204 GUGGENHEIM art. e 



Comparing formula (87) for two ionic species i and h of the 

 same valency z, we obtain 



At log ^ = iv' - V") ( N - k] ). (88) 



The right hand side of (88) will generally be small compared 

 with At and may often with sufficient accuracy be regarded as 

 zero. With this approximation (88) simplifies to 



N-' N-" 



Applying formula (87) to the two ionic species of an electro- 

 lyte composed of g+ cations of valency 0+ and g_ anions of 

 valency Z-, we obtain 



At\og(^-^j [jjj = (p' - p") iq^v^] - q-[v-]). 



(90) 



The right hand side of (90) will generally be small compared 

 with At and may often with sufficient accuracy be regarded as 

 zero. To this degree of accuracy we may replace the exact 

 formula (90) by the approximate one 



(N+')'^. (NJ)"- = (N+")'^.{N -")"-. (91) 



If we compare (90) for the membrane equilibrium of a solute 

 electrolyte with (32) for the equilibrium of the uncharged 

 solvent, we obtain 



^ /NV'Y fN-"Y g4-[M + q-[v-] . No" .^^. 



or 



{N+T (Njy- (N+'T (N-'T 



(No'y {No"y 



where r is defined by 



_ q+M + q-[v-] 



' ~ [vo\ 



(93) 



(94) 



