'332 PRINCIPLES OF CHEMISTRY 



If 100 gram-molecules of water, i.e. 1,800 grms, be taken and n 

 jgram-molecules of sugar, C^H^O,, ,i.e. ?*342 grms., be dissolved in 



'greater. For example, according to Schlamp (1894), for LiCl, with a variation of from 

 I'l to 6'7 grm. LiCl per 100 of water, i varies from 1'63 to 1'89. But for substances 

 'of the first series (HgCl 2 , &c.), although in -very dilute solutions i is greater than 1, 

 it approximates to 1 as the concentration increases, and this is the normal phenomenon 

 for solutions which do not conduct an electric current, as, for instance, of sugar. And 

 jwith certain electrolytes, such as HgCl 2 , MgSO^ &c., i exhibits a similar variation; 

 1-thus, for HgCl 2 the value of M is found to vary between 255 and 884 ; that is, i (as 

 the molecular weight = 271) varies between 1'06 and 0'81. Hence I do not believe that 

 I the difference between i and unity (for instance, for CaCl 2 , i is about 8, for KI about 2, 

 '.and decreases with the concentration) can at present be placed at the >asis of any 

 'general chemical conclusions, and it requires further experimental research. Among 

 other methods by which the value of i is now determined for dilute solutions is the 

 study of their electroconductivity, admitting that i = l + a(k-I), where a = the ratio 

 of the molecular conductivity to the limiting conductivity corresponding to an infinitely 

 large dilution (see Physical Chemistry), and k is the number of ions into which the 

 substance dissolved can split up. Without entering upon a criticism of this method 

 of determining i, I will only remark that it frequently gives values of i very close to 

 those found by the depression of the freezing point and rise of the boiling point ; but 

 that this accordance of results is sometimes very doubtful. Thus for a solution contain- 

 ing 5'67 grms. CaCl 2 per 100 grms. of water, i, according to the vapour tension = 2'52, 

 according to the boiling point =2'71, according. to the electroconductivity = 2'28, while 

 for solutions in propyl alcohol (Schlamp 1894) i is near to T38. In a word, although 

 these methods of determining the molecular weight of substances in ' solution show an 

 undoubted progress in the general chemical principles of the molecular theory, there are 

 still many points which require explanation. 



We will add certain general relations which apply to these problems. Isotonio 

 (Chapter I., Note 19) solutions exhibit not only similar osmotic pressures, but also the 

 same vapour tension, boiling point and freezing temperature. The osmotic pressure 

 bears the same relation to the fall of the vapour tension as the specific gravity of o. 

 solution does to the specific gravity of the vapour of the solvent. The general formulae 

 underlying the whole doctrine of the influence of the molecular weight upon the 

 properties of solutions considered above, are : 1. Raoult in 1886-1890 showed that 



z'. 12?. M =aconstantc 



p a m 



where p and p' are the vapour tensions of the solvent and substance dissolved, a the 

 amount in grms. of the substance dissolved per 100 grms. of solvent, M and m the 

 molecular weights of the substance dissolved and solvent. 2. Raoult and Recoura iu 

 1890 showed that the constant above C = the ratio of the actual vapour density d' of 

 the solvent to the theoretical density d calculated according to the molecular weight. 

 This deduction may now be considered proved, because both the fall of tension and the 

 ratio of the vapour densities d' Id give, for water T08, for alcohol T02, for ether 1-04, for 

 bisulphide of carbon TOO, for benzene 1'02, for acetic acid 1'68. 8. By applying the 

 principles of thermodynamics and calling L! the latent heat of fusion and Tj the 

 absolute ( = t + 278) temperature of fusion of the solvent, and L 2 and T 2 the corresponding 

 values for the boiling point, Van't Hoff in 1886-1890 deduced : 

 Depression of freezing point ^ Lj T^ 

 Rise of boiling point * LI ' T 2 * 



Depression of freezing point = T -J_^ 

 .LI MI 



Rise of boiling point = ^-*- f * 

 L 2 M, 



where A = 0-01986 (or nearly 0'02 as we took it above), a is the weight in grms. of the 



