206 GUGGENHEIM art. e 



is negligibly small compared with At, then the exact formula 

 (98) may be replaced by the approximate one 



(A^+0 «.(A^_') «-(/±') -'.+ "- = {N+") ".{N-") «-(/i") '.+ '- . (99) 



The corresponding formula for the membrane equilibrium of 

 a single ionic species in non-ideal solutions takes the form 



At log ^ + At log^' = (p' - p") M + z, FiV - F'OdOO) 



//' 

 but tells us nothing, as neither the term At log 77 on the left 



J* 

 nor the term Zi F(y' — V") on the right is physically deter- 

 minable. 



S2. Contact Equilibrium. A most important case of mem- 

 brane equilibrium is that of two phases with one common com- 

 ponent ion, the surface of separation forming a natural mem- 

 brane permeable to the common ion but impermeable to all 

 others. This may be referred to as "contact equiUbrium." 

 For example, for two metals in contact, say Cu and Zn, there is 

 equilibrium between the two phases as regards electrons El~ 

 but not as regards the positive ions Cm"''"*" or Zn^'^. The 

 equilibrium is completely defined by 



[M^z-]^« = [Uni-Y-, (101) 



the suffix denoting, as usual, the component, and the index the 

 phase. Similarly for a metaUic electrode of Cu, dipping into 

 a solution S containing ions of this metal, in this case Cw'''+, 

 the contact equilibrium is completely defined by 



[Mcu-]"'" = [Mcu-]^ (102) 



the electrode and solution being in equilibrium as regards the 

 metallic ions only. In neither of these cases of contact equilib- 

 rium is any "contact electric potential difference" thermo- 

 djoiamically definable. 



28. Purely Chemical Cell. Consider the system composed of 

 the following phases and membranes arranged in order, each 

 phase being separated by partially permeable membranes from 



