of Binary Liquid Mixtures. 297 



Also let 7^ = liquid pressure of pure X, 



7r 2 = ?? ■)•> 11 ■*- 5 



7Ti and 7r 2 '= partial liquid pressures of X and Y in 



the mixture, 

 7r = 7r 1 '4-7r 2 ' = total liquid pressure in mixture, 

 V*! and V 2 = molecular volumes of pure X and Y, 

 V^andVg^ „ „ of X and Y in the 



mixture. 



In general, V/ and V 2 ' will be slightly different from 

 V 1 and V 2 owing to the small volume changes which take 

 place on mixing. 



Consider first the partial liquid pressure 7r/ of the com- 

 ponent X. Before the N molecules of X are introduced 

 into the mixture, the liquid pressure of the pure X is given 

 by the relation 



^-NCVx-.&O' L 



where the constant R refers to the mass of N molecules. 

 Now add the n molecules of Y to the N molecules of X. 

 We have, volume of free space in mixture 



=N(V 1 '-6) + n(V 3 '-S 2 ). 



Hence partial pressure tt^ of component will be given by 

 the equation 



gT RT _ r n 



since the two "free spaces" (Vi' — bi) and (V 2 ' — b 2 ), being; 

 in the same mixture, are equal to one another. 

 Combining equations [5] and [6] we obtain 



< N Y 1 -b 1 N M 



where e x denotes the fractional increase in the " free space " 

 of the molecule of X by the mixing. 

 Similarly 



S=n^ (1 -^ ra 



N n 



If instead of sr T — — and ^- — we substitute the molar 



JN + n JN 4- n 



fractions x and (1 — x) in the usual way, equations [7] and 

 [8] become 



ir 1 ' = w l a ! (l-e 1 )\ [9] 



7r 2 ' = 7r 2 (l-^)(l-€ 2 ) [10] 



Phil. Mag. S. 6. Vol. 32. No. 189. Sept. 1916. X 





