Hydrogen Electrode Potentials as a Descriptor of Catalyst Reactivity for Sustainable Redox Chemistry: A Tutorial Review

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 (H₂), 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.

1. Introduction

Oxidation–reduction (redox) processes involve two important factors: (1) they are coupled with oxidation reactions and reduction reactions, and (2) they involve oxygen atoms, hydrogen atoms, or electron transfer from one material to another [1]. Redox reactions are involved in important activities, such as the rusting and dissolution of metals, and biological energy production through respiration. Redox potential is a measure of the tendency to acquire or lose electrons in the solution and serves as a key factor in determining those redox processes with significant implications for ecosystem health and environmental sustainability [2]. Redox potential measurement represents a critical analytical tool for evaluating the redox process in water or soil environments. Oxidation–reduction potential (ORP) can be measured by immersing a working electrode with a metal tip, connected to a reference electrode, into a sample solution. It can take up to several minutes to reach the equilibrium since the redox reaction can be complex. Moreover, the measured ORP is relative, not to the overall reaction, but to the particular redox reaction. In the working electrode metal, the reactions of all redox molecules, including oxygen (O₂), occur in a sample solution under aerobic conditions. Thus, when the ORP of a lake or river is high, dissolved O₂ and bacteria can decompose dead tissue and contaminants efficiently. In addition, the reference electrode (e.g., standard hydrogen electrode (SHE) and Ag/AgCl electrode) demonstrates a constant potential for any sample [3]. However, ORP is typically affected by all oxidizing and reducing agents and only provides the relative measures of a sample solution.

In electrochemistry, some redox catalysts can directly connect with electrodes in their catalytic reactions [4]. The electrode functions either as an electron donor or an electron acceptor in the redox reactions, while the complementary half reaction occurs on the catalyst. Linear free-energy relationships refer to the correlation between the free energy changes in chemical reactions and the corresponding changes undergone by the structure of reactants. The reaction constant k2 between the catalyst and the electrode depends on the formal potential of the electrode. When a redox catalyst is dissolved in the solution, its redox potential cannot be controlled by the electrode. As a result, the redox potentials of the catalysts can be designed by both the active center metals and ligands. The activity increases almost linearly with the redox potential of the catalyst up to a point and decreases thereafter [5]. These volcano-shaped correlations are very common in electrocatalysis and heterogeneous catalysis. However, instead of the redox potential, a parameter is typically used to describe the degree of oxidative product due to the interaction of O₂.

A reference electrode provides a stable reference potential against which the potential of the working electrode is measured. Hydrogen electrodes are reference electrodes, and their potentials define the zero level for all redox half reactions in electrochemistry. The potential of SHE is defined as 0.00 volts at all temperatures and serves as the basis of the thermodynamic scale for comparison with other electrochemical reactions [6]. In aqueous solutions, the SHE consists of a platinized Pt electrode immersed in an acidic solution, with a unit activity of a proton (H⁺) through which hydrogen gas (H₂) is supplied at a fugacity of 1.00 bar. This allows the electrolyte solution to be quickly saturated with gas. The standard potential of all redox catalysts in water solution is listed with respect to SHE, and the standard potential is a measure of the redox ability of the catalyst to accelerate redox processes. Specifically, a high redox value in catalysts increases the electron-accepting power from the reduced and enhances oxidation. Each aqueous solution with the redox catalyst contains different activities of H⁺ and H₂ fugacity. When one of these factors is not a unit, it is defined as the reversible hydrogen electrode (RHE), and its potential deviates from the SHE according to the Nernst equation. RHE exhibits potentials depending on pH and is usually used in practice associated with catalysis. The conversion of potential value between the RHE scale and SHE can be obtained by [7]:

$${\mathrm{E}}_{\mathrm{S}\mathrm{H}\mathrm{E}}={\mathrm{E}}_{\mathrm{m},\mathrm{R}\mathrm{H}\mathrm{E}}+{\mathrm{E}}_{\mathrm{R}\mathrm{H}\mathrm{E}}$$

