THE NEW THEORY OF SOLUTIONS. 



4i5 



BOILING-POINT. 



CO 



CO 



o: 

 a. 



a 

 < 

 > 



P 



*r AT-^ 



C 



r 

 — > 



If KL be a portion of the vapour-pressure curve of a 

 solvent, and MN be a 



portion of the curve for 'C.3. 



solution of a non-volatile 

 substance, at the tem- 

 perature /, ac is equal to 

 p — p' , the diminution in 

 the vapour-pressure of 

 the solvent brought about 

 by the presence of the 

 dissolved substance ; and 

 at the pressure p, ad is 

 equal to t' - t or AT, the 



corresponding rise in the TEMP 



boiling-point of the sol- 

 vent. If AT be obtained experimentally the measure- 

 ments may be utilised in two ways. If the vapour-pressure 

 curve of the solvent be known we may read off the change 

 p - p' in the vapour-pressure p, which corresponds with 

 the temperature difference AT, and the value of (p - p')lp 

 may then be used in the vapour-pressure formulae already 

 considered. On the other hand, the following treatment 

 due to Arrhenius (1889) shows how the values of AT itself 

 may be employed as a convenient means of investigating 

 the vapour-pressure laws of dilute solutions. 



If AT be small, that is, if the solution be dilute, the two 

 curves KL and MN (fig. 3) may be taken to be straight 

 and parallel, hence we may assume that p — p' = AT tan 

 adc = AT dpjdt where dpjdt is the rate of change of the 

 vapour-pressure of the solvent at its boiling-point, t, and thus 

 a constant. On introducing the above value of/ - p' into 

 Raoult's empirical vapour-pressure equation ( 1 ) we obtain— 



M'AT/^- = ApMjioo(dpldt) (7). 



From the ordinary thermodynamical relationship expressing 

 the heat of vaporisation of a liquid in terms of the volume, 

 pressure, and temperature of the vapour to which it gives 

 rise, on neglecting the volume of the liquid which is small 



