t 116 ] 



X. Observations on Mixtures with Maximum or Minimum 

 Vapour- Pressure. By J. P. Kuenen and W. G. Robson*. 



IN previous papers f an account was given of the properties 

 of certain mixtures which have a maximum in their 

 vapour-pressures at a given temperature and a minimum in 

 their critical temperatures; and more recently J a case was 

 investigated in which a minimum in the vapour-pressures 

 went hand in hand with a maximum critical temperature. 



This combination of corresponding properties follows as a 

 result from van der Waals' theory of mixtures, if the mix- 

 tures are assumed to have the simple characteristic equation 

 similar to van der Waals* well-known equation for simple 

 substances. This assumption involves the more general one 

 that the mixtures are normal, i. e. without association of 

 molecules, although the two suppositions are by no means 

 identical ; a simple substance may disobey van der Waals' 

 law (as it invariably does) and still be normal, as testified by 

 its obeying the law of corresponding states. 



It will be convenient to briefly restate the theoretical 

 conclusions on the above assumption. 



For mixtures which have a maximum vapour-pressure for 

 a given composition at a low temperature, the maximum 

 shifts towards the component with the higher vapour-pres- 

 sures, and may either disappear or remain up to the critical 

 condition. These mixtures have at the same time a minimum 

 in their " hypothetical " critical temperatures — i. e. the critical 

 temperatures which they would have if they did not split up 

 into mixtures of different composition but remained homo- 

 geneous, — at a composition coinciding with the composition of 

 maximum vapour-pressure at low temperatures, and have 

 accordingly a tendency towards a minimum in their real 

 critical temperatures. 



If there is a minimum vapour-pressure at a low tempera- 

 ture, the minimum shifts towards the component with the 

 lower vapour-pressures, and may disappear or remain up to 

 the critical point. These mixtures have a maximum critical 

 temperature at a composition near that of the minimum 

 vapour-pressure at low temperatures. 



If the mixtures are abnormal either because one or both 

 the components are so, or because of mutual association of 

 the two kinds of molecules, the above rules cannot be ex- 

 pected to hold good. A maximum vapour-pressure may be 

 due not to the low mutual attraction of the two substances, 



* Communicated by the Authors. 



t Phil. Mag. [5] xl. p. 173; xliv. p. 174. 



t Ibid. [6] i. p. 593. 



