Thermodynamic Discrimination between Energy Sources for Chemical Reactions

Abstract

•Reaction-independent, non-dimensional expression for chemical equilibrium is developed•Temperature, pressure, and voltage are compared as driving forces for chemical synthesis•Visualization reveals divide between electro- and thermochemical reactions The equilibrium of a chemical reaction can be shifted using various driving forces, including temperature (thermal energy), pressure (mechanical energy), and voltage (electrical energy). These driving forces are often compared with technoeconomic analyses that discriminate between mature chemical synthesis routes where associated costs can be tabulated. Here, we demonstrate how thermodynamic analyses provide a framework to compare and discriminate between energy sources for chemical reactions. This methodology is useful for comparisons of less developed synthetic routes where accurate costs cannot be ascribed. Specifically, our analysis provides a universal, non-dimensional framework through which the effect of temperature, pressure, and voltage on reactions can be understood. This is articulated in both the context of chemical equilibria and energy exchanges, providing understanding across industrially practiced and next-generation chemical synthesis routes. Chemical transformations traverse large energy differences, yet the comparison of energy sources to drive a reaction is often done on a case-by-case basis; there is no fundamentally driven, universal framework with which to analyze and compare driving forces for chemical reactions. In this work, we present a reaction-independent expression for the equilibrium constant as a function of temperature, pressure, and voltage. With a specific set of axes, all reactions are represented by a single (x,y) point, and a quantitative divide between electrochemically and thermochemically driven reactions is visually evident. Additionally, we show that our expression has a strong physical basis in work and energy fluxes to the system, although specific data about operating conditions are necessary to provide a quantitative energy analysis. Overall, this universal equation and facile visualization of chemical reactions provides a consistent thermodynamic framework for comparing electrochemical versus thermochemical energy sources without knowledge of detailed process parameters. Chemical transformations traverse large energy differences, yet the comparison of energy sources to drive a reaction is often done on a case-by-case basis; there is no fundamentally driven, universal framework with which to analyze and compare driving forces for chemical reactions. In this work, we present a reaction-independent expression for the equilibrium constant as a function of temperature, pressure, and voltage. With a specific set of axes, all reactions are represented by a single (x,y) point, and a quantitative divide between electrochemically and thermochemically driven reactions is visually evident. Additionally, we show that our expression has a strong physical basis in work and energy fluxes to the system, although specific data about operating conditions are necessary to provide a quantitative energy analysis. Overall, this universal equation and facile visualization of chemical reactions provides a consistent thermodynamic framework for comparing electrochemical versus thermochemical energy sources without knowledge of detailed process parameters. In chemical synthesis, the making and breaking of chemical bonds often requires traversing large energy differences. In fact, the basic chemical industry accounts for close to 20% of total delivered energy consumption in the industrial sector, which itself uses the most delivered energy of any end-use sector globally (54%).1EIAInternational energy outlook 2016. Technical report of the U.S. Energy Information Administration. May 2016.https://www.osti.gov/biblio/1296780Date: 2016Google Scholar,2IEAICCADECHEMATechnology roadmap: energy and GHG reductions in the chemical industry via catalytic processes. Technical report of the IEA, ICCA, and DECHEMA. June 2013.https://www.iea.org/reports/technology-roadmap-energy-and-ghg-reductions-in-the-chemical-industry-via-catalytic-processesDate: 2013Google Scholar Traditionally, industrial chemical synthesis has relied on pressure and temperature as driving forces to synthesize chemicals; a