Achieving the fundamental understanding of electrochemical processes occurring at the complex electrode-liquid interface is a grand challenge in catalysis. Herein, to gain theoretical insights into the experimentally observed potential-dependent activity and selectivity for CO2 reduction reaction (CO2RR) on the popular single-iron-atom catalyst, we performed ab initio molecular dynamics (AIMD) simulation, constrained MD sampling and the thermodynamic integration to acquire the free energy profiles for the proton and electron transfer processes of CO2 at different potentials. We have demonstrated that the adsorption of CO2 is significantly coupled with the electron transfer from the substrate while the further protonation does not show distinct charge variation. This strongly suggest that CO2 adsorption is potential-dependent and optimizing the electrode potential is vital to achieve the efficient activated adsorption of CO2. We further identified a linear scaling relationship between the reaction free energy (ΔG) and the potential for key elementary steps of CO2RR and HER, of which the slope is adsorbate-specific and not as simple as 1 eV per Volt as suggested by the traditional Computational Hydrogen Electrode (CHE) model. The derived scaling relationship can reproduce the experimental onset potential (Uonset) of CO2RR, potential of the maximal CO2-to-CO Faraday Efficiency (FECO), and the potential where FECO = FEH2. This suggests that our state-of-the-art model could precisely interpret the activity and selectivity of CO2RR/HER on Fe-N4-C catalyst under different electrode potentials. In general, our study not only provides an innovative insight into the theoretical explanation of the origin of solvation effect from the perspective of charge transfer but also emphasizes the critical role of electrode potential on theoretical consideration of catalytic activity, which offers a profound understanding of the electrochemical environment and bridges the gap between theoretical predictions and experiment results.