METHOD OF DETERMINING MOLECULAR WEIGHTS. 2J 



The constant B or B' may, moreover, be accurately calculated in 

 the following manner from the latent heat of vaporization and the 

 boiling point of the solvent, as has been pointed out by Arrhenius 

 (Zeitsch. physik Chem., 4, 550 [1889]). 



Suppose we have a solvent of molecular weight, il/, and of 

 boiling point, T (in absolute temperature), at pressure, ];. By dis- 

 solution of n gram-molecules in 100 grams of the solvent, the boiling 

 point rises to T+dT. The relation between this rise, dT, and the 

 dissolved mass, n, may be calculated thus : 



The solution boils under pressure p at the temperature T+dT. 

 The vapour pressure of the solvent at T is equal to p, it is equal to 

 p + dp at the temperature T+dT. Between dT and dp the following 

 relation exists according to the second law of thermodynamics, as 

 already shown by van't Hoff ^Zeitsch. phjsih. Chem., 1^ 494 [1887]): 



^P =clT. ^'^ ■ 



p '27'- 



where m= latent heat of vaporization of a gram-moleciile of the 

 solvent at temperature, T. 



Now, according to Kaoult's law, the relation between the diminu- 

 tion of vapour pressure and the number of molecules of tlie solvent 

 and of the dissolved substance is expressed by 



p—p' n 



or 



or 



p + dp N+n 



But, as the solution is very dilute, dp is very small compared to p, 

 and n very small compared to A^ The last equation may, therefore, 

 be written as 



