HISTORICAL INTRODUCTION 21 



This last equation is the equilibrium equation which states 

 that the product of the concentrations of a pair of diffusible 

 cations and anions on one side of the membrane is equal to the 

 product of the concentrations of the same pair of diffusible anions 

 and cations on the other side. Since on the side of the non- 

 diffusible (protein) anion the concentration of cations Na is the 

 sum of the cations in combination with the non-diffusible anion 

 plus the cations in combination with the Cl, while on the other 

 side of the membrane the concentration of the Na ions is only that 

 of Na in combination with Cl and equal to the concentration of 

 Cl, it is obvious that Donnan's equation (1) can only be fulfilled 

 if 



[Na] 1 >[Na] 2 

 and 



This inequality of concentration of the diffusible ions on the 

 opposite sides of the membrane accounts, as we shall see, for the 

 influence of electrolytes on all those properties which colloid 

 chemistry has vainly tried to explain on the basis of the disper- 

 sion and hydration hypotheses. The reader will notice that the 

 essential condition determining the equilibrium is the existence 

 of two phases separated by a membrane, one phase containing 

 an ion which cannot diffuse through a membrane which is easily 

 permeable for all the other ions. 



This difference in the concentration of the diffusible ions on 

 opposite sides of the membrane must lead to potential differences 

 on opposite sides of the membrane and Donnan shows that this 

 difference must be (on the basis of Nernst's well-known formula) 



RT, [Na] 2 RT, [Cl]i 

 TI - 7T 2 = log l ^ = -=- log l -^- 



[Na]x [Cl], 



prp 



or since -^r = 58 millivolts (at room temperature) the potential 

 r 



difference on opposite sides of the membrane should be in millivolts 



Tl _ T2=581og [4^ = 581og^ 

 [Na], [Cl], 



