Current Density
The rate of an electrochemical reaction is measured as current density, current per area. Common units are amps per square meter A m-2 or milliamps per square centimeter mA cm-2. This is related to mol m-2 s-1 by Faradays laws which say that with the passage of 96,485 coul of charge across the interface we have transformed one mole the substance if it was one electron per particle process. If it involved more than one electron, n electrons, then 1/n moles would have been reduced or oxidized. For a two electron process the passage of one mole of electrons would have reduced or oxidized 1/2 mole of material. So the reaction rate is given by
where F is the Faraday constant, 96,485 C mol-1. The Faraday constant is the charge on an electron multiplied by Avogadro's number.
1.602 ·10-19 coul · 6.022 ·1023 mol-1 = 96485 coul mol-1
For a typical current density of 10 mA cm-2 the rate is 10/96485 = 1.03 ·10-4 mol cm-2 s-1.
In an experiment the current is measured rather than the current density. The current is not only a function of the rate of the reaction but of the area of the electrode / solution interface as well. If a metal electrode is only partially submerged in the solution you can increase the current by lowering it further into the solution. (Most of the charge accumulates at the part in contact with the electrolyte rather than the air due to the double layer formation.) The larger the area of contact the more product will be formed per unit time but the current density will not change (provided you have not exceeded the limits of your power supply) (Figure 1). So while the current is a function of the mechanical arrangement it is the current density that is a characteristic of the reaction aside from the specifics of the particular apparatus.
Figure 1.
If you have a measured current and you want to know the current density you have to divide the current by the area of the electrode. The area of the electrode if often somewhat different than the area measured by macroscopic means. The surface area of an apparently smooth electrode is usually greater than the mechanical measurement due to microscopic roughness. A typical method is to measure the current in a standard solution of an electroactive substance (e.g., potassiun ferricyanide) where the current density is known for a certain concentration and applied potential. This gives you an electrochemical measurement based on a reaction at the interface. By dividing the measured current by the known current density you can calculate the active area.