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The A.C. impedance response of mixed ionic and electronic conductors (MIECs) is derived from first principles and quantitatively compared with experimental data of three model systems: [...] (system I), [...] (system II), and [...] (system III). For the equilibrium systems I and II, which differ in terms of the preparation of the electrolyte, a broad spectrum of electrical and thermodynamic properties is extracted solely from the measurement of impedance spectra over wide oxygen partial pressure ([...] - 0.21 atm) and temperature ranges (500 to 650 [...]C). Electrolyte parameters derived from quantitative fitting of the impedance spectra include the concentration of free electron carriers, the mobilities for both ion and electron transport, the entropy and enthalpy of reduction of Ce4+ to Ce3+, and, for system II, the space charge potential characterizing the grain boundary behavior. In addition, the electrochemical behavior of O2 and H2 at the Pt|ceria interface has been characterized from these measurements. Under oxidizing conditions, the data suggest an oxygen electro-reduction reaction that is rate limited by the dissociated adsorption/discussion of oxygen species on the Pt electrode, similar to Pt|zirconia. Under reducing conditions, the inverse of the electrode polarization resistivity obeys a [...] dependence, with an activation energy that is similar to that measured for the electronic conductivity. These results suggest that ceria is electrochemically active for hydrogen electro-oxidation and that the reaction is limited by the rate of removal of electrons from the ceria surface. For the nonequilibrium system III, examined from 550 to 650 [...]C, the cathode oxygen partial pressure was fixed at 0.21 atm and the anode H2 was varied from 0.2 to 1 atm. The combination of Open Circuit Voltage (OCV) measurement and quantitative fitting of the impedance spectra yields electrochemical information at the two interfaces. The results are consistent with the H2 electro-oxidation mechanism at the Pt|ceria interface of systems I and II, whereas the resistance to the electro-reduction at the [...]|ceria is negligible.