2>0 KXZBEDINaB l THE amebicab academy. 



This equation statea that the relative lowering of the activity 

 solvent by the addition of a small quantity of a solute is equal to the 

 number of mola of solute divided by the number of niols of i 



This statement comprises in itself practically all the laws of dilate 

 solutions. Raoult's law is a Bpecial but only approximate form of 

 equation XIX, lor equation XIX is true of every solution when infi- 

 nitely dilute, but Raoult's law is not true even at infinite dilution, 

 except when the vapor of the solvent is a perfect gas. 



It' the solute, X x , is dissolved, not in a pure solvent, but in a mixture 

 of X 2) X 3 , etc., then for the perfect dilute solution we fuid in plao 

 equation XIX, 



2*r a tfln& + iv r ,dln&+ ••• =-<L\\. XX' 



Some Applications of the Preceding Equation& 



Equations I-XX can be combined in a very great variety of v 

 to give important results. A few examples, however, will suffice 

 show the manner in which these equations may be employed. 



First, as a simple example, we may derive the formula lor the lower- 

 ing cf the freezing point of a perfect .solution. According to cquat 

 XIX, the activity of a pure liquid is always lowered by the additioi 

 a solute. If therefore a liquid and solid are together at the fi 

 point and a solute is added to the liquid, the activity of the latter will 

 become lower than that of the solid, and the solid will melt. On the 

 other hand, if we start again with liquid and solid .-it the freezing point 

 and lower the temperature, we see from equation VIII that the activity 

 of the solid will decrease faster than that of the liquid and the liquid 

 will disappear. It is obvious, therefore, that by adding a solute to a 

 freezing mixture ami at the Bame time lowering the temperature by a 

 suitable amount, the equilibrium between solid and liquid can be main- 

 tained. The necessary condition for tin- maintenance of equilibrium 

 is that the activity A> of the solvent X\, in the liquid state remain equal 

 to the activity £' 2 of X 2 in the solid state. Hence, 



tfln& = <*ln&. 



Now, assuming that the solid does ao\ dissolve any of the solute, 



change in activity of the -olid X.. is due merely to change of temp 1, 

 tore, and thus from equation VIII, 



