Free-energy dissipations via various surface intermediates on Rh-metals in the catalytic hydrogenation of propene at 314 K are evaluated from the values of a novel rate constant I (Yasuda and Kuno, 1998) determined empirically by the frequency response (FR) method, where a cell reactor composed of a proton-conducting membrane was adopted; hydrogen and propone were separated by the membrane in order to investigate separately various rate processes due to either hydrogen or propene. The dissipations concluded are (i) -0.27 mu(HZ)(R) over bar and -0.45 mu(HZ)(R) over bar via the surface intermediates H-2(a) and H(a), respectively, and (ii) +1.62 mu(EZ)(R) over bar and -1.31 mu(EZ)(R) over bar via the intermediates C3H6(a) and C3H7(a), respectively; mu(HZ) denotes the difference between chemical potentials of the reactant and product given by mu(H-2(g))-mu(C3H8(g)) and mu(EZ) is the difference given by mu(C3H6(g))-mu(C3H8(g)); (R) over bar is the appearance rate of propane. Because free energy of a system must dissipate in the course of any reaction according to the second law of thermodynamics, the stage accompanied by +1.62 mu(EZ)(R) over bar (> 0) cannot occur spontaneously and therefore that stage may be regarded as the "real" rate-determining step. Because free-energy dissipation via an intermediate is expected to play a fundamental role in a catalytic reaction, the present ER method could open new aspects of heterogeneous catalysis in a kinetic study.