Complex rate constant for an electrochemical system involving an adsorbed intermediate

Two different methods of obtaining the impedance of a system involving an electrochemical reaction with an adsorbed intermediate are compared. The earlier method combines in parallel an impedance derived separately for the overall reaction with that for the rest of the system. It is appropriate for a fully supported electrolyte system but seems much less applicable to the unsupported situation. In contrast, the method derived and discussed herein involves complex reaction rate constants which may be directly incorporated in expressions for the total system impedance. This method may, therefore, be applied to either supported or unsupported situations. Several specific cases of the general complex rate constant results are discussed, particularly, various frequency dependencies possible. The overall small-signal impedance may be inductive in some parts of the frequency range and the low frequency limiting differential resistance negative, zero, or positive under various conditions.