37* 



SCIENCE PROGRESS. 



by Arrhenius, involves, in addition to the other data, a 

 knowledge of the density of the solution. In the case of 

 concentrated solutions, however, the two methods may give 

 results which differ considerably, as is shown in the following 

 table. Here are given in the last column the values of the 

 molecular weight of alcohol obtained from the above data 

 on using in the freezing-point formula, instead of g y values 

 oi g or the number of grs. of alcohol in ioo cc. of solution. 



The values of M" now vary by only some 3 units. 

 In general, however, the method of Raoult gives values 

 which vary less with the concentration than those given by 

 the method of Arrhenius. This is well illustrated by the 

 recent work of Abegg (1894) on the freezing-point of very 

 strong solutions. Neither method is theoretically perfect, 

 Raoult's being probably the more correct. It may be taken, 

 however, that the above is a fairly typical instance of the 

 extent to which the molecular weio-fit varies with the con- 

 centration. 



It is of interest to compare this variation with that 

 shown by the molecular weights of gases at different con- 

 centrations. If we calculate the osmotic pressure of alcohol 

 in the above solutions by the equation which holds good for 

 a dilute solution, the values in atmospheres thus obtained 

 are given in the first column of the preceding table. Even 

 in the weakest solution the osmotic pressure is greater than 

 one atmosphere, and in the strongest it is greater than sixty 

 atmospheres. Now it is well known that if, by the equation 

 which applies to a gas of small concentration, we calculate 

 the molecular weight at pressures differing as widely as 

 the osmotic pressures of the above solutions, here also there 

 is considerable variation in the values obtained. This is 



