482 



J. H. van't HofiP on the Origin 



solutions in order to calculate the molecular weight. In this 

 way it was found that the formula of raffinose contained C 18 . 

 This conclusion has since been confirmed by the splitting up 

 of raffinose into equal quantities of the three sugars — glucose, 

 levulose, and galactose, — each containing six atoms of carbon. 

 We will now consider the laws associated with osmotic 



pressure. 



The Lowering of the Vapour-Pressure. — 

 If we suppose, with Arrhenius, that we 

 have osmotic equilibrium with a 1 per cent, 

 sugar-solution, as in fig. 3, where H is 

 the rise due to osmotic pressure, then the 

 column of solution H represents the 

 osmotic pressure and the column of vapour 

 H the lowering of the vapour-pressure. 

 Hence, for any solvent whatever, we obtain, 

 as before, 



Fig. 3. 



Lowering of vapour-pressure 

 Osmotic pressure 



M 

 0-08956^ 



Yapour-pressure 

 "760 



10005 



where s represents the specific gravity of the solvent and 

 M its molecular weight in the gaseous state. 



Should the osmotic pressure be equal to the gas-pressure, 

 then, by comparison with hydrogen, it will be 



10 s .760 



0-08956 



m 



for a 1 per cent, solution of a substance having the molecular 

 weight m. Hence 



Lowering of vapour-pressure A M 



V apour-pressure 



This is the w r ell-known law of Raoult, which states that the 

 molecular relative lowering of vapour-pressure is equal to 

 j^q of the molecular weight of the solvent. 



It is to be noted that here, as in all laws relating to dilute 

 solutions, we have only a limiting law which strictly applies 

 to infinitely dilute solutions, where the accurate expression of 

 the above law becomes 



dp 



pd 



m 



= M. 



The following table contains the results obtained with 

 fairly dilute solutions. 



