Avogadro's Law

Avogadro's Law, named after Amedeo Avogadro, was originally worded as Avogadro's hypothesis which stated that equal volumes of gases at identical pressures and temperature contain equal numbers of particles.

Stated as a law, which matches the other laws in form, Avogadro's Law would be that:

The volume of a gas in a flexible container at a given pressure and temperature is directly proportional to the amount of gas present.

In simpler English: as the amount of gas increases, so does the volume.

This can be stated mathematically:

or graphically:

So, why are the amount and volume of a gas proportional?

The answer to this question requires us to recall both the Un-named law and Boyle's law (in the same way that Charles' Law relied on Gay Lussac's Law and Boyle's Law).

Again, we will have to imagine our gas trapped in a container with very flexible (but not stretchy) walls, like a hot air balloon.

If the balloon is not getting larger or smaller when we start, then we know that the forces on the walls are balanced – that is, the air inside the balloon is pushing out on the walls exactly as hard as the atmosphere is pushing in on the walls.

As more air is put into the balloon, there are more particles colliding with the walls of the balloon, so the pressure inside the balloon rises (Un-named Law). When this occurs, the forces become unbalanced – the air inside the balloon is pushing out harder than the atmosphere is pushing in, and the walls are pushed out.

This increase in volume will cause a decrease in pressure, since it will take longer for the particles to move from wall to wall (Boyle's Law). This increase in volume will continue until the pressure inside the balloon is once again equal to the pressure outside and the forces on the walls are balanced.

In the end, the pressure will be what it was at the beginning (as if it had never changed), meaning that only the amount and volume will have changed measurably.