Atom and the Charge of Electricity carried by it. 533 



v if« fflj (4) 



Now dH./dm 3 depends solely upon the number of zinc atoms 

 in unit volume of the solution, while dB.ldm x is independent 

 of che solution altogether. Hence we see that the potential 

 difference between the zinc and the solution depends solely 

 upon the number of free zinc atoms in unit volume of the 

 solution. If this be constant the potential difference is the 

 same whatever salt of zinc is used. 



From the value found for H we see 



V = ^{— R 3 # log m 3 -ha term independent of m z \ , . (5) 

 thus 



dm 3 2 m 3 



An expression which shows how the potential difference varies 

 with the strength of the solution. 



We see from equation (5) that the magnitude and even the 

 sign of Y depends upon the value of m 3 , the number of free 

 zinc ions in the solution. If m 3 is less than a certain quantity 

 V is positive, that is the positive coating of the double layer 

 formed at the zinc surface is in the electrolyte, while the 

 negative is on the zinc; when m 3 exceeds this value, the signs 

 of the coatings are reversed. For infinitely dilute solutions 

 the value of V would be infinite. Though equation (5) 

 enables us to find the value of V when m z is known, the 

 equations are insufficient to determine this quantity in such 

 a case, for example, as when a zinc rod is immersed in a 

 solution of HC1 : here ZnCl 2 may be formed by chemical 

 action and dissolve in the zinc, and then partly be split up 

 into Zn and CI atoms. In this case we have in the solution 

 molecules of ZnCl 3 and HC1, atoms of Zn, H, and CI. Let 

 m 5 denote the number of atoms of H, m 6 the number of mole- 

 cules of HC1, the rest of the notation being the same as before. 

 Then to determine the variables we have the equations 2, 3, 4, 

 and since one way in which the system could vary would be 

 by an atom of hydrogen combining with an atom of chlorine 

 to form a molecule of hydrochloric acid, we have 



dR dR ^H_ Q 

 dm Q dm 5 dm^ 



Since the total number of hydrogen and chlorine atoms con- 

 tained in the solution must be equal to N, if N is the number 

 of hydrochloric acid molecules originally taken for the 