(1)

where E_SHE is the standard potential versus the SHE, E_m,RHE is the potential measured versus the RHE, and E_RHE is the potential of the RHE. Thus, the potential measured versus the RHE can be calculated using the potential of the RHE of the solution and the standard potential versus SHE. At pH = 7, since the potential of SHE is fixed at 0.00 V, the standard potential of CoQ/CoQH₂ is reported as 0.03 V (vs. SHE). Since RHE is calculated as −0.420 V (vs. SHE) at pH = 7 and H₂ fugacity is a unit, the potential of CoQ/CoQH₂ is measured as 0.45 V (vs. RHE). In contrast, since RHE is calculated as −0.24 V (vs. SHE) at pH = 7 and H₂ fugacity = 10⁻⁶, the potential of CoQ/CoQH₂ is measured as 0.27 V (vs. RHE) (Figure 1). When RHE is used for a reference electrode, the redox potential measured depends on the potential of RHE, even if the redox potential is stable for SHE. In this review, the potential of the RHE was calculated using the activity of H⁺, the fugacity (the vapor pressure) of H₂ and the temperature of the solution. Since the redox catalyst activities depend upon the redox potentials of the catalyst, the RHE potential of the solution could serve as a redox activity descriptor of catalyst addition to substrate concentration and the catalyst potential with respect to the SHE.

Figure 1. Comparison of the potential scales of the SHE, the reversible hydrogen electrode (RHE) for pH 7 and pH₂ 0, and the reversible hydrogen electrode for pH 7 and pH₂ 6. The potential of CoQ/CoQH₂ couples, +0.03 V SHE, could be calculated as +0.45 V RHE (pH 7 and pH₂ 0) and +0.27 V RHE (pH 7 and pH₂ 6).

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 (O₂) and hydrogen ions (H⁺) increase the redox potential of water [11]:

$$\mathrm{E}=1.23+0.015\times \left(\log \mathrm{D}\mathrm{O}\mathrm{T}\right)-0.059\times \mathrm{p}\mathrm{H}\left(\mathrm{V}\right) \mathrm{a}\mathrm{t} 25 °\mathrm{C},$$

(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 O₂, an aerobic system, has a positive redox potential. In practice, dissolved O₂ 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:

$$\mathrm{p}\mathrm{H}\left(\mathrm{X}\right)=\mathrm{p}\mathrm{H}\left(\mathrm{S}\right)+{\displaystyle \frac{\left({\mathrm{E}}_{\mathrm{X}}-{\mathrm{E}}_{\mathrm{S}}\right)}{0.059}} \mathrm{at} 25 °\mathrm{C},$$

(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:

$$\mathrm{E}=0-0.029\times \left(\log {\mathrm{P}}_{\mathrm{H}2}\right)-0.059\times \mathrm{p}\mathrm{H}\left(\mathrm{V}\right), \mathrm{at} 25 °\mathrm{C}$$

(4)

where P_H2 is dissolved hydrogen tension (bar), and pH is the negative logarithm of H⁺ activity in the solution. In practice, dissolved H₂ concentration can be measured using a Clark-type H₂ sensor, which measures the H₂ 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.

Figure 2. Pourbaix diagram of water, where the X axis corresponds to hydrogen ion activity (pH), the Y axis corresponds to voltage potential with respect to the standard hydrogen electrode, and the limits of stability of water are marked by the two dashed lines. Below the lower line (highly reducing conditions), water may be reduced to hydrogen gas. Correspondingly, above the upper line (highly oxidizing conditions), water may be oxidized into oxygen gas. The gray shading indicates the potential window for water.

The redox ladder is a series of redox reactions based on the standard redox potential of redox pairs [14]. Under aerobic systems, respiration occurs according to its redox ladder (Figure 3). The redox potential in the solution offers significantly more details about gaseous conditions than the dissolved oxygen tension measurement [15]. Under anaerobic systems, the redox gradient can form as a result of microbial processes and chemical composition of the environment (Figure 4) [16].

