or a straight line through the origin. The drawback is that it does not show experimental scatter, uncertainty or the quality of the data.

An accurately plotted graph uses measured or simulated data points. It can show scatter, anomalies and the strength of a relationship, although a poor scale or a small data range may hide the simple model. In practice, we often use both: a plotted graph to analyse evidence, and a sketch to communicate the ideal relationship.