OF ZINC, CADMIUM, LEAD, COPPER, AND LITHIUM 



6l 



The equation of Cady may also be used to calculate the electromotive 

 force from the heat of reaction and the concentration effect, supposing 

 these to be known. Indeed, this corresponds to Cady's first method of 

 expressing the results. In a subsequent section the heats of reaction are 

 calculated with the help of the temperature coefficient and the equation 

 of Helmholtz. Using the values for U there given and the values of the 

 concentration ratios already presented in this section, the given results 

 in table 18 are obtained from the Cady equation 



U RT , Ci 

 7r ^c-~ + ~f^ In ~ 

 vr vr c z 



On comparing these results in the fifth column with those in the sixth, 

 it is evident that Cady's equation is a much closer approximation to the 

 truth than von Turin's. The average deviation shown by Cady's equation 

 is only about 0.3 millivolt, whereas the average deviation shown by the 

 simpler equation is about 1.3 millivolt. In other words the departure of 

 the potential from the simple values indicated by the gas law may be 

 ascribed chiefly to the heat of reaction. Clearly, however, the differences, 

 although much smaller than before, are still probably in most cases beyond 

 the limit of error of the experimentation. It will be noticed that in the 

 case of the concentrated thallium cell the Cady equation is almost exactly 

 right ; in the cases of tin, zinc, and the concentrated lead cells the correc- 

 tion afforded by the heat of reaction is not enough to explain the deviation 

 from the simple concentration law ; in the cases of the indium cells and the 

 dilute thallium and lead cells, the heat of dilution supplies too large a cor- 

 rection, and in the case of cadmium the correction is in the wrong 

 direction. 



It is interesting to observe that, assuming U to be constant at different 

 temperatures, Cady's equation predicts that the difference between the 

 observed values and those calculated from the concentrations alone by 

 the simpler equation should be independent of the temperature also. By 

 reference to the tables this will be seen to be the case with considerable 

 approximation with all the metals concerned in these tables. 



The figures for thallium and lead (table 19), taken from foregoing 

 tables 2 and u, may serve as examples : 



TABLE 19. Difference between Observed Values and Concentration Values, 



in Millivolts. 



