Abstract Redox catalysts play a critical role in advancing sustainability by enabling cleaner, more efficient chemical transformations. The redox potential of a catalyst determines the reaction direction thermodynamically, as electrons are transferred from the substrate through the catalyst to the product. The accurate assessment of redox catalyst potential by in situ methods is fundamental for developing effective strategies to optimize the redox reactivity of these materials. Typically, the catalyst potential measured in situ is relative to the reference electrode in the same solution. The standard potential of the catalyst, or metal center, is commonly reported relative to the standard hydrogen electrode (SHE). In electrochemical measurements, the potential recorded in situ versus a reference electrode is converted to scale by adding the known potential of that reference electrode relative to the SHE. The potential measured with the reversible hydrogen electrode (RHE), one of the reference electrodes, depends on the fugacity of hydrogen (H 2), the activity of hydrogen ions (pH) and the temperature. In this review, RHE is introduced as a descriptor of the redox catalyst activity for sustainable redox chemistry. 2. Redox Potential and Water The potential window represents the electrochemical stable range between the oxidative potential and reductive potential of the solvent [ 8]. In this sense, water is the most widely used solvent with a thermodynamically potential window as narrow as 1.23 V [ 9, 10]. Although most solutes in water are electrochemically stable within the potential window, dissolved oxygen (O 2) and hydrogen ions (H +) increase the redox potential of water [ 11]: E = 1.23 + 0.015 ୍ଠ log D O T − 0.059 ୍ଠ p H V a t 25 ° C , (2) where DOT is the dissolved oxygen tension (bar), and pH is the negative logarithm of H + activity in the solution. The solution containing dissolved O 2, an aerobic system, has a positive redox potential. In practice, dissolved O 2 levels can be electrochemically measured by amperometric or Clark-type sensors. On the other hand, polarographic sensors require an outside voltage to detect a current proportional to DOT. The primary method for the measurement of pH involves the Harned cell and the potential difference of the Harned cell, which can be electrochemically measured [ 12]. In practice, the pH of solution X can be measured using the standard pH solution S as follows: p H X = p H S + E X − E S 0.059 at 25 ° C , (3) where E X is the ORP in solution X, and E S is the ORP in solution S measured by the glass electrode. Hydrogen partial pressure (P H2) and hydrogen ion activity (pH) also reveal the redox potential of the solution, unless HER occurs, as follows: E = 0 − 0.029 ୍ଠ log P H 2 − 0.059 ୍ଠ p H V , at 25 ° C (4) where P H2 is dissolved hydrogen tension (bar), and pH is the negative logarithm of H + activity in the solution. In practice, dissolved H 2 concentration can be measured using a Clark-type H 2 sensor, which measures the H 2 partial pressure via a silicone membrane to the platinum electrode as the current [ 13]. The Pourbaix (E-pH) diagram presents the potential windows with aerobic and anaerobic systems, alongside acidic, neutral and alkaline water solutions ( Figure 2). The two lines in the figure serve as the OER and HER and represent the electrochemical stability (potential window) of water. H 2 is the second most abundant reduced element, with a total atmospheric burden estimated between 136 and 157 Tg, and the current emissions of H 2 are estimated at approximately 70 Tg/year [ 17]. H 2 in the ocean surface is supersaturated up to 15-fold relative to its atmospheric concentration, with the ocean serving as a significant source of H 2 emissions into the atmosphere [ 18]. H 2 typically remains in the atmosphere for approximately 2 years and is used by soil microbiomes as an energy source [ 19]. Bacteria in the soil oxidize H 2, including below atmospheric concentration, using hydrogenases linked to aerobic respiratory chains [ 20]. However, the extremely low concentration of H 2 in the atmosphere, 530–555 parts per billion, presents significant uncertainty due to our limited understanding of the processes involved and significant challenges associated with the measurement of H 2 concentration in the solution, due to its low solubility. 