RATIO OF PARTITION 53 



displacement 0-55 cm., and hence for the molecular weight 

 of naphthalene 



tv6 = xx L -^- ? 3 

 0-1266 



x 123 



which for practical purposes agrees sufficiently with the 

 formula C 10 H 8 = 128. 



Ratio of partition. As remarked on p. 43 a measure- 

 ment of molecular weight may be based on the ratio of 

 partition, and the law with regard to this may be most 

 simply arrived at by considering the equilibrium of the 

 vapour of the dissolved body, the mutual solubility of 

 the two liquids being neglected. If the molecular weights 

 in the vapour and in the two liquid phases be m, (m) /v and 

 (m) ; , 2 respectively, and the concentrations c, c v c 2 , then on the 

 one hand 



and on the other 



= & 2 , 



^2 



so that 



l - = -^- = i and (w~) = (77) ^ 



where c 1? c 2 , (7 1? (7 2 are the concentrations as found in two 

 experiments. 



Hence if n^ is known, i. e. the molecular magnitude in 

 one liquid, then two measurements of partition will give n. 2 , 

 the magnitude in the other solvent. 



As a rule the molecular magnitude is the same in both 

 solvents, being simple in each, and so we have 



?&! = n 2 and - = k, 



i. e. constant ratio of partition, as found in certain cases by 

 Berthelot and Jungfleisch 1 . But as hydroxylic substances 



1 Ann. de Chim. et de Phys. (4) 26. 396, 408. 



