﻿On the Ideal Refr activities of Gases. 29 



gram-molecular mass, M, o£ a gas enclosed in a volume v, 

 we have 



* = * (4) 



V 



Equations (2), (3), and (4) then enable us to express the 

 variation of fi for a given gas for a definite wave-length, 

 with temperature and pressure ; for from (2) and (4) we 

 have 



M * fK\ 



V =J=i> ' (5) 



and by substituting the value of v from (5) in (3) we further 

 have : 



If the value of fi for a given wave-length for a gas is 

 known at a standard temperature and pressure, and, in 

 addition, the critical constants of the gas, then all the mag- 

 nitudes in (6) are known with the exception of k. The 

 value of k is then determined by solution of (6). If this 

 value of k is then substituted in (6) we obtain a cubic equa- 

 tion in (fi — 1), the solution of which gives the value of juu at 

 any desired temperature and pressure. This equation cannot, 

 however, hold strictly up to the critical point, where the 

 applicability of Berthelot's equation fails *. 



It is easily seen from the theoretical considerations, on 

 which the Lorentz-Lorenz equation is based, that the problem 

 is complicated by the deviations of real gases from Avogadro's 

 hypothesis. D. Berthelot | has shown that these deviations 

 lead to the introduction of a correcting term, which, for a 

 given temperature and pressure, can be calculated from his 

 characteristic equation. This equation then assumes the 

 form 



p.v = B,.T. |i +i |^.^. t (1^6t) 2 J 3 . . (7) 



where R denotes the value of the gas-constant for the par- 

 ticular choice of the units of p and of v; ir and r denote the 

 ratios p/p c and T c /T respectively, where p c and T c denote 

 the critical pressure and critical temperature respectively. 



* Cf. Nernst, Theoretisehe Chemie, 7th edit. p. 241 (1918). 



t Berthelot, loc. cit. p. 52 : Nernst, he. cit. 



