The Ideal Gas Equation regularly fails. Johannes Diderik van der Waals was a school teacher who completely changed our understanding of the physics of gases.

In this video, we take a look at the van der Waals Gas Equation - a brilliant upgrade to the Ideal Gas Equation, which uses sound logical arguments to improve on the Ideal Gas Model.

To understand the changes made by van der Waals, we start by understanding the Ideal Gas Equation.It tells us that the product of the pressure and volume of a gas is equal to the product of the amount of gas (in moles), the temperature of the gas (in kelvin), and the molar gas constant, R. To arrive at this equation, physicists had to make a couple of somewhat silly assumptions.

Firstly, they assumed that all gas particles were infinitesimally small, or in other words that they had no volume. This isn't realistic, as all gas particles have some real volume, albeit quite small. The ideal gas equation therefore only works when the GAS volume is much much bigger than the volume of the PARTICLES combined.

The second assumption of the Ideal Gas model is that there are no inter-particle interactions (such as due to electromagnetic forces between particles). The particles only interact when they collide with each other, and not by just passing close by to each other. Again this is unrealistic as electromagnetic forces can sometimes be quite strong between gas particles. So the Ideal Gas model only works for gases with very weak interparticle interactions.

Here's where van der Waals comes into the picture. He made two modifications to the Ideal Gas model so it would work in many more scenarios.

Firstly, he replaced the volume per mole term with (volume per mole - b). The quantity "b" is the molar volume of just the particles of the gas (i.e. not the space they occupy). By subtracting this from the space the occupy, we now account just for the available space BETWEEN molecules, and also encode into our mathematics the idea that these particles have actual volume that isn't zero.

Secondly, he replaced the pressure term with (pressure + a/(molar volume)^2). This term accounts for the reduced pressure experienced by the container of the gas, because the particles of the gas exert forces on each other even when they aren't colliding. The logic is that particles close to the centre of the container "pull in" particles near the walls, thus reducing the forces with which the particles near the walls can hit the walls. And the more particles there are, the more the pressure reduces. The quantity "a" is just the proportionality constant.

We also see that in specific scenarios (where the Ideal Gas model worked anyway) the van der Waals gas equation actually reduces to (or becomes) the Ideal Gas Equation - success!

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Timestamps:
0:00 - Johannes Diderik van der Waals
1:40 - The Ideal Gas Equation and its Assumptions
4:15 - First Modification: Volume
6:35 - Second Modification: Pressure
9:50 - The van der Waals Gas Equation is Just... Better!