A general framework for a model of the stochastic behaviour of the electrochemical interface only governed by chemical or electrochemical reactions is presented. It leads to both the current-voltage curve, the electrochemical impedance and the electrochemical noise. An experimental arrangement and a special signal processing are described for analyzing the current fluctuations in potentiostatic regime: the power spectral density of the electrochemical noise is measured through the cross spectrum of the responses of two measurement channels. An application to the passivation of iron in acidic medium is presented both from the theoretical and experimental points of view. The agreement between the model predictions and the experimental data is good in the low current range while there is a discrepancy in the higher current range. Some interpretations are discussed.