What are some examples of the Avogadro's law?

I've got a nice example for you:

You have a `V_(i nitial)`-L balloon at room temperature (`22^@C`) and normal pressure (`1 atm`). What will the final volume of the balloon be after you remove 1/3 of the initial number of moles present in the balloon and then double the remaining number of moles in the balloon?

So, let's go about solving this using Avogadro's law; according to this, the volume a gas occupies is proportional to the number of gas molecules present in that respective volume - at constant pressure and temperature.

`V/n = c on st ant -> V_1/n_1 = V_2/n_2`, this describes how volume and number of moles are related for transitions between two stages.

Let's break this problem up into two stages: after the removal of moles (1) and after the addition of moles (2). So, the initial number of moles in the balloon was `n`

`V_(i nitial)/n = V_1/(2/3n) -> V_1 = (2/3n * V_(i nitial))/n = 2/3 V_(i nitial)` - for (1)

The number of moles went from `n` to `(n - 1/3*n) = 2/3n` - notice that the volume decreased to match the drop in the number of moles. Now,

`V_1/(2/3n) = V_2/(2 * 2/3n) -> V_2 = (4/3n * V_1)/(2/3n) = 2V_1` - for (2)

The number of moles doubled - from `2/3n` to `4/3n`, which caused the volume to double. If we express this in terms of `V_(i nitial)` and `n`, we get

`V_(f i nal) = V_2 = 2 * V_1 = 2 * 2/3V_(i nitial) = 4/3 V_(i nitial)` and
`n_(f i nal) = 4/3n`

Again, an overall increase in the number of moles caused the volume to match this increase.

Here's a video of other Avogadro's law examples;

http://socratic.org/chemistry/the-behavior-of-gases/gas-laws/avogadros-law