3. SHE and RHE The redox potential is fundamentally linked with Gibbs free energy because it is measured under the equilibrium (i.e., the reversible conditions of classical thermodynamics). In practice, the standard electrode potential of other half-reactions can be determined with respect to SHE, with an assigned potential of 0.00 V [ 23]. The electrochemical potential measurements generally use the connection between cells. When the concentration or composition is different across the connection between cells, the difference in mobilities of cations and anions can cause a liquid junction potential. The SHE consists of a platinized Pt electrode and an acidic solution where pH is 0, a unit activity of proton (H +), and H 2(g) is supplied to form small bubbles at a fugacity of 1.00 bar (f(H 2) = 1.00 bar) under the standard pressure (p 0 = 1.00 bar). Therefore, the acidic solution can be quickly saturated with dissolved H 2, with the reaction: 2H +(aq) + 2e − ⇄ H 2(diss) ⇄ H 2(gas). Proton and dissolved H 2 are equilibrated, and the potential is given by the Nernst equation: E = E 0 − R T F l n f H 2 / P 0 a H + ( V ) , (5) where E 0 is the potential of SHE (0.00 V), f(H 2) is the fugacity of H 2 in bar, P 0 is the standard pressure (p 0 = 1.00 bar), and a(H +) is the activity of H + ( Table 1). Substitution in the respective equations for pH (negative logarithm of activity of H +) and pH 2 (negative logarithm of the fugacity of H 2) leads to: E = 2.3026 R T 2 F p H 2 − 2.3026 R T F p H ( V ) , (6) where pH = −log[a(H +)] and pH 2 = −log[f(H 2)/P 0]. The potential of RHE can be calculated by pH, pH 2 and temperature. Although H 2 is one of the rare gases in the atmosphere and considered to be zero, the fugacity of H 2 is controlled at 1 bar for the RHE. The RHE serves as a practical, pH-dependent version (often E RHE can be calculated as E SHE − 0.059 × pH) used directly in the electrolyte, providing an accurate, stable reference with H 2(g) at a fugacity of 1.00 bar (f(H 2) = 1.00 bar) under standard pressure (p 0 = 1.00 bar) in actual experimental conditions. However, it is sometimes unclear whether the RHE was experimentally calibrated against the SHE or whether its potential was calculated theoretically. Gaseous H 2 above the solution is dissolved and equilibrated with dissolved H 2 in the solution. According to Henry’s law, the amount of dissolved gas is proportional to its partial pressure in the gas phase [ 24]. The value of Henry’s constant of H 2 and water is 1.28 × 10 5 atm mol −1 kg. At 1 atm P H2, the concentration of H 2 is 7.7 × 10 −4 mol/L, with the amount of H 2(diss) being very low. For a liquid phase in equilibrium with its vapor phase, the fugacity will be approximately equal to the vapor pressure when the vapor pressure is not excessively high [ 25]. It is important that: (i) the fugacity of H 2 in the solution can be measured in the gas phase equilibrated with the solution, and (ii) pH 2 can be approximated as the negative logarithm of the H 2 concentration [C(H 2)] under atmospheric pressure (1 bar): p H 2 = − log C H 2 , (7) RHE is also a practical, pH 2-dependent version (often E RHE ≈ E SHE + 0.029 × pH 2) used directly in the electrolyte, providing an accurate, stable reference in the solution, pH = 0. When the atmosphere demonstrates 0.53 ppm-H 2, the liquid junction potential can yield approximately +180 mV compared to 1 bar-H 2. Therefore, the theoretical potential of RHE can be calculated using pH and PH 2, which can be measured by the glass electrode potential in the solution and the H 2 concentration of the gas above the solution. The electrode potential can be regarded as the potential difference between a point in the metal conductor (M) and the other point in the electrolytic solution (S), corresponding to the Galvani potential (ΔϕMS) [ 26]. The Galvani potential is not directly measurable because it is impossible to separate the electrical energy from the chemical work to transfer a charge across two different phases [ 27]. In practical measurements, the electrode potential is measured as a relative value by introducing an additional electrode (reference electrode). When the RHE is used as a reference electrode, the in situ potential of the catalyst, E cat, in the solution can be calculated by the standard potential of the catalyst, E 0cat, and the theoretical potential of RHE, E RHE, from Equation (1) as: E c a t = E 0 c a t − E R H E (8) Therefore, the catalyst potential in solution depends on the standard potential of the catalyst, temperature, pH, and H 2 concentration above the solution. While the fugacity of H 2 is assumed to be unit, the pH is varied between 0 and 14. The in situ potential of the catalyst is calculated from Equations (6) and (8): E c a t ≈ E 0 c a t + 0.059 ୍ଠ p H , V , a t 25 ° C (9) As the pH increases or as H + activity decreases, the in situ potential of the catalyst increases 0.059 V per pH unit ( Figure 6). While the pH is assumed to be unit, the concentration of H 2 varies between 0.53 × 10 −6 and 1.0. The in situ potential of the catalyst is calculated from Equations (6) and (8): E c a t ≈ E 0 c a t − 0.029 ୍ଠ p H 2 , ( V ) a t 25 ° C (10) As the concentration of H 2 increases, or as pH 2 decreases, the in situ potential of the catalyst increases by 0.029 V per pH 2 unit ( Figure 7). Catalysts with a higher in situ potential exhibit greater electron-accepting power, thereby enhancing the oxidation reactions of substrates. Factors such as pH and the concentration of H 2 above the solution can therefore affect the oxidation reactions through changes in the catalyst potential [ 28]. 