Junk 6, 19()2. j 



SCIENCE. 



891 



osmotic pressure in the case of dilute solu- 

 tions, the observations made by Raoult and 

 others furnished a number of facts ready 

 for testing- the theory. He found that, while 

 in many cases the osmotic pressure cal- 

 culated from his formula PV=RT agreed, 

 within the limits of experimental error, 

 ■with the value calculated from the observa- 

 tion, there were a very considerable num- 

 ber where the observed value differed from 

 that given by the formula. He accord- 

 ingly modified the formula by the introduc- 

 tion of a factor i, so as to make it PV^iBT. 

 This factor i is unity in the cases where 

 observation by Raoult 's method gives re- 

 sults agreeing with the formula PV^^RT; 

 in other cases it is greater or less than 

 tmity, and indicates the extent of the dis- 

 agreement. Arrhenius, to whom van't 

 Iloff showed these numbers, pointed out 

 that all the substances which had i greater 

 than unity were electrolytes, and that the 

 deviation had to do with their splitting up 

 into ions. Arrhenius* had before this time 

 (1887) been working at the subject of elec- 

 trolysis and of the relation between the 

 readiness with which substances undergo 

 electrolysis and the readiness with which 

 thejr enter into chemical reactions. He had 

 been looking for an explanation of the fact 

 that the conductivity of a solution of an 

 electrolyte is not proportional to its concen- 

 tration, and had come to the conclusion that 

 this must depend on some of the molecules 

 of the solute being 'active,' that is, taking 

 part in the conduction— while others were 

 inactive, behaving like molecules of a non- 

 electrolyte, and that the proportion of ac- 

 tive molecules increases with dilution. 



van't Hoff's factor i enabled Arrhenius 

 to give precision to these ideas, and inl887f 

 he formulated the theory that the 'active' 



* Arrhenius, Bihang till kongl. Svenska vetensk. 

 Akad. Handlingar, 18S4, Nos. 13 and 14. 



t Arrhenius, Zeitschrift f. physik. Chemie, I., p. 

 631 (1887). 



molecules were those which were split into 

 ions. It was now possible to calculate i in 

 two ways and compare the results. Ar- 

 rhenius gives a list of eighty-four sub- 

 stances, for which there existed at that time 

 data for such calculations, and, calcu- 

 lating the value of i as deduced on his 

 new theory from the conductivity, com- 

 pares it with the value of i derived 

 from freezing-point observations in each 

 of the eighty-four substances. The agree- 

 ment does not at first sight strike one as 

 very close, but there are several circum- 

 stances which have to be considered in judg- 

 ing them. The whole mass of published ob- 

 servations was taken, the limits of probable 

 error are very different in different cases, 

 and the freezing-point measurements were 

 all made at temperatures a little below 0°, 

 while the conductivity measurements were 

 made at 18°. The comparison was made, 

 not as a demonstration of the theory, but 

 rather as a preliminary trial with such ma- 

 terials as were at hand. The real testing of 

 the theory necessarily came later. So I think 

 we may agree with Arrhenius that, consid- 

 ering all the circumstances, the agreement 

 is not unsatisfactory, except in the case of 

 nine of the siibstances, and tliat most of 

 these nine cases are liable to suspicion on 

 other grounds. In 1887, almost at the 

 time when Arrhenius published the paper 

 of which I have just been speaking, 

 Planck* discussed the subjects of the 

 diminution of the vapor pressure and the 

 lowering of the freezing-point in dilute salt 

 solutions from the thermodynamic point 

 of view, and starting from the principle of 

 the increase of entropy, deduced formulae 

 connecting these quantities with the molec- 

 ular weight. He says, in conclusion: 

 "This formula claims exact numerical 

 validity. It gives for most substances a 

 greater molecular niunber than that usually 

 assumed, i. e., a partial or complete ehem- 

 * Planck, Wied., XXXII., p. 495 ( 1887 ) . 



