The Ideal Gas Equation (Oxford AQA International A Level Chemistry)

Revision Note

Richard Boole

Written by: Richard Boole

Reviewed by: Stewart Hird

Ideal Gas Calculations

Kinetic theory of gases

  • The kinetic theory of gases states that molecules in gases are constantly moving

  • The theory makes the following assumptions:

    • That gas molecules are moving very fast and randomly

    • That gas molecules hardly have any volume

    • That gas molecules do not attract or repel each other (no intermolecular forces)

    • No kinetic energy is lost when the gas molecules collide with each other (elastic collisions)

    • The temperature of the gas is related to the average kinetic energy of the molecules

  • Gases that follow the kinetic theory of gases are called ideal gases

  • However, in reality, gases do not fit this description exactly but may come very close and are called real gases

Ideal gases

  • The volume that an ideal gas occupies depends on:

    • Its pressure

    • Its temperature

  • When a gas is heated (at constant pressure) the particles gain more kinetic energy and undergo more frequent collisions with the container wall

  • To keep the pressure constant, the molecules must get further apart and therefore the volume increases

  • The volume is therefore directly proportional to the temperature (at constant pressure)

Diagram showing the particles in an ideal gas as they are heated alongside a graph showing the proportional relationship between temperature and volume
The volume of a gas increases upon heating to keep a constant pressure (a); volume is directly proportional to the temperature (b)

Limitations of the ideal gas law

  • At very low temperatures and high pressures real gases do not obey the kinetic theory as under these conditions:

    • Molecules are close to each other

    • There are instantaneous dipole- induced dipole or permanent dipole- permanent dipole forces between the molecules

    • These attractive forces pull the molecules away from the container wall

    • The volume of the molecules is not negligible

  • Real gases therefore do not obey the following kinetic theory assumptions at low temperatures and high pressures:

    • There is zero attraction between molecules (due to attractive forces, the pressure is lower than expected for an ideal gas)

    • The volume of the gas molecules can be ignored (volume of the gas is smaller than expected for an ideal gas)

Ideal gas equation

  • The ideal gas equation shows the relationship between pressure, volume, temperature and number of moles of gas of an ideal gas:

PV = nRT

  • P = pressure (pascals, Pa)

  • V = volume (m3)

  • n = number of moles of gas (mol)

  • R = gas constant (8.31 J K-1 mol-1)

  • T = temperature (kelvin, K)

Worked Example

Calculating the volume of a gas

Calculate the volume occupied by 0.781 mol of oxygen at a pressure of 220 kPa and a temperature of 21 °C

Answer:

  1. Rearrange the ideal gas equation to find volume of gas:

    • V = fraction numerator n R T over denominator P end fraction

  2. Check and convert values to the correct units

    • P = 220 kPa = 220 000 Pa

    • n = 0.781 mol

    • R = 8.31 J K-1 mol-1

    • T = 21 oC = 294 K

  3. Calculate the volume the oxygen gas occupies

    • V = fraction numerator 0.781 cross times 8.31 cross times 294 over denominator 220000 end fraction

    • V = 0.00867 m3 = 8.67 dm3

Worked Example

Calculating the molar mass of a gas

A flask of volume 1000 cm3 contains 6.39 g of a gas. The pressure in the flask was 300 kPa and the temperature was 23 °C.

Calculate the relative molecular mass of the gas.

Answer:

  1. Rearrange the ideal gas equation to find the number of moles of gas:

    • n = fraction numerator P V over denominator R T end fraction

  2. Check and convert values to the correct units:

    • P = 300 kPa = 300 000 Pa

    • V = 1000 cm3 = 1 dm3 = 0.001 m3

    • R = 8.31 J K-1 mol-1

    • T = 23 oC = 296 K

  3. Calculate the number of moles:

    • n = fraction numerator 300000 space P a cross times 0.001 space m cubed over denominator 8.31 space J space K to the power of negative 1 end exponent m o l to the power of negative 1 end exponent cross times 296 space K end fraction = 0.12 mol

  4. Calculate the molar mass using the number of moles of gas:

    • n = fraction numerator m a s s over denominator m o l a r space m a s s end fraction

    • molar mass = fraction numerator 6.39 space g over denominator 0.12 space m o l end fraction = 53.25 g mol-1

Examiner Tips and Tricks

To calculate the temperature in Kelvin, add 273 to the Celsius temperature, e.g. 100 oC is 373 Kelvin.

You must be able to rearrange the ideal gas equation to work out all parts of it.

The units are incredibly important in this equation - make sure you know what units you should use, and do the necessary conversions when doing your calculations! 

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Richard Boole

Author: Richard Boole

Expertise: Chemistry

Richard has taught Chemistry for over 15 years as well as working as a science tutor, examiner, content creator and author. He wasn’t the greatest at exams and only discovered how to revise in his final year at university. That knowledge made him want to help students learn how to revise, challenge them to think about what they actually know and hopefully succeed; so here he is, happily, at SME.

Stewart Hird

Author: Stewart Hird

Expertise: Chemistry Lead

Stewart has been an enthusiastic GCSE, IGCSE, A Level and IB teacher for more than 30 years in the UK as well as overseas, and has also been an examiner for IB and A Level. As a long-standing Head of Science, Stewart brings a wealth of experience to creating Topic Questions and revision materials for Save My Exams. Stewart specialises in Chemistry, but has also taught Physics and Environmental Systems and Societies.