4. Redox Catalyst Activities and Redox Potential Redox catalysis can be regarded as a catalytic process involving the formation or breaking of chemical bonds through redox reactions, typically mediated by transition metals. Most redox catalysts can be coupled with electrode reactions in which the initial chemical reaction is directly followed by the electron transfer [ 29]. Current–potential curves obtained from catalyst–electrode reactions offer the electron transfer rate constant, the redox potential of the catalyst active site, and the rate-determining step (RDS). When catalysts are confined on the electrode surface, the catalyst can accelerate chemical reactions without being consumed by the reaction. The electrode reaction kinetics are typically given by the Butler–Volmer equation [ 30]. The rate constants (k) for oxidation and reduction are given by: k o x = k 0 e x p 1 − α F E − E ° R D S R T , k r e d = k 0 e x p − α F E − E ° R D S R T (11) where E ° R D S is the redox potential of RDS, while k 0 is the standard rate constant and α is the transfer coefficient at RDS. The Butler–Volmer equation is a fundamental relationship that describes how the current at an electrode depends on the electrode potential of the catalysts in the electrolyte solution [ 31]. In this situation, a half reaction of catalysis, oxidation or reduction, may be measured as the current, whereas the other half reaction can be replaced by the electrode ( Figure 8). 5. Redox Catalyst Activities and RHE The electrochemical potential of a catalyst can be measured by wiring it to external circuits. Introducing low concentrations of redox-active molecules between the catalyst and sensing electrode has been recently demonstrated to have potential for scaling the oxidative dehydrogenation of formic acid on a catalyst supported on platinum [ 35]. Although E probe remained >500 mV positive of E cat, introducing a silicotungstic state redox sensor resulted in the equality of E probe and E cat. This approach allowed for the quantification of the equilibrium potential of E cat under H 2 pressure (0.1–1 bar) or pH (1–4.46). The rate–potential scaling revealed that turnover frequency varied by a factor of 2.3 among the three catalyst formulations studied. E RHE may also affect both the E cat and the catalyst reaction rate. Experimental techniques of steady state catalyst potential measurements have been reported during hydrogenation and oxidation reactions of Pt catalysts in slurry reactors [ 36]. Slurry reactors have been characterized by the presence of a solid catalyst or reactant suspended in a liquid phase, with a gas phase often being present as well. The aerobic oxidation of alcohols is typically catalyzed by Pt catalysts with a broad range of catalyst potentials (ca. 100–850 mV) during the reaction. The Pt and Pd surfaces in aqueous solutions may be partially covered by H 2 below 0.3–0.4 V and by O 2 above 0.6–0.7 V [ 37]. A generalized correlation between the current and the catalyst potential is shown in Figure 10. The current increases up to a maximum and then declines. As the catalyst potential increased, more active sites were covered by the oxidizing species, and fewer free sites were available for alcohol adsorption. Accordingly, the observed reaction rate decreased rapidly above the optimum. Deactivation of the catalysts by high catalyst potential is termed over-oxidation in the literature [ 38]. The stability of Pd-based catalysts has focused on the alcohol oxidation kinetics, especially in the direct ethanol fuel cells [ 39]. The composition of electrolytes and individual dissolved molecules directly affects the activity of the catalyst. The catalytic activity can be estimated by measuring the onset potential and the peak current density. Catalyst and dissolved molecules play a crucial role in determining current density and power for efficient ethanol electrooxidation [ 40]. Instead of the catalyst potential, H 2 in the solution could be used as the potential of RHE because the catalyst surface may be covered by H 2 below 0.3–0.4 V. 6. Redox Catalyst Activities Related to Potential of RHE in the Solution Under high-temperature pressurized water, assuming the interior of a typical nuclear reactor, intergranular stress corrosion cracking (ISCC) of the stainless-steel piping has been identified through the changes in dissolved O 2 content of the de-oxygenated water [ 41]. Although dissolved O 2 is typically necessary to make an oxide film, at 20 ppm dissolved O 2, the oxide film on the surface of stainless-steel piping was peeled from the matrix, resulting in intergranular stress corrosion cracking. ISCC in boiling water reactor (BWR) nuclear plants can be successfully mitigated during normal power operation using moderate hydrogen water chemistry [ 42]. The potential of BWR water with normal H 2 water chemistry has been typically observed as +150 mV SHE. Under moderate hydrogen water chemistry, electrochemical corrosion potential can be lowered to <−230 mV (SHE), at which IGSCC can be mitigated, by reducing the concentration of oxidants (H 2O 2 and O 2) in the bulk coolant, and up to 2 ppm feedwater hydrogen may be required [ 43]. Studies have shown that the potential can only be accurately measured in situ for proper H 2 dosage control. Because