The approximate intermolecular distance can be found by taking the molecules at an instant of time to be uniformly distributed in space with number density n0. Place a cube around each molecule in the gas. Then each molecule sits at the center of a cube of side length d. The number of these cubes per unit volume is n0. The volume of one of them is d3 = 1/n0; or d ~ 1/n/3 = 3.34 x 10-9 m = 3.34 nm (at STP). Note that the radius of a molecule r0 is only a few times 10-10 m = 0.1 nm (several tens of times less than the intermolecular distance). In a liquid or a solid intermolecular distances are on the order of the molecular sizes (see Table 2.1).
Atomic refresher The Bohr atom has radius a = h2e0/nmeQ^, where €0 = 8.85 x 10- Fm (permittivity constant), h = 6.63 x 10-34J s (Planck's constant), Qe = 1.60 x 10-19 C (electron charge), me = 9.11 x 10-31 kg (electron mass). The Bohr radius for a hydrogen atom is a = 5.29 x 10-11 m = 0.0529 nm. Most high school or college chemistry books describe the Bohr model of the hydrogen atom.
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