410 SCIENCE PROGRESS. 



In the last column are given the values of ioo CM, 

 which, if Raoult's conclusion be valid, should be unity. The 

 mean value is 1*03, the average divergence being '03. The 

 whole of the foregoing empirical results may therefore be 

 expressed by — 



{(*-/) #f}-x (100 M'/M)- A (.) 



where A is very nearly equal to unity and is evidently the 

 diminution of the vapour-pressure produced on dissolving 1 

 gram-molecule of substance in 100 gram-molecules of 

 solvent. Since Wiillner's law is not strictly obeyed, the 

 values of A, which were obtained for solutions containing 4 

 to 12 gram-molecules of substance per 100 of solution, de- 

 pend to some extent on the concentrations of the particular 

 solutions employed. For more dilute solutions, however, 

 the values will be practically the same. 1 



That the value of A should not be exactly unity but 

 might in particular cases be considerably larger, became 

 evident from a study of solutions in acetic acid, made by 

 Raoult and Recoura in 1890. For these solutions A had 

 the exceptional value of 1 "63. Now acetic acid differs from 

 all the solvents in the preceding table in having an abnormal 

 vapour-density, and at the temperature at which the vapour- 

 pressure observations were made, d'/d, the ratio of the 

 actual to the theoretical vapour-density is 1 '64 and thus 

 almost identical with the value of A. It was therefore con- 

 cluded that A = d' '/d, and a reason was thus furnished for 

 the mean value of A already given being slightly greater 

 than unity, because, in general, the densities of the 

 saturated vapours of the solvents used are slightly larger 

 than the theoretical values. The following table (Raoult, 

 1893) gives for six solvents, at the temperature t, the values 

 of A as obtained from the vapour-pressures of dilute solu- 



1 If A be deduced from the depression produced by 1 gram-molecule 

 of substance per 100 of solution its mean value A' is slightly lower than 

 1 -03, viz., -98. If, however, values of A' be determined in the case of 

 each dissolved substance for concentrations varying between 3 and 15 

 gram-molecules per 100 of solution, and the values of A' be then found for 

 an extremely dilute solution by treating A' as a function of the concentra- 

 tion, the numbers thus obtained for A' are almost the same as those above 

 obtained for A. 



