of Binary Liquid Mixtures. 299 



Similarly , _ <a 2 '-a 2 ) 



J p 2 '=2> 2 (l-x)e RT 



and _ ( A i'~ A i) _ ( A 2 r -A 2 ) 



p=pi +p 2 ' =P\%e RT H-j? 2 (l""^)fi" RT • 



. . . [13] 



The last equation is of the same form as the equation 



Van Laar has obtained for the total vapour pressure of a 



binary mixture on thermodynamic grounds. Van Laar's 



expression is 



_ (Mi'— Mi) _ W-M2) 



p=p l xe RT +p 2 (l — x)e RT , 



where /^ and /x 2 are the thermodynamic potentials of the two 

 components *. 



Equation [13] can also be written in the more convenient 

 form 



_dAi 3a 2 



p=p 1 xe RT +p 2 (l — x) RT , . . [14] 



where dA x and c)A 2 represent the increase in the work done 

 by evaporating a molecule of X or Y from the mixture over 

 the work done when the molecule is evaporated from the 

 pure liquid. 



Furthermore, it will be seen that r3A x and ~dA 2 are 

 practically identical with the excess of the molecular 

 latent heats of vaporization BL^ and c)L 2 of the two 

 components in the mixture over their molecular latent heats 

 in the pure state. Hence we may write f 



dig _ dLa 



p=p l xe RT +p 2 (l— x)e RT . . . [15] 



We may develop equation [15] still further. Expanding 

 e RT and e RT we have, since QLj. and ^L 2 are small, 



p = Pi x(l-^ \ + p 2 (l-x) (±- -j^jfj 



=p 1 x+p 2 {l—x) -^-\p 1 %"dL 1 +p 2 {l--x)'dL 2 I. 



Now if p is the vapour pressure of the mixture calculated 



* Zeit. Phys. Chem. lxxii. p. 723 (1910) ; {bid. lxxxiii. p. 599 (1913) ; 

 and other papers. 



t Equation [15] indicates that 'ftp^'dL, or that as regards the vapori- 

 zation of liquids, increase in thermodynamic potential is equivalent to 

 increase in latent heat of vaporization. 



X2 