the addition of H 2 lowers the RHE potential, the stainless-steel piping with a higher in situ potential possesses a higher tendency to acquire electrons and consequently provides stronger protection against ISCC. This behavior arises because corrosion is fundamentally a redox reaction. The pH and pH 2 are the logarithms of the activity of H + and the fugacity of H 2, respectively. Using the Nernst equation, a 10-fold change in H 2 corresponds to a 30 mV decrease in the RHE potential. When air (21% O 2) with 100 ppm-H 2 was bubbled into the PBS, the ORP decreased to 60 mV compared to that of air without H 2, which was estimated by the Nernst equation [ 44]. Aerobic respiration involves a series of redox reactions within the electron transport chain. Succinate dehydrogenase (respiratory chain complex II) catalyzes the oxidation of succinate to fumarate while simultaneously reducing ubiquinone to ubiquinol. Forward-electron transport (FET) can be assessed by monitoring the oxidation of reduced nicotinamide adenine dinucleotide hydrate (NADH), which is also coupled to the reduction of ubiquinone to ubiquinol through respiratory complex I [ 45]. Succinate promotes the reduction of ubiquinone to ubiquinol through complex II and can induce reverse electron transport (RET), which is associated with an increase in NADH levels. The addition of H 2 altered the direction of electron flow from the succinate-induced RET toward FET. Because the addition of H 2 decreased the potential of RHE, the in situ potential of mitochondrial respiratory complexes could increase, thereby promoting NADH oxidation and FET. During aerobic respiration, the direction and reactivity of the redox catalyst (enzyme) could therefore be related to the RHE potential, which is determined by the fugacity of H 2. 7. Conclusions The redox potential serves as a critical parameter for understanding the energy-related behavior of redox catalysts. However, each redox center has an independent redox potential, and it is difficult to control its in situ redox potential. In this review, RHE potential is introduced to determine the in situ potential using the standard potential of each redox catalyst. The RHE potential is proportional to both the pH and the vapor pressure of H 2. As the pH in the solution or the vapor pressure of H 2 above the solution increases, the in situ catalyst potential also increases. The Butler–Volmer equation predicts that the current increases as the potential difference becomes more positive. Provided that suitable reaction conditions are selected, the in situ catalyst–potential measurements may enable the real-time determination of catalyst function in the liquid phase, which is difficult to achieve using other analytical methods. However, catalyst performance depends on many aspects, e.g., kinetics, adsorption, surface structure, mass transfer, solvent effects, catalyst stability, and reaction mechanism. As a result, the assessment and control of redox catalyst potential can contribute to sustainable catalysis by optimizing reaction conditions through the RHE or by improving the process through H 2-producing microbiomes in green redox transformations. Funding This research received no external funding. Institutional Review Board Statement Not applicable. Informed Consent Statement Not applicable. Data Availability Statement No new data were created or analyzed in this study. Data sharing is not applicable to this article. Conflicts of Interest The authors declare no conflict of interest. Abbreviations The following abbreviations are used in this manuscript O 2Oxygen H 2O Water H +Hydrogen ion H 2Hydrogen ORP Oxidation Reduction Potential SHE Standard Hydrogen Electrode RHE Reversible Hydrogen Electrode DOT Dissolved Oxygen Tension LFER Linear Free Energy Relationship ISCC Intergranular Stress Corrosion Cracking BWR Boiling Water Reactor ECP Electrochemical Corrosion Potential H 2O 2Hydrogen Peroxide FET Forward Electron Transfer RET Reverse Electron Transfer NADH Reduced Nicotinamide Adenine Dinucleotide RDS Rate Determining Step atm Atmosphere References Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. © 2026 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license. MDPI and ACS Style Kiyama, T. Hydrogen Electrode Potentials as a Descriptor of Catalyst Reactivity for Sustainable Redox Chemistry: A Tutorial Review. Sustainability 2026, 18, 5791. https://doi.org/10.3390/su18115791 AMA Style Kiyama T. Hydrogen Electrode Potentials as a Descriptor of Catalyst Reactivity for Sustainable Redox Chemistry: A Tutorial Review. Sustainability. 2026; 18(11):5791. https://doi.org/10.3390/su18115791 Chicago/Turabian Style Kiyama, Teruo. 2026. "Hydrogen Electrode Potentials as a Descriptor of Catalyst Reactivity for Sustainable Redox Chemistry: A Tutorial Review" Sustainability 18, no. 11: 5791. https://doi.org/10.3390/su18115791 APA Style Kiyama, T. (2026). Hydrogen Electrode Potentials as a Descriptor of Catalyst Reactivity for Sustainable Redox Chemistry: A Tutorial Review. Sustainability, 18(11), 5791. https://doi.org/10.3390/su18115791
