Ideal gas behaviour

IB Chemistry Higher Level· Topic 1.5· 15 min read

1. Postulates of Kinetic Molecular Theory★★☆☆☆⏱ 5 min

An ideal gas is a hypothetical model that simplifies the behaviour of real gases to allow predictable calculations based on particle motion. The kinetic molecular theory (KMT) outlines 5 core assumptions that define an ideal gas.

📘 Definition

Ideal Gas

A hypothetical gas that follows all postulates of kinetic molecular theory exactly, with no intermolecular interactions and negligible particle volume

Example:

Most real gases approximate ideal behaviour at low pressure and high temperature

Gases consist of large numbers of tiny particles far apart relative to their size, so individual particle volume is negligible
All collisions between particles and container walls are elastic (no net loss of kinetic energy)
Gas particles are in constant, random, rapid motion
There are no attractive or repulsive intermolecular forces between gas particles
Average kinetic energy of particles is proportional to absolute temperature

2. The Ideal Gas Equation★★☆☆☆⏱ 6 min

Combining Boyle's law ( $P \propto 1/ V$ ), Charles' law ( $V \propto T$ ), and Avogadro's law ( $V \propto n$ ) gives the combined ideal gas equation that relates all measurable properties of an ideal gas.

PV = nRT

📐 Worked Example

A 0.250 mol sample of nitrogen gas occupies 12.0 L at 30.0 °C. Calculate the pressure of the gas, given $R = 8.314 kPa L mol^{- 1} K^{- 1}$ .

1
Convert temperature from Celsius to Kelvin:
2
$T = 30.0 + 273.15 = 303.15 \text{ K}$
3
Rearrange the ideal gas equation to solve for pressure $P$ :
4
$P = \frac{nRT}{V}$
5
Substitute values and calculate:
6
$P = \frac{(0.250 \text{ mol})(8.314 \text{ kPa L mol}^{-1} \text{K}^{-1})(303.15 \text{ K})}{12.0 \text{ L}} = 52.6 \text{ kPa}$

✓ Quick check

Check your unit conversion understanding

What absolute temperature should you use for a gas at 25 °C?
- 25 K
- 298 K
- 248 K
- -248 K
Reveal answer
298 K —
Correct: 25 + 273 = 298 K. The ideal gas equation only works with absolute temperature.

3. Calculating Molar Mass and Gas Density★★★☆☆⏱ 5 min

The ideal gas equation can be rearranged to calculate the molar mass or density of an unknown gas, using the relationship $n = \frac{m}{M}$ , where $m$ is mass of gas and $M$ is molar mass.

🔬 Derivation

Goal:

Derive the formula for molar mass of an unknown gas

Starting from:

$P V = n R T$ and $n = \frac{m}{M}$

1
Substitute $n = \frac{m}{M}$ into the ideal gas equation:
2
$PV = \frac{mRT}{M}$
3
Rearrange to isolate $M$ :
4
$M = \frac{mRT}{PV}$
5
Substitute density $ρ = \frac{m}{V}$ to get the density relationship:
6
$M = \frac{\rho RT}{P} \implies \rho = \frac{PM}{RT}$

Result:

These rearranged formulas are commonly used to identify unknown gases from experimental data in IB exams.

📐 Worked Example

An unknown gas has a mass of 1.25 g, occupies 0.550 L at 100.0 kPa and 25 °C. Calculate its molar mass, using $R = 8.314 kPa L mol^{- 1} K^{- 1}$ .

1
Convert temperature to Kelvin:
2
$T = 25 + 273.15 = 298.15 \text{ K}$
3
Substitute values into the derived formula for $M$ :
4
$M = \frac{(1.25 \text{ g})(8.314 \text{ kPa L mol}^{-1} \text{K}^{-1})(298.15 \text{ K})}{(100.0 \text{ kPa})(0.550 \text{ L})} = 56.3 \text{ g mol}^{-1}$

4. Deviations from Ideal Gas Behaviour★★★☆☆⏱ 6 min

The ideal gas model is a simplification: all real gases deviate from ideal behaviour because the two core KMT assumptions are never perfectly true for real particles.

Real gas particles have non-negligible volume: this becomes significant at high pressure when particles are forced close together
Real gas particles have attractive intermolecular forces: this becomes significant at low temperature when particles move slowly enough for forces to act

Deviations are largest at high pressure and low temperature. Gases with larger molecular size and stronger intermolecular forces deviate more than small, nonpolar gases.

📐 Worked Example

Which gas shows the greatest deviation from ideal behaviour at 10 atm and 100 K: He, H₂, or NH₃? Explain your answer.

1
Compare intermolecular forces and molecular size for each gas:
2
He and H₂ are small, nonpolar molecules with very weak London dispersion forces. NH₃ is polar with strong hydrogen bonding between molecules.
3
At low temperature and high pressure, intermolecular forces are highly significant.
4
Conclusion: NH₃ deviates most from ideal behaviour because of its strong intermolecular forces.

5. Common Pitfalls

Wrong move:

Using temperature in Celsius instead of Kelvin in the ideal gas equation

Why:

The ideal gas equation relies on absolute temperature where 0 K = 0 kinetic energy. Celsius values give incorrect proportionality.

Correct move:

Always add 273.15 to Celsius temperature to get Kelvin before substituting into the equation.

Wrong move:

Mismatching units of pressure/volume with the units of R

Why:

R has different numerical values for different unit sets, so mismatches give wrong orders of magnitude for results.

Correct move:

Check that units of P and V match the units of R you use, convert units if needed before calculating.

Wrong move:

Claiming all deviations are caused only by intermolecular forces

Why:

At very high pressure, non-negligible particle volume is the dominant cause of deviation, not intermolecular forces.

Correct move:

Distinguish between causes: low temperature deviations come from intermolecular forces, high pressure deviations come from particle volume.

Wrong move:

Stating deviations are largest at low pressure and high temperature

Why:

These are the conditions where ideal assumptions are closest to true, so deviations are smallest here.

Correct move:

Remember deviations are largest at high pressure and low temperature, when particles are close and moving slowly.

6. Quick Reference Cheatsheet

Concept	Key Formula / Fact
Ideal Gas Equation	$P V = n R T$
Molar Mass of Unknown Gas	$M = \frac{m R T}{P V}$
Gas Density	$ρ = \frac{P M}{R T}$
Core Assumption 1	Negligible individual particle volume
Core Assumption 2	No intermolecular forces between particles
Core Assumption 3	Average KE $\propto$ absolute temperature
Minimum Deviation Conditions	Low pressure, high temperature
Maximum Deviation Conditions	High pressure, low temperature
Most Deviant Gas Type	Strong intermolecular forces, large molecules

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 1
Identify conditions for ideal gas deviation
2023 · 2
Calculate molar mass of unknown gas
2021 · 1
State postulates of KMT for ideal gases

Going deeper

simulationPhET Ideal Gas Properties SimulationVisualise particle motion and ideal gas relationships

What's Next

Understanding ideal gas behaviour is the foundation for all gas-related topics in IB Chemistry, including reaction stoichiometry involving gaseous products, entropy calculations, and acid-base reactions with gaseous reactants. The distinction between ideal and real gas behaviour also underpins your later study of intermolecular forces, where you will explore how particle interactions affect bulk properties of matter. The calculation skills you developed here are regularly tested in both Paper 1 multiple choice and Paper 2 short answer questions, so regular practice rearranging the ideal gas equation for different unknowns is key to exam success.