# What are some examples of the Avogadro's law?

Dec 27, 2014

I've got a nice example for you:

You have a ${V}_{i n i t i a l}$-L balloon at room temperature (${22}^{\circ} C$) and normal pressure ($1 a t m$). 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.

$\frac{V}{n} = c o n s t a n t \to {V}_{1} / {n}_{1} = {V}_{2} / {n}_{2}$, 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 $n$

${V}_{i n i t i a l} / n = {V}_{1} / \left(\frac{2}{3} n\right) \to {V}_{1} = \frac{\frac{2}{3} n \cdot {V}_{i n i t i a l}}{n} = \frac{2}{3} {V}_{i n i t i a l}$ - for (1)

The number of moles went from $n$ to $\left(n - \frac{1}{3} \cdot n\right) = \frac{2}{3} n$ - notice that the volume decreased to match the drop in the number of moles. Now,

${V}_{1} / \left(\frac{2}{3} n\right) = {V}_{2} / \left(2 \cdot \frac{2}{3} n\right) \to {V}_{2} = \frac{\frac{4}{3} n \cdot {V}_{1}}{\frac{2}{3} n} = 2 {V}_{1}$ - for (2)

The number of moles doubled - from $\frac{2}{3} n$ to $\frac{4}{3} n$, which caused the volume to double. If we express this in terms of ${V}_{i n i t i a l}$ and $n$, we get

${V}_{f i n a l} = {V}_{2} = 2 \cdot {V}_{1} = 2 \cdot \frac{2}{3} {V}_{i n i t i a l} = \frac{4}{3} {V}_{i n i t i a l}$ and
${n}_{f i n a l} = \frac{4}{3} n$

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;