Theory of Direct Coulometry

Direct coulometry is often referred to as coulometry at controlled potential. In the direct method, the electrode reaction nearly always involves the analyte 

5 Text and illustrations in this section are taken from Analytical Chemistry , James 

Although coulometric principles for analytical work were discussed by Szebeledy and Somogyi [101] in 1938, Hickhng [102] wrote of determining copper by controlled potential coulometry in 1942. The current in direct coulometry decreases exponentially with time. The time to reach a quantitative completion, for most analytical apphcations, can be taken as that time when the current has decreased to a value indicative of analyte concentration in solution of 10- M or less. The final concentration will depend upon the requirement for analytical completion for the reaction involved. Alternatively, the critical time can be determined when some indicator system shows the required analyte or reactant concentration has been reached. 

The ciurrent-time relationship can be evaluated for area within the hmits of the initial time and the time to reach quantitative completion by an integrator. It is apparent that the result will be obtained from  

In applying the integrator technique, the value of Q at any time t will be given by  

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