• 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).

      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!