MOLECULES AND ATOMS 881 



also many experimental discrepancies which cannot as yet be ex. 

 plained by theory. 27bi * 



27 bis The osmotic pressure, vapour tension of the solvent, and several other means 

 applied like the cryoscopio method to dilute solutions for determining the molecular 

 weight of a substance in solution, are more difficult to carry out in practice, and only the 

 method of determining the rise of the boiling point of dilute solutions can from its 

 facility be placed parallel with the cryoscopic method, to which it bears a strong 

 resemblance, as in both the solvent changes its state and is partially separated. In the 

 boiling point method it passes off in the form of a vapour, while in cryoscopic deter- 

 minations it separates out in the form of a solid body. 



Van't Hoff, starting from the second law of thermo-dynamics, showed that the 

 dependence of the rise of pressure (dp) upon a rise of temperature (dT) is determined by 

 the equation dp = (Jimp /2T-) rfT, where k is the latent heat of evaporatipn of the solvent, 

 TO its molecular weight, p the tension of the saturated vapour of the solvent at T, and T 

 the absolute temperature (T = 273 + <), while Raoult found that the quantity (p-p') Ip 

 (Chapter I., Note 50) or the measure of the relative fall of tension (p the tension of the 

 solvent or water, &ndp' of the solution) is found by the ratio of the number of molecules, 

 n of the substance dissolved, and N of the solvent, so that (p -p') !p = Cn /(N + n) where 

 C is a constant. With very dilute solutions pp' may be taken as equal to dp, and the 

 fraction n/(N + n) as equal to n ,'N (because in that case the value of N is very much 

 greater than 'n), and then, judging from experiment, C is nearly unity hence: 

 dp Ip = n ,'N or dp np!13 t and on substituting this in the above equation we have 

 (kmp /2T 2 ) dT = np ,'N. Taking a weight of the solvent m. N = 100, and of the substance 

 dissolved (per 100 of the solvent) q, where q evidently =nM, if M be the molecular 

 weight of the substance dissolved, we find that w/N = 2?n/100M, and hence, according to 



the preceding equation, we have M - TT~' * na ^ * 8 ' ^ v taking a solution of q 



grms. of a substance in 100 grins, of a solvent, and determining by experiment the rise 

 of the boiling point dT, we find the molecular weight M of the substance dissolved, 

 because the fraction 0'02 T* Ik is (for a given pressure and solvent) a Constant ; for water 

 at 100 (T = 878) when 7c = 534 (Chapter I., Note 11), it is nearly 5'2,for ether nearly 21, 

 for bisulphide of carbon nearly 24, for alcohol nearly 11*5, &c. As an example, we will 

 cite from the determinations made by Professor Sakurai, of Japan (1893), that wheri" 

 water was the solvent and the substance dissolved, corrosive sublimate, HgCl 2 , was taken 

 in the quantity q = 8'978 and 4'25S grms;, the rise in the boiling point dT was = Cf 179 and 

 '084, whence M =261 and 268, and when alcohol was the solvent, j = 10'873 and 8'765 

 and dT = 0-471 and 0-380, whence M = 266 and 265, whilst the actual molecular weight of 

 corrosive sublimate =271, which is very near to that given by this method. In the 

 same manner for aqueous solutions of sugar (M = 842), when q varied from 14 to 2-4, and 

 the rise of the boiling point from 0< 21 to 0> 085, M was found to vary between 889 and 

 864. For solutions of iodine I.> in ether, the molecular weight was found by this method 

 to be between 255 and 262, and I 2 = 254, Sakurai obtained similar results (between 247 

 and 262) for solutions of iodine in bisulphide of carbon. 



We will here remark that in determining M (the molecular weight of the substance 

 dissolved) at small but increasing concentrations (per 100 grms. of water), the results 

 obtained by Julio Barpni (1893) show that the value of M found by the formula may 

 either increase or decrease. An increase, for instance, takes place in aqueous solutions 

 of HgCl 2 (from 255 to 834 instead of 271), KNO 3 (57-66 instead of 101), AgNO 3 (104-107 

 instead of 170), K 2 SO 4 (55-89 instead of 174), sugar (328-348 instead of 342), &c. On the 

 contrary the calculated value of M decreases as the concentration increases, for solu- 

 tions of KC1 (40-89 instead of 74'5), NaCl (33-28 instead, of 58'5), NaBr (60-49 instead 

 of 103), &c. In this case (as also for LiCl, Nal, C. 2 H 3 NaO 2 , &c.) the value of (Chapter 

 I., Note 49), or the ratio between the actual molecular weight and that found by the 

 rise of the boiling point, was found to increase with the concentration, i.e. to be greater 

 than 1, and to differ more and more from unity as the strength of the solution becomes 



