Gases and the ideal gas equation

Chemistry· 45 min read

1. Key Assumptions of an Ideal Gas★☆☆☆☆⏱ 10 min

An ideal gas is a hypothetical model that simplifies gas behaviour for calculations. All gas laws and the ideal gas equation are built on four core assumptions about gas molecules.

📘 Definition

Ideal Gas

A hypothetical gas that obeys all ideal gas assumptions and the ideal gas equation under all temperature and pressure conditions.

Example:

No perfectly ideal gas exists, but most real gases behave almost ideally at low pressure and high temperature.

Gas molecules have negligible volume compared to the total volume of the gas container
There are no attractive intermolecular forces between gas molecules
All collisions between molecules and container walls are perfectly elastic (no net energy loss)
Gas molecules move randomly in straight lines at a range of speeds

📐 Worked Example

State the four core assumptions of an ideal gas, required for full marks in a CIE exam question

1
1. Gas molecules have negligible volume compared to the total volume of the container
2
1. There are no attractive intermolecular forces between gas molecules
3
1. All collisions between molecules are perfectly elastic, with no net energy loss
4
1. Gas molecules move randomly at a range of different speeds

Exam tip:

CIE mark schemes award one mark per assumption; always list all four when asked, do not just give two or three.

2. The Ideal Gas Equation and Calculations★★☆☆☆⏱ 20 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, which relates all four measurable properties of a gas.

PV = nRT

Where: $P$ = pressure, $V$ = volume, $n$ = number of moles, $R$ = the universal gas constant ( $8.31$ J K $^{- 1}$ mol $^{- 1}$ for SI units), $T$ = absolute temperature in Kelvin.

📐 Worked Example

A 0.250 g sample of CO $_{2}$ occupies 142 cm $^{3}$ at 100 °C. Calculate the pressure of the sample, using $R = 8.31$ J K $^{- 1}$ mol $^{- 1}$ .

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Step 1: Calculate moles of CO $_{2}$ and convert all units to SI units
$n = \frac{mass}{M_r} = \frac{0.250}{44.0} = 0.00568 \text{ mol} \\ V = 142 \text{ cm}^3 = 142 \times 10^{-6} \text{ m}^3 \\ T = 100 + 273 = 373 \text{ K}$
2
Step 2: Rearrange the ideal gas equation to solve for $P$
$P = \frac{nRT}{V}$
3
Step 3: Substitute values and calculate the final pressure
$P = \frac{0.00568 \times 8.31 \times 373}{142 \times 10^{-6}} = 124000 \text{ Pa} = 124 \text{ kPa}$

3. Molar Volume at Room Temperature and Pressure★☆☆☆☆⏱ 10 min

At r.t.p. (defined by CIE as 25 °C / 298 K and 1 atm / 101325 Pa), one mole of any ideal gas occupies a fixed volume. This value is given in the CIE data booklet, but memorising it speeds up calculations significantly.

📘 Definition

Molar Volume at r.t.p.

V_m

The volume occupied by one mole of any gas at r.t.p.

Example:

V_m = 24.0 dm $^{3}$ mol $^{- 1}$ (24000 cm $^{3}$ mol $^{- 1}$ ) at r.t.p.

📐 Worked Example

Calculate the mass of 3.0 dm $^{3}$ of oxygen gas ( $O_{2}$ ) at r.t.p.

1
Step 1: Calculate moles of $O_{2}$ using the molar volume at r.t.p.
$n = \frac{V}{V_m} = \frac{3.0}{24.0} = 0.125 \text{ mol}$
2
Step 2: Calculate mass from moles and molar mass of $O_{2}$
$mass = n \times M_r = 0.125 \times 32.0 = 4.0 \text{ g}$

4. Deviations of Real Gases from Ideal Behaviour★★★☆☆⏱ 15 min

The ideal gas assumptions do not hold for real gases. Two core assumptions break down under extreme conditions, leading to measurable deviations from the ideal gas equation $P V = n R T$ .

