332 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



From Equation 112, the ratio of the activities of the un-ionized mole- 

 cules for any two conditions of the solution may be determined if the 

 potential change is known. Similarly, the ratio of the activity products 

 of the ions may be determined from Equation 113. The actual value of 

 the activity product is not in general determinable. At low concentra- 

 tions, however, as is apparent from Equation 109, the activity a ap- 

 proaches a value equal to that of the concentration C. If the potential 

 can be determined at sufficiently low concentrations, that is, in solutions 

 sufficiently dilute so that the laws of dilute solutions become applicable, 

 the true values of the activity products may be determined. In systems 

 in which a reaction takes place among the constituents the concentra- 

 tions C are not usually determinable, so that the value of the true activity 

 coefficients a remains undetermined. For practical purposes, therefore, a 

 new activity coefficient has been introduced, defined by the equation: 



where C s is the total concentration of the electrolyte. Further, instead 



ol employing the values of the product of the activity coefficients, some 

 function of the product of these coefficients is employed which makes the 

 resulting coefficient more nearly comparable with that of a solution of a 

 single molecular species. For electrolytes, Lewis and Randall have intro- 

 duced a coefficient a f) defined by the equation: 



1 



(115) 



where a f and C r may be called the reduced activities and the reduced 

 concentrations of the ions. 15 In a solution of a binary electrolyte: 



15 The nature of the various coefficients may be further elucidated by writing the 

 equations for the potential sum in somewhat more explicit form. We have : 



(117) 2nM = RT2n log C + Sni + ZnJ, 

 where 



ZnJ = RT 2tt log |. 



It is evident that this equation is not capable of being employed practically as an inter- 

 polation function, since C is not determinable. If, now, C" is replaced by C gt the total 



salt concentration of the electrolyte in solution in pure water, 



(118) 2nM = RT 2n log C 8 + 2ni + 2nJ a 



If the values of ZnM are known for different values of C , then the variation in the 

 function SwJ g over the concentrations in question is likewise known. In Equation 117, 



"ZnJ measures the change in the value of the potential of a substance in a real system 

 above that in an ideal system at the same concentration. When the reduced concentration 



