# Ideal Gases

> Chemistry SL · IB Diploma Programme SL
> Source: https://www.owlsprep.com/study/ib-chemistry-sl-u4-ideal-gases/

This module covers ideal gas assumptions, the unified ideal gas law, molar volume at IB STP, and real gas deviations, with step-by-step calculation practice aligned to IB SL mark schemes.

**Prerequisites:** [Understand mole concept and basic stoichiometric ratios](https://www.owlsprep.com/study/ib-chemistry-sl-u4-mole-concept/); Convert standard units of temperature, pressure and volume correctly

## Learning objectives

- State the 5 core assumptions of the ideal gas kinetic molecular model
- Apply the ideal gas law to solve for unknown pressure, volume, moles or absolute temperature
- Use the IB-defined molar volume at STP for gas stoichiometry calculations
- Explain conditions that cause real gases to deviate from ideal behaviour

## Core Assumptions of the Ideal Gas Model

The ideal gas model is a simplified framework derived from kinetic molecular theory that describes gas particle behaviour, eliminating complex real-world interactions to enable predictable, consistent calculations.

**Ideal Gas** — A hypothetical gas that perfectly follows all 5 kinetic molecular theory assumptions for gas particle behaviour, with no intermolecular forces and negligible total particle volume relative to the container.

- Gas particles have negligible total volume compared to the total container volume
- There are no attractive or repulsive intermolecular forces between gas particles
- Gas particles move in constant, random, straight-line motion
- All collisions between gas particles and container walls are perfectly elastic, with no net kinetic energy loss
- The average kinetic energy of gas particles is directly proportional to absolute temperature in Kelvin

> **mnemonic**
>
> Use the acronym NICE V to memorise all 5 assumptions: No intermolecular forces, Elastic collisions, Random motion, KE proportional to T, Negligible Volume.

**Check your understanding**

Test your understanding of core ideal gas rules

1. Which of the following is NOT a valid assumption of the ideal gas model?

   - Particles have no intermolecular forces
   - Particles have zero mass
   - Collisions are perfectly elastic
   - Particle volume is negligible

   *Why:* Ideal gas particles have mass, just negligible total volume relative to the container.

## The Ideal Gas Law and Unit Consistency

Combining Boyle’s Law, Charles’s Law, Avogadro’s Law and Gay-Lussac’s Law gives the unified ideal gas equation, which relates all four state variables for a fixed amount of gas.

$$PV = nRT$$

- P = pressure, measured in Pascals (Pa)
- V = volume, measured in cubic metres (m³)
- n = amount of substance, measured in moles
- R = universal gas constant = 8.314 J mol⁻¹ K⁻¹
- T = absolute temperature, measured in Kelvin (K)

> **warning**
>
> IB exam markers will deduct marks if you use Celsius instead of Kelvin for T. Always add 273.15 to Celsius values to convert to absolute temperature.

**Worked example:** Calculate the pressure exerted by 0.250 mol of helium gas in a 0.010 m³ container at 25 °C.

1. First convert temperature from Celsius to Kelvin:

   $$T = 25 + 273.15 = 298.15 \text{ K}$$
2. Rearrange the ideal gas law to solve for pressure P:

   $$P = \frac{nRT}{V}$$
3. Substitute all known values into the equation:

   $$P = \frac{0.250 \times 8.314 \times 298.15}{0.010}$$
4. Calculate the final pressure, rounded to 3 significant figures:

   $$P = 61900 \text{ Pa} = 61.9 \text{ kPa}$$

**Exam command terms**

IB exam command terms for this topic carry specific mark requirements:

- **Show that** — You must write every substitution step to earn full marks, no skipped working

- **Calculate** — Final answer must have correct units and 3 significant figures to match given data

## Molar Volume of an Ideal Gas at STP

IB defines standard temperature and pressure (STP) as 273 K and 100 kPa, not the older 1 atm definition. Under these conditions, one mole of any ideal gas occupies exactly 22.7 dm³, a value you can use directly for stoichiometry calculations.

