30 PROCEEDINGS OF Till: AMERICAN ACADEMY. 



where - ie the electromotive for ind <-., are the molecular volui 



i>t' the metal in the two amalgams, and y is the heat <»i the process in 

 trical units. From this, 



//»„- = A' Tin ''- + !\ 



''1 



hut ne w is the electrical work per gram-molecule, which is equal to 

 tlir change of free energy, Bince the cell is ;i reversible one. Therefore 



A = a < ., -, or 



A = R 7' In ''-' +• U. 

 '■1 



which is identical with (48 ")• 



When we consider solutions of all concentrations, varying from the 



state where oik' of the constituents of tin- phase i- in grea( excess to the 



Btate where tlie other constituent is in <_rr»:it exc . for < sample, 



when water is added continuously to a definite amount of alcohol, then 



tin- form which the osmotic pressure curve assumes i- very complicated. 



Here equation (41) must be used, and , - and will both be com- 



ii /-, 1/ /-, 



plex functions oi r,. may be looked upon as the sum of two quanti- 



ties, one due to the attraction of unlike, the other to the attraction of like 

 molecules. Concerning the manner in which the former will change 

 we are ignorant. The latter, however, according to reasoning exactly 



similar to that which led van der Waal 8 to the term -, may he 



shown to be inversely proportional to the square of the volume, or equal 



to 2 " . We see from this that equation < ! 1 > is at least of the 



third degree in »v Bredig ' and Noyesf have each proposed a general 

 formula for osmotic pressure based upon kinetic reasoning. Both these 

 equations are of the third degree in v. The osmotic pressure curve 

 represented by equation 1 1 1 1 is not necessarily, therefore. Bingle valued. 

 There maj be 1 v than one volume corresponding to one osmotic pres- 

 sure. This is a further an logj between solutions and gases. In fact, 

 a number of Cases are known in which the osmotic pre.-sure may he 

 shown to he the same at two different concentrations, namely, the c 

 of liquids that are mutually soluble to a limited extent, thus forming two 

 phases in equilibrium with each other. It is evident that in order to 



* Zeit Phys. Chem., IV. Hi. 1 Zeit. Phys. Chem., V. CD. 



