570 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



Fig. 13 — Schematic distribution of neighbors in an assembl}- of particles when 

 forces of interaction are present. Repulsive forces are reflected in the appearance 

 of a distance a, of closest approach of two particles, attractive forces b}- the ex- 

 ponential ma.ximum at a . 



mum, i.e., inside 6 = 5 /2k/cT', as ion pairs, and the rest as unpaired. Noj 

 thought is given to the small fraction of nearest neighbors which involvesi 

 ions of like sign, as it must be small inside r = h. Nor is any thought 

 given to the possibility that a given positive nearest neighbor may be the 

 nearest neighbor of two negative ions simultaneously. Such a coincidence 

 would be very improbable at a distance short enough to be within r = b. 

 Thus if the entire theory can be made to depend on what happens inside 

 b, its foundations are reasonable, except for the choice oi h = N. 



To obviate this difficulty Fuoss had further to devise a means of per- 

 forming all calculations under conditions where the choice of /i = iVi 

 was not inconsistent. He assumed (following Bjerrum) that paired and 

 unpaired ions were in dynamic equilibrium and that the law of mass ac- 

 tion could be applied to this equilibrium. Thus if P represents the con-| 

 centration of pairs, N — P denotes the concentration of unpaired ions of; 

 one sign and the mass action expression is 



P 



(N - py 



= fi 



(7.10)1 



where Q, is an equilibrium constant independent of concentration. At 

 infinite dilution, where the assignment h = N is valid, U should be the' 

 same as at higher concentrations. Therefore (7.4) can be used to evalu-' 



