MEMBRANE POTENTIALS 223 



Pt-Cl2 electrode, or a Hg-HgCl electrode which is reversible for 

 C1-) and unite the electrodes by a metal conductor, we shall find that 

 no current can flow through this system, since it is in equiUbrium. 

 But the electrode potentials are not equal to each other. Thus, if in 

 the final state of equilibrium the Cl~ concentration on the left is 

 ci and on the right is C2, then the potential difference between the two 



electrodes is equal to RT In -. In order that the entire system (or 



^ C2 



this chain) be entirely devoid of an electric current flowing through 

 it, we must assume that necessarily a potential amounting to — RT 



In ~ be present at the membrane, 



C2 



If we should now assume that in addition to KCl also HCl is pres- 

 ent, then a different state of equihbrium will ensue. This equilibrium 

 can also be evaluated. If we designate again the concentrations of 

 CI- in the left and right solutions Ci and C2 respectively (which are now 

 different, of course, from the Ci and C2 used in the preceding example), 



the potential difference will be — RT In -. But we can use hydrogen 



electrodes now, and even then the chain will not yield any electric 

 current. But this may only be true if the membrane potential is 



equal to RT In 77, where hi and h2 represent the [H+] of the two solu- 

 112 



tions. The same conditions will prevail in the presence of anj^ of 



the common ions along with our non diffusible ion. And thus by 



determining, after equilibrium has been attained in the system, the 



concentrations of any of its component ions, for instance that of the 



H-ions, which are always present, and which are easily determined, 



we can calculate from it the following: 



1. The membrane potential. 



2. The distribution of any of the ionic species between the two 

 solutions. 



When all the ions present are univalent, and letting the ratio of 

 the H+-concentrations, of that in the left to that in the right solu- 

 tion be 7 : 1, then 



1. The potential = RT In 7. 



2. The ratio of the concentrations of any of the positive diffusible 

 ions, that in the left to that in the right solution, is likewise = 



7, and for the negative ions it is = — . 



