198 Critical Phenomena of some Substances and Mixtures. 



better shown in the following manner : the condition for the 

 niin. of ajb x may be written thus : — 



_1 B«5 I "bbx _ q 



ff* d# b ~dx ~ ' 



and the condition for point B 



1 "da x 2 d&a 



~dx '3b x ^x 



= 0. 



When ^ > (in which case also ^ > 0), as is the 



case in the three combinations investigated, the first equation 

 gives a higher value of x than the second *. 



40. But another question arises — What happens to the 

 maximum at very low temperatures ? This can be found 

 from the same equation given above (in 39) by putting v x 

 (volume of the liquid) equal to b x and neglecting l/v 2 . The 

 result is the same equation as holds for the min. cr tempera- 

 ture. Probably therefore, if the equation does not mislead 

 us here too much, approximately the same mixture which has 

 a min. cr. temp, will be the mixture of maximum vapour- 

 pressure at low temperatures. We may therefore expect the 

 mixtures of C 2 H 6 with N 2 0, C 2 H 2 , and C0 2 which contain 

 about 0*5 of each to have a max. vapour-pressure at low tem- 

 peratures. By raising the temperature this maximum moves 

 towards the substance of higher vapour-pressures (N 2 0, C 2 H 2 , 

 and C0 2 ). As we saw for C 2 H 2 -C 2 H 6 , this motion has been 

 very small, the points B and A almost coinciding. It is not 

 impossible that for other mixtures which have a max. pressure 

 at low temperature the maximum reaches one of the com- 

 ponents at higher temperature and thus disappears. Those 

 mixtures would still have a minimum for a x /b x and, if the 

 real critical temperatures are not too much above the hypo- 

 thetical ones, they would also show a minimum critical 

 temperature. 



Instances of maximum vapour-pressures are : — ethyl alcohol 

 and carbon disulphide (Berthelot f), chloroform and carbon 

 bisulphide (Guthrie J), ether and carbon disulphide (Guthrie), 

 propyl alcohol and water (Konowalow §). Some of these 

 combinations would be worth investigating at higher tempera- 

 tures up to the critical condition. 



* Van der Waals, Kon. Ah. 29 June, 1895, pp. 11-12. 

 t Berthelot, Comptes Renclus, lxvii. p. 430. 

 \ Guthrie, Phil. Mag. (5) xviii. pp. 513. 

 § Konowalow, Wied. Ann. xiv. p. 34. 



