Maximum or Minimum Vapour-Pressure, 129 



Further consideration of the pressure-temperature diagram 

 leads to some important results. On the three-phase curve 

 the gaseous mixture is in equilibrium both with the liquid 

 mixture and with the solid phase; i.e. with pure solid 

 -carbon dioxide. It follows that the partial pressure of 

 carbon dioxide in the vapour must be approximately the 

 vapour-pressure of the solid at each temperature. As this 

 quantity is known, the composition of the vapour-phase may 

 be deduced from the pressures. We may test this conclusion 

 at the point M, where the maximum curve reaches the three- 

 phase curve, considering that for the maximum mixture the 

 composition of the vapour is the same as for the liquid, and 

 thus the same as the composition of the mixture as a whole. 

 The pressure at M is 4*94 atmospheres ; the pressure of solid 

 carbon dioxide at the same temperature ( — 65°-15) being 

 '212 atmospheres : the maximum mixture thus contains 

 2*72/4'94='55 parts of carbon dioxide, which is in exact 

 accordance with our former results. 



We are thus enabled to determine by the same method 

 the composition of the gas-phase all along the three-phase 

 curve. In this manner we find at 0, the top of the curve, 

 3*85/5 , 33 = , 72 parts of carbon dioxide and '28 parts of 

 ethane. In our experiments we were not able to observe the 

 temperature and pressure at which the gas was in equilibrium 

 with a trace of liquid and of solid, so that we do not know 

 where the gas curve for the mixture *30 cuts the three-phase 

 curve. We cannot therefore compare the result about the 

 point with experiment. 



An approximate value for the volume of the vapour may 

 now be found from the composition and the pressure by 

 applying the gas laws, and we are thus enabled to determine 

 the heat of transformation of the mixture on the three-phase 

 curve from the formula 



H = tJv, (1) 



where V represents the change of volume of the transforma- 

 tion corresponding to the heat H. 



The value of H is of special interest at M, where, as we 

 saw, vapour and liquid have the same composition ; the trans- 

 formation at this point thus consists of the evaporation of 

 the liquid mixture as a whole, the solid taking no part in the 

 transformation. H in this case is simply the latent heat of 

 evaporation of the mixture, and V the difference between 

 vapour and liquid volumes, precisely as with pure substances. 

 It is clear that we might apply the same calculation to any 

 other point of the maximum curve. 



Phil. Mag. S. 6. Vol. 4. No. 19. July 1902. K 



