122 HYDROGEN ION CONCENTRATION 



where D is the dielectric constant of the solvent and n the valence of 

 the ions. Therefore, for aqueous solutions it becomes 



- log fa = 0.32 • n2 \/c (2) 



This formula is derived under certain assumptions from the one 

 above (la). But it is to be used only as an approximation for rough 

 estimates. The factor 0.32 is in reality not quite accurately applic- 

 able to the different electrolytes; thus for KCl it appears, according 

 to Bjerrum, that the factor 0.25 and for HCl the factor 0.2 are more 

 exact. Let us now calculate for an example the value of fa for a 

 0.1 A'^ KCl solution, from the formula — log fa = 0.25 n'-\/c then c 

 being given as 0.1, 



- log fa = 0.25 V^ = 0.25 • 0.464 = 0.116 

 log fa = 0.884 - 1 

 fa = 0.766 



This formula is quite serviceable for dilute solutions up to 0.1 A''. 

 Besides, as stated above, the appropriate factor for \/c must be 

 chosen for each kind of electrolyte. As for the practical application 

 of this formula no more will be said for the present. 



2. But the most accurate method for the determination of fa is 

 the following : It is well established that in extremely dilute solutions 

 fa = 1, i.e., the activity and concentration become identical. With- 

 out this assumption the concept of activity has no meaning. Now, 

 if we set up a concentration chain with hydrogen electrodes and two 

 HCl solutions of which one is extremely dilute (ci) and the other of 

 any conveniently chosen concentration Co, then according to our 

 above outlined consideration the electromotive force developed will 

 not be 



E = -— - In — 

 F C2 



but 



E = — - In 



F c; ' i 



a 



For the very dilute solution of concentration Ci we may omit the 

 activity factor, for it is here = 1, Since the values of Ci, C2 and E are 

 either known or measurable, fa may therefore be calculated from the 



