ELECTRODE POTENTIALS 159 



RT 



This integration constant can be replaced by -;^ X In P and our 



r 



equation becomes 



RT P 



TT = — X In - (1) 



F p 



When p = P, then w = 0. Hence P represents that osmotic 

 pressure of the ionic species involved against which the electrode 

 has potential. Herein lies the physical interpretation or signifi- 

 cance of the integration constant. 



Since in very dilute solutions the osmotic pressure is proportional 

 to the concentration, the above equation can also be stated as 



TT = —- X In - (2) 



1" c 



where c is the ionic concentration in the given solution and C that 

 concentration against which the electrode potential would be = 0. 

 The meaning of the osmotic pressure of an ionic species must be 

 here further dealt with in somewhat greater detail. For extremely 

 dilute solutions there is no difficulty in this respect, for here con- 

 centration and pressure are proportional to each other. But in 

 higher concentrations this is no longer strictly true, and in such 

 cases equation (1) above must be used, in terms of pressures. Form- 

 erly no doubt was entertained in accepting as the osmotic pressure 

 that value which was obtained from freezing point determinations. 

 Thus, for example, if it was found that the lowering of the freezing 

 point of a 1 A'' KCl solution was 1.8 times as great as that of a 1 iV 

 cane-sugar solution, it was concluded that the "osmotic pressure" 

 of the KCl solution was 1.8 times as great. Furthermore, it was 

 assumed that, because of incomplete dissociation, there were 1.8 

 times (instead of twice) as many individual molecules (i.e., ions) 

 in the KCl solution as in the sugar solution. Now we assume that 

 there are actually twice as many molecules in the KCl solution 

 (see page 116), but that the electrostatic forces have an effect upon 

 the lowering of the freezing point. We have also shown that these 

 forces also exercise another influence upon the active 77iass of the 

 ions, and it is this active mass that we must obviously take to rep- 

 resent the "pressures" p and P above. Thus, when in following 

 the old convention, we speak of "osmotic pressure," it must be 



