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2.3. THEORETICALELECTROCHEMISTRY 35 1. The reference potential is set to that of the standard hydrogen electrode (SHE). Then, at U = 0 V, 298 K, pH=0, and equilibrium between electrolyte and 1 bar of H2 in gas phase the following relation applies: + − 1 G H +e ≡G 2H2 , (2.39) which means that the free energy change for reaction 2.37 is equal to the negative of the free energy change for reaction 2.35: 1 ∆G2.37 = G(HO∗)+G 2H2 −G(H2O)−G(∗) = −∆G2.35 = G(HO∗)+GH+ +e−−G(H2O)−G(∗). (2.40) In the same way, the free energy change for reaction 2.38 is the same as the negative of reactions 2.35 + 2.36: ∆G2.38 = − (∆G2.35 + ∆G2.36 ) . (2.41) This means that the free energies of electrochemical reaction steps, where the electron transfer is associated with hydrogen transfer, can be obtained from the corresponding heterogeneous reactions. This is not limited to H+ +e−, but any electrochemical reaction associated with a well known experimental equilibrium voltage can be handled the same way. As an ex- ample, the free energy change of the electrochemical reduction of Cl2: 21Cl2 +e− −↽−⇀− Cl−, (2.42) which is at equilibrium at standard conditions and U =1.37 V vs SHE, can be obtained directly from the free energy change of the associated heteroge- neous reaction 1 ∆G = G(Cl∗)−G(∗)−G 2 Cl2 . (2.43) This is illustrated in Figure 2.1. 2. The electrolyte is modeled by introducing one or more monolayers (ML) of H2O on the surface in the unit cell. In some situations, such as for rutile RuO2 (1 1 0) surfaces[107], the water layer is left out as the effect on the adsorption energies of intermediates is found to be very small[107, 114]. 3. Thefreeenergyofintermediates,withoutappliedpotential,atstandardstate can be calculated as ∆G = ∆Ew,water +∆ZPE −T∆S (2.44)PDF Image | Studies of Electrode Processes in Industrial Electrosynthesis
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