( :4s ) 



mixtures of COj with CH, Cl and of H Cl with C, Hj are drawn 

 twice in it, one time with the one component, the other time with the 

 other component at A. Of the lines for mixtures of carbon dioxide 

 with hydrogen or oxygen we could draw only a small portion in 

 the neighbourhood of carbon dioxide (point A). 



These critical lines til into the system of cur\es in a satisfactory 

 way, except the line CO^ — 0„. Also the beginning of the line 

 CO, — Hj fits well into the diagram, but its further portion, if it is 

 to terminate at the point H^, cannot liut deviate strongly from it. 



6. The drawing of fig. 1 enables us also to determine how we 

 must choose the pure mixtures in order that the mixtures may 

 jiossess definite properties. ' Van der Waals (loc. cit.) has pointed 

 out the circumstance that the course of the critical lines (even when 



<^'ij '^ ^u ^23 ) excludes the existence of a maximum critical tempe- 

 rature or of a maximum or minimum critical pressure. Yet mixtures 

 occur which show ') a minimum critical temperature, and in our 

 case we find as conditions for its existence ') : 



jr, + T, > 2 Ti 1/:Ti and also > 2 y/:r,. 



The area, within which the second component must lie, if the 

 critical temperature is to reach a minimum for one of tiie mixtures, 

 is therefore bounded by the two curves 



and 



2.- — 1 



represented in fig. 1 by OAF and GAH respectively. The first 

 line is one of the critical lines, namely that which has a vertical 

 tangent at a; the other contains all the points of the critical lines 

 where the tangent is vertical. It may be easily seen that the second 

 component must lie between those two curves, i. e. in the fields 2 

 and 3. On tiie strength of this we may predict that in general a 

 minimum critical temperature will be observed when tlie critical 



') Tiie elements of the mixture for whicli the critical temperature is minimum, 

 are here determined by : 



n-,— T, j/jTi (j/jr, — l)(jr,— T, l/.-T,) 



'V,nt = y'^i 



{jt, +Tj— 2tj yji,) 



^) The general conditions for the existence of a minimum critical temperature 

 are given in llie Molecular Theory of van per Waals. 



