MEMBRANE POTENTIALS 221 



This initial state is soon altered through diffusion, and, considered 

 quahtatively, results in the following redistribution of ions: 



(1) (2) 



Since electroneutrality must be maintained in the solution on both 

 sides of the membrane, it follows that, after the diffusion equilibrium 

 had been estabhshed, [Na+]i = [R-] + [Q-]: and [Na+Ja = [Cl-]2, 

 and that neither [Na+]i = [Na+Ja nor [Cl-]i = [Cl-Ja. This equilib- 

 rium is characterized by the fact that the maximal work which could 

 be gained from the reversible and isothermic transport of a very small 

 amount of Na-ions in one direction must be equal to the work 

 expended in the reversible transport of the Cl-ions in the same direc- 

 tion. In other words, the algebraic sum of the work, 5 A, which can 

 be obtained from the simultaneous transport of a very small amount, 

 6 n, of Na-ions and of the same amount of Cl-ions must be equal to 

 zero. The work which can be gained from the transport of 5 n moles 

 of Na+, involving the change of concentration from [Na+]i to [Na+ja 



is = 5 n X RT In tzt^- The same condition being true for the 



[iNa+Ji 



Cl-ions, after the estabhshment of equilibrium we should have 



6n X RT In |^^ + 5n X RT In p|l^ = O 

 [Na+]i [Clii 



Hence it follows that 



[Na+]2 X [Cl-]2 = [Na+]i X [CI"], 



Certain difficulties which Donnan encountered in regard to the 

 possible presence of undissociated molecules may be considered today 

 as having been overcome. These difficulties were due to the inexact 

 figures concerning the degree of dissociation of strong electrolytes 

 obtained from calculations based on conductivity data. Therefore, 

 we need not at present dwell at any greater length upon these 

 difficulties. 



Since in solution (2) we must have [Na+Ja = [Cl-ja, but in solution 

 (1) [Na+]i cannot be = [Cl~]i, it can be stated that 



[Na+], X [Clii = [Na+]? = [Cli^ 