Molecular volume is not negligible: At high pressure, molecules are pushed close together, so the volume of the molecules themselves becomes a significant fraction of total volume
Intermolecular forces are not zero: At low temperature, molecules move slower, so attractive intermolecular forces become significant, pulling molecules away from container walls

The largest deviations occur at high pressure, low temperature, and for gases with larger molecular size or stronger intermolecular forces.

📐 Worked Example

Explain why propane deviates more from ideal behaviour than helium at the same temperature and pressure.

1
Step 1: Identify the key difference between the two gases
2
Propane has a larger molecular size and much stronger intermolecular forces than helium.
3
Step 2: Link to broken ideal gas assumptions
4
Both the assumption of negligible molecular volume and the assumption of no intermolecular forces are less valid for propane, leading to greater deviation from ideal behaviour.

Exam tip:

When comparing deviations between two gases, always link the degree of deviation to intermolecular force strength and molecular size, not just mass.

5. Common Pitfalls

Wrong move:

Forgetting to convert temperature from °C to Kelvin

Why:

The ideal gas equation requires absolute temperature; using °C gives a value for $T$ that is off by 273, leading to a completely incorrect result.

Correct move:

Always add 273 to any temperature given in °C before substituting into the ideal gas equation.

Wrong move:

Using mismatched units for pressure and volume with $R = 8.31$

Why:

$R = 8.31$ J K $^{- 1}$ mol $^{- 1}$ requires pressure in Pa and volume in m $^{3}$ ; using incorrect units gives a result with the wrong order of magnitude.

Correct move:

Convert cm $^{3}$ to m $^{3}$ by multiplying by $1 0^{- 6}$ , dm $^{3}$ to m $^{3}$ by $1 0^{- 3}$ , and kPa to Pa by multiplying by $1 0^{3}$ .

Wrong move:

Only listing two assumptions of an ideal gas when asked for all

Why:

CIE 3-4 mark questions for this topic award one mark per assumption, so you will lose marks for incomplete answers.

Correct move:

Memorise all four assumptions and always list every one when asked to describe an ideal gas.

Wrong move:

Claiming high temperature increases deviation from ideal behaviour

Why:

At high temperature, intermolecular forces are negligible because molecules move too fast to be attracted, so behaviour is closer to ideal.

Correct move:

Remember that low temperature and high pressure increase deviation from ideal behaviour for real gases.

6. Quick Reference Cheatsheet

Quantity	Required SI Unit	Common Conversions
Pressure ( $P$ )	Pascal (Pa)	1 atm = 101325 Pa; 1 kPa = 1000 Pa
Volume ( $V$ )	Cubic meter (m $^{3}$ )	1 cm $^{3}$ = 10 $^{- 6}$ m $^{3}$ ; 1 dm $^{3}$ = 10 $^{- 3}$ m $^{3}$
Temperature ( $T$ )	Kelvin (K)	$T (K) = T (°C) + 273$
Gas constant ( $R$ )	J K $^{- 1}$ mol $^{- 1}$	$R = 8.31$ for SI unit calculations
Molar volume at r.t.p.	dm $^{3}$ mol $^{- 1}$	$V_{m} = 24.0$ dm $^{3}$ mol $^{- 1}$

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 · 21
Calculate molar mass of unknown gas
2023 · 12
State ideal gas assumptions
2024 · 22
Compare real gas deviations

What's Next

Mastering the ideal gas equation is a core foundation for all further physical chemistry topics in CIE A-Level, including calculations for gaseous equilibria, enthalpy changes, and reaction kinetics. The concepts of intermolecular forces and deviations from ideal behaviour you learned here connect directly to the study of other states of matter, and help explain bulk properties like boiling point and volatility. Getting comfortable with unit conversions for ideal gas calculations also prevents simple, costly errors in all future physical chemistry questions involving gases, which appear frequently in both multiple choice and structured questions.