226 HYDROGEN ION CONCENTRATION 



tial as a function of two variables, a ("colloid" ion concentration) 

 and CI2 (which is in general the concentration in the outer solution of 

 any ion having a charge opposite to that of the "colloid "-ion). 



Let us now consider the relation of the ratio hi/h2 to a. From 

 equation (5) we see that when a = (i.e., in the absence of a "col- 

 loid" ion), hi/h2 = 1, and that therefore the potential = RT In 1 

 = 0; and that the greater the value of a the greater the difference 

 between hi/h2 and 1, and thus the greater the resulting potential. 



Now for the relation of hi/h2 to the value of CI2. It is such that the 

 ratio hi/h2 increases, without forming a maximum or minimum, with 

 increasing values of CI2. In fact, the greatest value for hi/h2 = 1 is 

 when CI2 = 00 , and its lowest value is when CI2 = . For, if we- 

 write (5) in the form 



y = - x-fv/x^ + 1 



and assume that x is very large (i.e. that CI2 is very small) in respect 

 to 1, then we can express the term \/x2 + 1, by developing it in a 

 binomial series, as 



11 ,1 11 

 xH — — , and hence, y= — + — 



2x 8x3 ' ' -^ 2x 8x3 



For X = 00 (i.e., for CI2 = 0), y (i.e., hi/h2) becomes = Q. 



It is quite easy, therefore, in a serial experiment, keeping the value' 

 of a constant, to increase the outer concentration of the Cl-ion, CI2, 

 by simply adding to the whole system HCl or any chloride. Hence it 

 follows that : 



1. The value of the ratio hi/h2 approaches 1 (the potential 

 approaches 0) with the addition of HCl. 



2. The same effect is obtained on the addition of any chloride, e.g.;. 

 NaCl. This leads to the following physiologically important 

 conclusion: 



All membrane potentials are decreased by the addition of neutral salts; 

 and in colloidal solutionis rich in electrolytes only very small membrane- 

 potentials are developed. 



It will be interesting to see just what potentials are to be expected 

 under certain assumptions. If the concentration of the molecularly 

 dispersed non-diffusible cation is taken as a = 0.01 N, then by apply- 

 ing equation (5) (page 225) we shall find in the outer solution the- 