Figure 3. A redox ladder showing the redox potential of common aerobic metabolic redox molecules. Metabolic process includes electron transfer from the reduced state to the oxidized state in glycolysis or respiration. The gray shading indicates the potential window for water. The oxidation reaction proceeds in the direction of the arrow.

Figure 4. A redox ladder showing anaerobic redox-active elements as the redox potential declines. When oxygen is depleted, the electron acceptor consists of nitrate, followed by manganese, ferric iron, sulfate, and finally carbon dioxide/methane. The gray shading indicates the potential window for water. The reduction reaction proceeds in the direction of the arrow.

H₂ is the second most abundant reduced element, with a total atmospheric burden estimated between 136 and 157 Tg, and the current emissions of H₂ are estimated at approximately 70 Tg/year [17]. H₂ in the ocean surface is supersaturated up to 15-fold relative to its atmospheric concentration, with the ocean serving as a significant source of H₂ emissions into the atmosphere [18]. H₂ 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 H₂, including below atmospheric concentration, using hydrogenases linked to aerobic respiratory chains [20]. However, the extremely low concentration of H₂ 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 H₂ concentration in the solution, due to its low solubility.

Redox potential is one of the critically important factors in the water solution, among others, such as the dissolved O₂ tension, pH, H₂ partial pressure and temperature. In many redox reactions in solution, the high redox potentials of the redox pair hinder oxidation, resulting in a slow reaction rate [21]. Thus, catalysts with suitable redox potentials, accompanied by reducing and oxidizing reactions, are required to execute thermodynamically demanding reactions (Figure 5) [22].

Figure 5. Redox catalysis with electron transfer from electron donor to electron acceptor according to redox potential [22].

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 H₂(g) is supplied to form small bubbles at a fugacity of 1.00 bar (f(H₂) = 1.00 bar) under the standard pressure (p⁰ = 1.00 bar). Therefore, the acidic solution can be quickly saturated with dissolved H₂, with the reaction:

2H⁺(aq) + 2e⁻ ⇄ H₂(diss) ⇄ H₂(gas).

Proton and dissolved H₂ are equilibrated, and the potential is given by the Nernst equation:

$$\mathrm{E}={\mathrm{E}}^0-{\displaystyle \frac{\mathrm{R}\mathrm{T}}{\mathrm{F}}}\mathrm{l}\mathrm{n}\left({\displaystyle \frac{\sqrt{\mathrm{f}\left({\mathrm{H}}_2\right)/{\mathrm{P}}^0}}{\mathrm{a}\left({\mathrm{H}}^{+}\right)}}\right) (V),$$

(5)

where E⁰ is the potential of SHE (0.00 V), f(H₂) is the fugacity of H₂ in bar, P⁰ is the standard pressure (p⁰ = 1.00 bar), and a(H⁺) is the activity of H⁺ (Table 1).

Table 1. List of abbreviations and units.

Abbreviation	Definition	Units
PH2	partial pressure of H2	bar or Pa
pH2	negative logarithm of H2 fugacity	None
f(H2)	fugacity of H2	bar or Pa
C(H2)	concentration of H2	parts per billion (ppb)
ERHE	potential of reversible hydrogen electrode	V
ESHE	potential of standard hydrogen electrode	V
Ecat	potential of catalyst	V

Substitution in the respective equations for pH (negative logarithm of activity of H⁺) and pH₂ (negative logarithm of the fugacity of H₂) leads to:

$$\mathrm{E}={\displaystyle \frac{2.3026\mathrm{R}\mathrm{T}}{2\mathrm{F}}}{\mathrm{p}\mathrm{H}}_2-{\displaystyle \frac{2.3026\mathrm{R}\mathrm{T}}{\mathrm{F}}}\mathrm{p}\mathrm{H} (V),$$

(6)

where pH = −log[a(H⁺)] and pH₂ = −log[f(H₂)/P⁰]. The potential of RHE can be calculated by pH, pH₂ and temperature.

