 # Ideal Gases and Real Gases

## Ideal Gases

Ideal gases are gases which are not influenced by real world factors like intermolecular forces. They are a concept that developed over hundreds of years and follow a law known as the ideal gas law, which is a combination of three other gas laws which were all independently discovered. These three gas laws are: Boyle’s law, which states that at a constant temperature, the volume and pressure of a gas are inversely proportional (P1V1=P2V2); Charles’ Law, which states that the volume of a gas is directly proportional to its absolute temperature at constant pressure (V1/T1 = V2/T2); and Avogadro’s law, which states that at an equal temperature and pressure all gases have the same number of moles per liter (n1/V1 = n2/V2). When combined, these form the ideal gas law (PV = nRT), which was compiled by Dmitri Mendeelev.

P = pressure, V = volume, n = number of moles of the gas, R = the universal gas constant (8.314 kPa L mol−1 K−1) and T = absolute temperature (in Kelvin). If any of the three variables are known, the law can be used to find the fourth. All three of the laws that made up the ideal gas law were found through experimentation and, like them, the ideal gas law can be proved through experiments but also be proved theoretically and mathematically.

All ideal gases follow the ideal gas law but not all gases are ideal. There are three important approximations of an ideal gas:

1. The only interactions between particles are perfectly elastic collisions.
2. Particles do not occupy any space (they have no volume).
3. There aren’t any intermolecular forces affecting movement of particles within the gas.

At high temperatures and low pressures, these are pretty good approximations, as all particle interactions become negligible due to the increase in volume, leading to lots of ‘space’ between the particles. Also, the increase in kinetic energy causes other intermolecular forces to have less of an effect. At low temperatures and high pressures, these intermolecular forces become significant and the gases no longer act in an ideal manner. At STP (standard temperature and pressure of 0°C and 100 kPa), one mole of an ideal gas will have a volume of 22.4 litres. Sadly, the ideal gas law runs into some issues when considering real life situations: real gases have intermolecular forces and particles that occupy space.

## Real Gases

Real gases are gases that do not follow the ideal gas law perfectly. This is especially noticeable in high pressures and low temperatures, but also often outside of these circumstances and it usually is due to the fact that volume and pressure do not change proportionally even the gas is sealed in a lab (same number of moles) and at a constant temperature. This is due to intermolecular forces and the space that is taken up by Deviations in the Ideal Gas Law

particles in a gas. It took scientists a long time to figure this out, since molecules were not widely accepted to be real until recently. The issue with the ideal gas law in many situations is that it does not account for the space taken up by the particles in the container, so a constant “b” is introduced based on the size of the particles in the gas. In an ideal gas, the space taken up by the molecules in negligible but that is not the case with real gases. In real gases, the pressure must also be adjusted to account for the intermolecular forces, such as the attraction between the particles, introducing the constant “a”. The values of a and b depend on the specific gas, which fixes the distortion of the inverse proportionality of volume and pressure caused by intermolecular forces and the volume occupied by the molecules themselves. These changes to the equation can be attributed to a 19th century scientist Johannes Diderik van der Waals, and it is therefore called the van der Waals equation. The van der Waals equation for real gases