SURFACES OF DISCONTINUITY 687 



64. Gibbs' Comments on Electrode Potentials 



Leaving these matters, and turning to a few brief comments 

 on Gibbs' own pages, we meet a statement in a footnote to page 

 333 to the effect that for a cell with electrodes consisting of zinc 

 dissolved in mercury in different proportions equilibrium would 

 be impossible. For, considering a certain solution, if we slightly 

 alter the relative masses for two constituents but maintain the 

 pressure constant, then dp is zero and so (mi/v)dni + {m2/v)dn2 

 is also zero ; so that if d/xi is positive, dn2 must be negative, or an 

 increase in ^i involves a decrease in nz. Hence if Hm' > y-J' 

 then /i/ < Hz" . Thus it would be impossible for the conditions 

 of equilibrium 



■m } 



V + a„Mm' = V" + a„M 



to be true simultaneously. 



With regard to paragraph (II), p. 334, a discharged ion going 

 into solution would no longer be related to other components by 

 equation [683] ; it would be an independent component with in 

 general an entirely different chemical potential from the charged 

 ion. If there were current flowing, a charged ion would appear 

 to have no definite chemical potential since it would not be in 

 equilibrium, but we would infer by [687] that for small currents 

 its chemical potential, if it were a cation, would increase as it 

 travelled towards the cathode, (if an anion, towards the anode) 

 on account of changing electric potential in the solution. The 

 discharged ion would not be affected by the electric field. How- 

 ever, the paragraph indicates the case of minor interest where 

 the chemical potential might remain unchanged by the dis- 

 charge. Paragraph (III) introduces the possibility of an 

 equilibrium being effected by absorption of an ion by the elec- 

 trodes, as in the case of the well known polarizing effect of 

 hydrogen bubbles in a simple copper-zinc cell. The phe- 

 nomena of polarization and of overvoltage can be studied in 

 standard texts. (See for example Chapter VIII of Newman's 

 book, cited above. Chapter VI of the same work gives a good 

 account of the experimental methods used to measure electrode 

 potentials.) 



