DIMENSIONS OF ATOMS AND MOLECULES 47 



from the value of the constant b which appears in Van der 

 Waal's equation 



This constant is introduced in the formula because the molecules 

 occupy an appreciable fraction of the total volume, v, of the gas. 

 It can be shown that 



b^ — Ntro^ 

 3 



A determination of b may be made by observing the departure 

 from Boyle's Law in the behaviour of the gas, or from critical 

 data. 



In both these last cases the " diameter " of the molecule, 

 regarded as spherical in shape, represents the shortest distance 

 between the centres of two molecules when they come into 

 collision, and we would therefore expect that estimates of the 

 diameters by these two methods would be the same. That this 

 is actually the case is shown by such a table as the following, 

 due to Chapman [Phil. Trans. Roy. Soc, 216 A, p. 347) : 



Helium 



Argon 



Krypton 



Xenon 



Hydrogen 



Nitrogen 



Oxygen 



Air 



Carbon dioxide 



In these calculations the molecule has been regarded as a 

 spherical body. Although it may be legitimate to do this in 

 the case of a monatomatic gas, a molecule containing several 

 atoms must be regarded as more complex in shape. The quan- 

 tity TTo-* which enters into the expression for the free path does 

 not, however, depend for its interpretation on the assumption 

 that the molecule is spherical. It is introduced as representing 

 the size of the target which the molecule presents to other 

 molecules approaching it from all directions, and it has a definite 

 meaning even if the molecule is not spherical in form. This 

 will be referred to later in considering Rankine's results on the 

 dimensions of molecules. 



The discovery of the diffraction of X-rays by crystals, and 

 the consequent elucidation of the arrangement of the atoms in a 