**Molar Volume** — The volume occupied by one mole of an ideal gas at specified temperature and pressure, equal to 22.7 dm³ mol⁻¹ at IB STP.

*Notation:* Vₘ

**Worked example:** Calculate the volume of carbon dioxide produced when 5.0 g of calcium carbonate fully decomposes at STP.

1. Write the balanced decomposition reaction:

   $$CaCO_3(s) \rightarrow CaO(s) + CO_2(g)$$
2. Calculate moles of CaCO₃, molar mass = 100.09 g mol⁻¹:

   $$n(CaCO_3) = \frac{5.0}{100.09} = 0.050 \text{ mol}$$
3. 1:1 mole ratio gives n(CO₂) = 0.050 mol
4. Multiply moles by molar volume at STP:

   $$V(CO_2) = 0.050 \times 22.7 = 1.1 \text{ dm}^3$$

## Deviations of Real Gases from Ideal Behaviour

Real gases only approximate ideal behaviour at low pressure and high temperature. Two extreme conditions break the core ideal gas assumptions, leading to measurable deviations from PV = nRT predictions.

- At high pressure, gas particles are forced very close together, so their total volume is no longer negligible relative to the container volume
- At low temperature, particle kinetic energy drops, so weak intermolecular forces become significant, slowing particles near collision points

> **info**
>
> IB exam questions almost always use nitrogen, oxygen or carbon dioxide as examples of real gases that deviate from ideal behaviour under non-standard conditions.

## Common pitfalls

- **Wrong:** Using Celsius instead of Kelvin for temperature in PV=nRT
  - Why it fails: Celsius values give negative or incorrectly low pressure/volume outputs, losing 1-2 calculation marks
  - Correct: Always convert temperature to Kelvin first before substituting into the ideal gas law
- **Wrong:** Using 22.4 dm³ mol⁻¹ as molar volume at STP
  - Why it fails: IB uses the updated 100 kPa STP definition, not the old 1 atm standard, so 22.4 is incorrect
  - Correct: Memorise 22.7 dm³ mol⁻¹ as the IB specified molar volume at STP
- **Wrong:** Using units of dm³ for volume directly in PV=nRT
  - Why it fails: The gas constant R = 8.314 uses m³, so dm³ values will give answers 1000x too small
  - Correct: Convert all volume values to m³ by dividing dm³ by 1000 before calculation
- **Wrong:** Stating that real gases deviate because particles have mass
  - Why it fails: Ideal gas assumptions do not state particles have zero mass, only that their volume is negligible
  - Correct: Link deviations explicitly to non-negligible particle volume and existing intermolecular forces
- **Wrong:** Forgetting to give final answers to 3 significant figures
  - Why it fails: IB mark schemes penalise answers that do not match the precision of given data
  - Correct: Round all final calculation outputs to 3 significant figures unless specified otherwise

## Cheatsheet

| Quantity | SI Unit | Conversion Factor | Ideal Gas Value at STP |
| --- | --- | --- | --- |
| Pressure | Pascal (Pa) | 1 atm = 101325 Pa, 1 kPa = 1000 Pa | 100000 Pa |
| Volume | Cubic metre (m³) | 1 dm³ = 0.001 m³ | 0.0227 m³ mol⁻¹ |
| Temperature | Kelvin (K) | °C + 273.15 = K | 273 K |
| Gas Constant R | J mol⁻¹ K⁻¹ | Fixed value | 8.314 |

## What's next

Mastering ideal gas calculations is a critical foundational skill for higher difficulty stoichiometry questions that combine gas volume data with titration and percentage yield calculations, which make up 15-20% of the IB SL Paper 2 marks. You will next apply these rules to solve reacting gas volume problems using Avogadro’s law, then move on to explore the properties of liquids and intermolecular forces in the periodicity unit. Regular practice of unit conversion and full working for calculation steps will eliminate avoidable mark losses in your exam.

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