146 Physical Properties [OH. vi 



163. If we could calculate the term 2Sr< (r) in equation (335) for any 

 law of intermolecular force, we should have a complete knowledge of the 

 corrections to be applied to Boyle's Law. Unfortunately this is not possible 

 even in the simplest cases. 



164. If there were no intermolecular forces, the probability that the 

 centre of molecule A should lie at a distance between r and r + dr from the 

 centre of B would be 



(836) . 



In this expression 4>7rr*dr is the volume of a spherical shell of radius r, 

 and we neglect the possibility of B being within a distance r of the boundary 

 of the containing vessel, as we legitimately may if r is sufficiently small. 

 The probability of the centre of A lying within a distance between r and 

 r + dr from the centre of C is also equal to expression (336), so that the 

 probability of the centre of A lying within this range of distance from the 

 centre of some other molecule is (Nl) times expression (336), except for 

 a correction arising from the possibility of two of the (N 1) shells of radius 

 r which surround these molecules intersecting. Ignoring this correction for 

 the present, and replacing N 1 by N, it follows that the number of pairs of 

 molecules of which the centres lie at a distance intermediate between r and 

 r + dr apart, would, in the absence of intermolecular forces, be 



(337). 



When, however, molecules at a distance r attract one another with a force 

 < (r), it will be seen, upon examination of the results of 85, that expression 

 (337) must be modified in two ways. The probability of finding two mole- 

 cules at a distance r apart is, by 85, less than the probability of finding 

 the same two molecules at a distance oo apart (oo here denoting any dis- 

 tance great enough for the molecules to be out of range of each other's 

 action) in the ratio 



e * r 



And again the probability of finding two molecules at a distance oo apart is 

 greater than it would be if there were no intermolecular forces, because some 

 positions for the molecules, not at great distances apart, are less likely, on 

 account of the intermolecular forces, than they would otherwise be. The 

 former consideration requires us to multiply expression (337) by a factor 



e -2hj r <!>(r)dr ^ (338); 



the latter requires us to modify the factor -^r in expression (337), which is 

 only accurate if all positions of the molecules are equally probable. 



