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The distance between particles in a gas can be calculated using a common approximation in chemistry, that the volume of an ideal gas at STP is 22.4 Litres/mol. For simplicity, we assume that the gas is Helium.

As there are 6x1023 helium atoms in a mole of helium gas, the volume occupied by a helium atom is 22.4/6x1023 = 3.7x10-23 litres. A litre is 10x10x10cm, so a helium atom occupies a cube of volume 3.7x10-20 cm3, or a cube of side 3.3x10-7cm. If we assume that the helium atom sits, on average, at the centre of the cube, then the distance to the helium atom at the centre of an adjacent cube is 2x(cube edge length/2) = 3.3x10-7cm, or 3.3 nanometres.

This distance will vary hugely by orders of magnitude, depending upon the conditions. For hotter gases, the distance will increase, as the volume increases. For gases under pressure, the distance will be less.

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