• # Question: how many particles are there in an avarge sized empty room

Asked by 279smbd53 to Aaron, Abbey, Keith, Natalie, Pete on 16 Nov 2015.
• Keith Franklin answered on 16 Nov 2015:

If you mean “How many gas molecules are there in an average room?” then we can calculate that:

600000000000000000000000 molecules of gas occupy 22.4 litres (6 with 23 zeros)

An average room is 2.5m x 5m x 5m = 62.5 cubic metres

22.4 litres = 0.02 cubic metres

62.5 / 0.02 = 3125

3125 x 600000000000000000000000 =
2 000 000 000 000 000 000 000 000 000

(why don’t you try to check my calculation – I might have made a mistake!)

• Aaron Boardley answered on 16 Nov 2015:

ANSWER: about 6,000,000,000,000,000,000,000,000,000, or six octillion particles (depending on the size of the room).

WORKING OUT:
First, let’s work out what we mean by ‘average’ sized. Perhaps if we think of my office, or your classroom, how big is this? Perhaps 8 metres wide, 10 metres long, 3 metres high? – Let’s use this as our size. The volume of the room is therfore 8 x 10 x 3 = 240 cubic metres (m^3) – which, if the classroom is empty, is all air.

In chemistry, we learn that one ‘mole’ of particles takes up 24 cubic decimetres (dm^3) when it is a gas (at normal temperature and pressure)

There are 1000 dm^3 in 1 m^3, so our room has 240 x 1,000 = 240,000 dm^3 of air in it.

Therefore, it was 240,000 / 24 = 10,000 moles of air in it.

A ‘mole’ is a large number of particles – the number is known as Avogradro’s constant, which is approxmiately 600,000,000,000,000,000,000,000 (6 with 23 zeroes, or 6 x 10^23). There are 6 x 10^23 particles in one mole of gas.

Therefore, in 10,000 moles of air there will be 10,000 x 6 x 10^23 = 6 x 10^27 particles.

Avogadro’s constant and the amount of space a mole of gas takes up are fixed – so this answer is really dependent on how big your room is. You may have noticed I deliberately picked a room with easy dimensions to work with!

• Natalie Garrett answered on 16 Nov 2015:

Maybe this is a trick question since you specified that the room is empty, therefore there’s no air in it (in other words, it’s a vacuum).

So in this case there would be no particles!