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Kinetic Theory : Molecular Diameter



In spite of the high values of the molecular speeds the diffusion of one gas into another takes place slowly. Previous experiments shows that bromine vapour diffuses upwards only very slowly, although at 17° the speed of the bromine molecules must be:

metres per sec.

The rate of bulk motion of the bromine vapour is not more than about one hundred thousandth of the molecular speed.

The reason is that the molecules of bromine do not move uninterruptedly in straight lines; they collide with one another and with the air molecules, and a great number of them must be deflected back again to the region from which they started. The molecules describe zigzag paths, and it is only after making a great number of collisions that a molecule can get appreciably forward.

The same effect is familiar to us when we walk rapidly into a crowd of people, and if we were thrown back every time we happened to encounter anyone else our progress would be still further impeded.

It is clear that this effect is due to the finite size of the molecules; if they were mere points, occupying no space, they would not offer any obstacles to the motions of other molecules. From the rate of diffusion the diameters of molecules may be calculated; the diameter of the oxygen molecule, assumed spherical, is of the order of 3 x 10-8 cm. = 3 A.U.

Platinum wires can be drawn to 10-4 cm. in diameter; ordinary gold-leaf is 10-5 cm. thick; the black parts of soap-films are 6 x 10-7 cm. thick, and oil-films on water are only 10-7 cm. thick, or even less.

The distance of the nearest fixed star is reckoned in light-years, 1 light-year being the distance traversed by light (3 x 1010 cm./sec.) in a year, or 1018 cm. It is therefore incorrect to regard the minuteness of molecules as the counterpart of the vast interstellar distances. The molecules are small, it is true-too small to be visible (when their presence would be confusing), but their refinement has not been overdone.


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