Although H₂ is one of the rare gases in the atmosphere and considered to be zero, the fugacity of H₂ 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 H₂(g) at a fugacity of 1.00 bar (f(H₂) = 1.00 bar) under standard pressure (p⁰ = 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 H₂ above the solution is dissolved and equilibrated with dissolved H₂ 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 H₂ and water is 1.28 × 10⁵ atm mol⁻¹ kg. At 1 atm P_H2, the concentration of H₂ is 7.7 × 10⁻⁴ mol/L, with the amount of H₂(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 H₂ in the solution can be measured in the gas phase equilibrated with the solution, and (ii) pH₂ can be approximated as the negative logarithm of the H₂ concentration [C(H₂)] under atmospheric pressure (1 bar):

$${\mathrm{p}\mathrm{H}}_2=-\log \left[\mathrm{C}\left({\mathrm{H}}_2\right)\right],$$

(7)

RHE is also a practical, pH₂-dependent version (often E_RHE ≈ E_SHE + 0.029 × pH₂) used directly in the electrolyte, providing an accurate, stable reference in the solution, pH = 0. When the atmosphere demonstrates 0.53 ppm-H₂, the liquid junction potential can yield approximately +180 mV compared to 1 bar-H₂. Therefore, the theoretical potential of RHE can be calculated using pH and PH₂, which can be measured by the glass electrode potential in the solution and the H₂ 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, E⁰cat, and the theoretical potential of RHE, E_RHE, from Equation (1) as:

$${\mathrm{E}}_{\mathrm{c}\mathrm{a}\mathrm{t}}={{\mathrm{E}}^0}_{\mathrm{c}\mathrm{a}\mathrm{t}}-{\mathrm{E}}_{\mathrm{R}\mathrm{H}\mathrm{E}}$$

(8)

Therefore, the catalyst potential in solution depends on the standard potential of the catalyst, temperature, pH, and H₂ concentration above the solution. While the fugacity of H₂ 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):

$${\mathrm{E}}_{\mathrm{c}\mathrm{a}\mathrm{t}}\approx {{\mathrm{E}}^0}_{\mathrm{c}\mathrm{a}\mathrm{t}}+0.059\times \mathrm{p}\mathrm{H}, \left(\mathrm{V}\right), \mathrm{a}\mathrm{t} 25 °\mathrm{C}$$

(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).

Figure 6. Potential difference between the catalyst and reversible hydrogen electrode (RHE) at different pH values, indicating that the potential difference increased with increasing pH, while the activity of hydrogen ions decreased.

While the pH is assumed to be unit, the concentration of H₂ varies between 0.53 × 10⁻⁶ and 1.0. The in situ potential of the catalyst is calculated from Equations (6) and (8):

$${\mathrm{E}}_{\mathrm{c}\mathrm{a}\mathrm{t}}\approx {{\mathrm{E}}^0}_{\mathrm{c}\mathrm{a}\mathrm{t}}-0.029\times {\mathrm{p}\mathrm{H}}_2, \left(\mathrm{V}\right) \mathrm{a}\mathrm{t} 25 °\mathrm{C}$$

(10)

As the concentration of H₂ increases, or as pH₂ decreases, the in situ potential of the catalyst increases by 0.029 V per pH₂ 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 H₂ above the solution can therefore affect the oxidation reactions through changes in the catalyst potential [28].

Figure 7. Potential difference between the catalyst and reversible hydrogen electrode (RHE) at different pH₂ values, indicating that the potential difference increased with increasing H₂, while the pH₂ decreased.

