220 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS 



amount of electrical charge passing per second through a plane of 1 cm 2 

 area, called the current 'density , I, is 



/ = nwq 



If A' is the number of molecules per mole: n/N is the concentration, c, in 

 moles/cc; and qN is the charge per mole. The charge required to oxidize or 

 reduce 1 mole of anything is zF, where F is the charge (96,500 coulombs per 

 equivalent weight) required to oxidize or reduce 1 g equivalent weight, and 

 Z is the number of equivalent weights per mole (i.e., the number of electrons 

 transferred in the redox reaction). This is Faraday's law. 

 Summed (2) for all different ions, s, then 



I = FZc s 



WsZ s 



Since c s is moles/cc and w s is cm/sec, the current density has the dimensions: 

 coulombs per cm 2 per sec, or amperes per cm 2 . 



Note that the current increases linearly with the concentration of charged 

 particles, with their speed, and with the charge they carry. 



Specific Conductivity of a Solution, k 



This is defined as the current which passes for an impressed voltage gradi- 

 ent, 13 , of 1 v/cm. That is, k = //I). This is a form of Ohm's law. Now 

 although the dissociation of ions of a salt is usually complete, sometimes 

 there is association and always there is hydration, and hence often the ef- 

 fective "degree of dissociation," a, is less than 1. Introducing this concept 

 gives 



FjLc sWl z s am p S 



k = a or ohm ' cm 



TJ volt/cm 



One more concept completes the picture. If the mobility, i± s , which is the 

 speed under an impressed voltage gradient of 1 v/cm, is defined as w s /\), 

 then 



* = Fj^c s n s z s a 



Note that this expression describes the rate of the electrical transport 



process. Thus k is the rate in amperes at which charge is transferred across 1-cm 2 



area of electrolyte if the voltage gradient along the path is I v per cm. The value is 



proportional to the concentration. The proportionality constant factors into 



three constants (a, z, F) and the mobility, fi; and n is really the specific rate 



constant for the process. Therefore n plays the same role for conductance as 



does k for chemical reactions, D for diffusion, and 4> for fluid flow, respec- 



cm / v 

 tively. The units of /x are / . Values of the mobilities of small ions 



sec/ cm 



