The qualitative changes in behaviour that can take place during an impedance spectroscopy study of an electrosorption reaction in the presence of an attractive interaction in the adsorbed phase have been investigated along with the mechanisms associated with switching between the branches of the electrosorption reaction isotherm. Isotherm branch switching corresponds to a tangent bifurcation and can entail a critical slowdown during impedance measurements. The transition between a low-amplitude harmonic cycle and a high-amplitude relaxation cycle is brutal but continuous and is not a true bifurcation.