• 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.
    • Photo: Keith Franklin

      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!)

    • Photo: Aaron Boardley

      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!

    • Photo: Natalie Garrett

      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!

Comments

  • Photo: Aaron

    Aaron commented on :

    I notice Keith and I worked out our answer at the same time – and that I have forgotten precisely how much space a mole of gas takes! Oh well, I was close enough for an estimate 🙂 – my room was a bit larger, too, but you’ll see that either way you are talking several octillion particles!