How far would an air particle travel in a soap bubble in 1 second?

Imagine the air in a small soap bubble, about the size of the tip of your little finger. All those little molecules dashing about bumping into each other.

Watch the bubble for one second. Each molecule does a crazy zig-zag journey, colliding with other molecules and bouncing off the sides of the bubble. Suppose that you could measure the length of each of these journeys, and add them up. What do you think they would come to?

What is the total distance travelled by the air molecules inside a small bubble in one second? A hundred metres? A hundred kilometres? A thousand kilometres?

The actual answer is...one million light-years!
You don’t believe me? Read on...

To work out the total distance, we need to multiply the average speed of the air molecules by the number of molecules inside the bubble.

Physics textbooks tell us that the average speed is roughly 500 metres per second.

To work out how many molecules are in the bubble, start with the fact that one mole of a perfect gas occupies 22,400 cubic centimetres at everyday temperature and pressure.

Our bubble contains about one cubic centimetre of air, so there are 1/22,400 moles of gas in there.

Now one mole of anything contains 6 x 10^23 molecules (Avogadro’s number).

So the number of molecules in the bubble is 6 x 10^23 divided by 22,400, which comes to about 2.5 x 10^19 molecules.

And if each molecule travels 500 metres in one second, the total distance travelled is about 10^22 metres.

As a light year is about 10^16 metres, this means that the total distance travelled in one second by the molecules in the bubble is 10^6 (a million) light years.

What this result brings home is not the speed of the molecules – Concorde flew faster – but just how many of the little blighters there really are.