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:

$${\mathrm{k}}_{\mathrm{o}\mathrm{x}}={\mathrm{k}}^0\mathrm{e}\mathrm{x}\mathrm{p}\left[{\displaystyle \frac{\left(1-\mathsf{\alpha }\right)\mathrm{F}\left(\mathrm{E}-{\mathrm{E}°}_{\mathrm{R}\mathrm{D}\mathrm{S}}\right)}{\mathrm{R}\mathrm{T}}}\right]\mathrm{and}, {\mathrm{k}}_{\mathrm{r}\mathrm{e}\mathrm{d}}={\mathrm{k}}^0\mathrm{e}\mathrm{x}\mathrm{p}\left[{\displaystyle \frac{-\mathsf{\alpha }\mathrm{F}\left(\mathrm{E}-{\mathrm{E}°}_{\mathrm{R}\mathrm{D}\mathrm{S}}\right)}{\mathrm{R}\mathrm{T}}}\right]$$

(11)

where ${\mathrm{E}°}_{\mathrm{R}\mathrm{D}\mathrm{S}}$ is the redox potential of RDS, while k⁰ 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).

Figure 8. The relationship between current density and the redox potential of the catalyst is based on the linear free energy relationship (LFER) [4].

Alternatively, when both oxidative and reductive half-reactions occur simultaneously on the same catalyst surface, the catalyst exhibits a mixed potential provided that the catalyst is electrically conductive and that a suitable molecule is present near the active sites [32]. The mixed potential theory can be explained to quantitatively discuss the multiple, simultaneous oxidation and reduction reactions (i.e., corrosion) that occur on a catalyst surface, where the net current is zero. The current density derived from each half-reaction, reduction or oxidation, exponentially increases with increasing overpotential, according to the Butler–Volmer equation. When the absolute values of the reduction and oxidation current densities are balanced, the electrochemical potential is referred to as the corrosion potential. The potential–current curve presents a volcano correlation in which the current increases due to the reduction reaction up to the corrosion potential and then decreases as oxidation becomes dominant on the catalyst surface (Figure 9). The potential shift from the corrosion potential will decrease the overpotential compared to the equilibrium potential of either reduction or oxidation, resulting in a decrease in current density. Mixed-potential-driven catalysis may produce a different catalytic reaction rate, such as a volcano-correlation, compared to single-potential-driven catalysis with an electrode, which usually exhibits a linear type of reaction rate. Although the potential of a catalyst may be stable related to SHE, the in situ potential of a catalyst must be determined using RHE to consider the potential–current relationships of catalysis. It has been understood for decades that the electrolyte pH affects the activity of multistep, electrochemical processes; however, the origins of this effect remain under debate [33,34]. The reaction kinetics, represented by the current density, generally depend not on the absolute electrode potential but on the in situ potential relative to the RHE.

Figure 9. Corrosion potential (E_corr) and corrosion current density (i_corr), estimated from two stationary polarization curves [29].

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 H₂ 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 H₂ below 0.3–0.4 V and by O₂ 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, H₂ in the solution could be used as the potential of RHE because the catalyst surface may be covered by H₂ below 0.3–0.4 V.

Figure 10. General correlation between the current of the alcohol oxidation reaction and the catalyst potential.

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 O₂ content of the de-oxygenated water [41]. Although dissolved O₂ is typically necessary to make an oxide film, at 20 ppm dissolved O₂, 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 H₂ 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 (H₂O₂ and O₂) 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 H₂ dosage control. Because the addition of H₂ 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 pH₂ are the logarithms of the activity of H⁺ and the fugacity of H₂, respectively. Using the Nernst equation, a 10-fold change in H₂ corresponds to a 30 mV decrease in the RHE potential. When air (21% O₂) with 100 ppm-H₂ was bubbled into the PBS, the ORP decreased to 60 mV compared to that of air without H₂, 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 H₂ altered the direction of electron flow from the succinate-induced RET toward FET. Because the addition of H₂ 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 H₂.

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 H₂. As the pH in the solution or the vapor pressure of H₂ 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 H₂-producing microbiomes in green redox transformations.