OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 



It is easy to see that neither of these equations will give very different 

 results from the concentration-equations in the present cases. Indeed, if 

 the atomic volume of the substance in solution is the same as that of 

 mercury, the two roads lead to exactly the same numerical goal, as is 

 seen from the following logic. 



It is obvious that in general JV = = . where N equals the number 



M A 



of gram-molecules, W the total weight of substance, V the total volume of 

 substance and M and A the atomic weight and atomic volume, respectively. 

 Using capital letters to denote the solvent and small letters to denote the 

 dissolved substance, we have the following expression : 



e + * 



+ n A 



n 



NI + n = 

 n 



a 



n 



N 2 + n A a 



if a is taken to mean the atomic volume of the dissolved substance in its 

 dissolved state, that is to say, the increased volume which a gram-atom 

 causes in the mercury, and v the similar volume of the amount of the 

 substance under consideration. In this equation when A a both cancel, 

 and the last member of the equation takes a form identical with the 

 preceding and gives like results, but with V and v in place of N and n. 

 This consequence might not be perceived at first sight from Lewis's paper. 

 On the other hand, when A~>a, the Raoult law will give a lower theo- 

 retical value than the concentration law; and when A<a, the opposite is 

 true. The metals concerned at present have so nearly the same atomic 

 volumes that the deviations are very slight, as is shown in the following 

 table (all the cells were at oC.) : 



TABLE 20. Comparison of Raoulfs Equation with Concentration Equation. 



* These values are calculated from the densities of amalgams on page 13. 



On comparing the last two columns, the differences are seen to be 

 small, and with more dilute amalgams they are yet smaller. 



It will be observed that in cases of this kind both of these equations 

 give results very different indeed from the mode of calculation which 



