The ideal gas equation is an amalgamation of Boyle’s law, Charles’s law and Avogadro’s law and it describes the behaviour of an ideal gas.
PV = nRT
P is pressure (Pa); V is volume (m3);
n is the number of moles; R is the gas constant (8.314 JK-1mol-1); T is temperature (k)
We can use it to calculate the volume or pressure or temperature of a fixed amount of gas, or to determine the effect of changing these conditions on the behaviour of a gas – essentially we are able to predict the behaviour of a gas under non-standard conditions.
It is important that we understand that we are talking about ideal gases here, in which case we are making two assumptions:
1. there are negligible intermolecular forces between particles
2. the size of the particles are negligible compared with the size of the container
At high pressures and low temperatures these assumptions hold less true.
Intermolecular forces may become significant if the particles are very strongly attracted to each other, causing them to collide less often with the sides of the container and so the pressure of the real gas is less the ideal model predicts.
i.e. gases with strong intermolecular forces will deviate most from ideal gas behaviour as predicted by our model / calculations using the ideal gas equation.
https://ed.ted.com/lessons/1207-1-a-bennet-brianh264 is a great introduction to the gas laws!
Where does the ideal gas equation come from?
Boyle’s law and Charles’s law describe how the pressure, volume and temperature of a gas are related to each other.
- Boyle’s law
Boyle’s law states that at constant temperature, the volume of fixed amount of an ideal gas is reduced in proportion as the pressure increases. If the volume is halved, the pressure doubles but it is NOT a linear relationship.
Pressure is found to be proportional to 1/V in a linear relationship.
This ‘constant’ is a proportionality constant – it is the ratio between two directly proportional quantities (in this case, between P and 1/V).
- Charles’s law
Charles’s law states that the volume of a fixed amount of gas at constant pressure is proportional to the absolute temperature. If the absolute temperature doubles, the volume doubles in a linear relationship (the gas particles have more kinetic energy at higher temperatures, there are more collisions and they occupy a greater volume).
- Avogadro’s law
Avogadro’s law states that equal volumes of gases at constant temperature and pressure contain equal numbers of molecules. The volume of an ideal gas depends only on the number of moles of gas regardless of what that gas is and it explains the idea of a molar volume.
Combining these three equations gives us the ideal gas equation:
You need to know how to convert units …
| Conversion | Function |
|---|---|
| kPa ⇾ Pa | x 103 |
| °C ⇾ K | + 273 |
| dm3 ⇾ m3 | x 10-3 |
| cm3 ⇾ m3 | x 10-6 |
Let’s looks at a simple calculation …
What is the pressure of 5.6g of methane, CH4, in a container that has a volume of 40cm3 at 35°C?
Practice questions …
You can find a set of exam style questions on all the gas calculations you are likely to meet (relevant for all A level exam boards) by following the link 😎.