156 OXIDATION-REDUCTION POTENTIALS 



vicinity of the small drop of mercury issuing from the capillary tube of the cathode that 

 determine the " voltammetric curve." Under the conditions of the polarographic 

 method, with a minute cathode and a current flowing through the circuit conditions 

 throughout the system are not uniform as in the ordinary methods of measuring 

 electrode potentials, described in previous chapters. In the immediate vicinity of 

 the drop of mercury the oxidation-reduction system may be almost completely 

 reduced whilst in the main bulk of the solution the system is entirely in the oxidised 

 condition, so it is important not to confuse conditions at the cathode with the 

 general condition of the system. 



When low potentials are applied to the system no current flows until the 

 decomposition potential is reached. But at potentials above this the system is 

 reduced at the cathode, that is it loses its negative charge to the cathode and a 

 current flows. It will be evident that at any given electrode potential a characteristic 

 proportion of the system will be reduced in the immediate vicinity of the cathode. 

 Eventually when the limiting current is reached the solution immediately surrounding 

 the drop of mercury is completely depleted of oxidised form and the current 

 flowing is dependent only on diffusion of the non-reduced form from the 

 body of the solution to the layer of the mercury drop. Now the rate of this 

 diffusion can be shown to be dependent only upon the concentration of the oxidation- 

 reduction system in the body of the fluid and to be independent of the applied 

 potential, so the current- voltage curve becomes flat. 



The Ilkovic equation giving the value of the diffusion current (Id in amperes) 

 at any time is as follows : — 



I, = 0-732n FD^ Cm^ t« 



where n is the number of electrons concerned in the oxidation-reduction reaction, 

 F is the Faraday (96,500 coulombs), D is the diffusion coefficient of the electroactive 

 material (in cms. per second), C its concentration (in moles per ml.), m the weight 

 (in g.) of mercury flowing from the capillary per second, and t the time (in seconds) 

 of the period of life of the drop. The Ilkovic equation can be simplified and the 

 following equation gives the mean current flowing : — 



I^ = 605n D* CmS t^^ 



where the current is in microamperes and the concentration is in millimoles per litre. 

 It is interesting to note that the mean current flowing during the whole life of the 

 drop is equal to six-sevenths of the maximum current flowing just before the drop 

 falls. Although the current flowing fluctuates throughout the life of the drop it 

 is possible, as mentioned above, to obtain a steady reading by using a galvan- 

 ometer with a long period of vibration. 



In the above equations all the factors for any system are constant except 

 the concentration so that the current flowing is proportional to the concentration : — 



Id = kC. 



Hence with any particular oxidation-reduction system once the current for any 

 known concentration has been determined the measure of the current flowing in 

 other solutions will give the concentration of the system. 



