36 ELECTROCHEMICAL INVESTIGATION OF LIQUID AMALGAMS 



a result more nearly in accord with the expected value, but still below its 

 full magnitude. The computation of the result is not worth while, as there 

 can be no doubt that this experiment, like the others, has no more than 

 qualitative value. 



The small per cent of tin in a tin amalgam which remained wholly 

 liquid at o corresponds to a heat of dilution which would cause a change 

 of only 0.002 in the calorimeter an amount too small to be determined 

 within 50 per cent by means of our thermometers. Hence an attempt to 

 carry out this experiment was without object. 



In view of all these circumstances, we are inclined to agree with Carhart 

 in thinking that the electrical method of determining the heats of dilution 

 of amalgams is to be preferred to the thermochemical method. 



It is worthy of note, in this connection, that the Helmholtz equation 

 shows at once why the temperature coefficient of the electromotive force 

 divided by the electromotive force approaches the coefficient of expansion 

 of a perfect gas as the dilution of the amalgam proceeds. To illustrate 

 this relation, the equation may be cast into a somewhat less familiar form. 

 The normal form, transposed, is thus: 



Dividing through by vF-n-T, we obtain 



ATT _i_ U 



~ T 



Evidently, because U, the heat of dilution, diminishes as the dilution pro- 

 ceeds, the last term will become smaller and smaller. Finally, when the 

 heat of dilution becomes negligible at great dilution, the equation will 



become simply ^_, = 



?rA 1 j 



Simultaneously, the equation of Cady 



RT . c m U 



' ~- 





loses its last term, and becomes the simple concentration equation. 



It is equally clear that a positive heat of dilution ( + U) will cause the 

 potential to be high and the temperature coefficient to be low. In the case 

 of thallium and indium, this was found actually to be the case. On the 

 other hand, with a negative heat of dilution ( U) the potential will be 

 low and the temperature coefficient high. This was found to be the case 

 with tin, and by Richards and Forbes with zinc. 



Thus the theory of these cells seems to be complete, except for the 

 quantitative understanding of the minor deviations from the equation of 

 Cady. These deviations, which are probably to be traced primarily to the 



inaccuracy of the simple concentration ratio as an index of the precise 



Cn 