reactor requires an exchange of heat and work in order to drive a chemical transformation.2IEAICCADECHEMATechnology roadmap: energy and GHG reductions in the chemical industry via catalytic processes. Technical report of the IEA, ICCA, and DECHEMA. June 2013.https://www.iea.org/reports/technology-roadmap-energy-and-ghg-reductions-in-the-chemical-industry-via-catalytic-processesDate: 2013Google Scholar, 3Friend C.M. Xu B. Heterogeneous catalysis: a central science for a sustainable future.Acc. Chem. Res. 2017; 50: 517-521Crossref PubMed Scopus (128) Google Scholar, 4Arora A. Gambardella A. Implications for energy innovation from the chemical industry.in: Accelerating Energy Innovation: Insights from Multiple Sectors. University of Chicago Press, 2011: 87-111Crossref Google Scholar Yet, with the advent of abundant and accessible renewable electricity, it is attractive to consider driving chemical reactions that are conventionally driven with temperature and pressure with electrical voltage instead.5van Geem K.M. Galvita V.V. Marin G.B. Making chemicals with electricity.Science. 2019; 364: 734-735Crossref PubMed Scopus (44) Google Scholar, 6Gu S. Xu B. Yan Y. Electrochemical energy engineering: a new frontier of chemical engineering innovation.Annu. Rev. Chem. Biomol. Eng. 2014; 5: 429-454Crossref PubMed Scopus (56) Google Scholar, 7Schnuelle C. Thoeming J. Wassermann T. Thier P. von Gleich A. v. Goessling-Reisemann S. Socio-technical-economic assessment of power-to-X: potentials and limitations for an integration into the German energy system.Energy Res. Soc. Sci. 2019; 51: 187-197Crossref Scopus (28) Google Scholar, 8Schiffer Z.J. Manthiram K. Electrification and decarbonization of the chemical industry.Joule. 2017; 1: 10-14Abstract Full Text Full Text PDF Scopus (114) Google Scholar, 9Botte G.G. Electrochemical manufacturing in the chemical industry.Interface Mag. 2014; 23: 49-55https://www.electrochem.org/dl/interface/fal/fal14/fal14_p049_055.pdfCrossref Scopus (72) Google Scholar Hence, one is confronted with the question, “why should a given chemical reaction be driven preferentially with temperature (thermal energy), pressure (mechanical energy), or voltage (electrical energy)?” The response to this question is generally either broad and qualitative or extremely reaction specific. Broadly, if a reaction is highly endothermic (results in a very positive change in enthalpy), then one may prefer an electrochemical approach that avoids excessively high operating temperatures to shift the equilibrium toward products.9Botte G.G. Electrochemical manufacturing in the chemical industry.Interface Mag. 2014; 23: 49-55https://www.electrochem.org/dl/interface/fal/fal14/fal14_p049_055.pdfCrossref Scopus (72) Google Scholar,10Wang Z. Roberts R.R. Naterer G.F. Gabriel K.S. Comparison of thermochemical, electrolytic, photoelectrolytic and photochemical solar-to-hydrogen production technologies.Int. J. Hydr. Energy. 2012; 37: 16287-16301Crossref Scopus (121) Google Scholar Additionally, if a reaction requires high pressures to drive conversion to products via Le Chatelier’s principle, then one may prefer using voltage to avoid these excessively high pressures. Technoeconomic analyses are also often used to discriminate between thermochemical and electrochemical driving forces based on feedstock costs and system efficiencies.11Jouny M. Luc W. Jiao F. General techno-economic analysis of CO2 electrolysis systems.Ind. Eng. Chem. Res. 2018; 57: 2165-2177Crossref Scopus (428) Google Scholar, 12Zhao Y. Setzler B.P. Wang J. Nash J. Wang T. Xu B. Yan Y. An efficient direct ammonia fuel cell for affordable carbon-neutral transportation.Joule. 2019; 3: 2472-2484Abstract Full Text Full Text PDF Scopus (66) Google Scholar, 13Na J. Seo B. Kim J. Lee C.W. Lee H. Hwang Y.J. Min B.K. Lee D.K. Oh H.S. Lee U. General technoeconomic analysis for electrochemical coproduction coupling carbon dioxide reduction with organic oxidation.Nat. Commun. 2019; 10: 5193Crossref PubMed Scopus (73) Google Scholar, 14Müller K. Brooks K. Autrey T. Hydrogen storage in formic acid: a comparison of process options.Energy Fuels. 2017; 31: 12603-12611Crossref Scopus (58) Google Scholar, 15Jouny M. Hutchings G.S. Jiao F. Carbon monoxide electroreduction as an emerging platform for carbon utilization.Nat. Cat. 2019; 2: 1062-1070Crossref Scopus (89) Google Scholar, 16Verma S. Lu S. Kenis P.J.A. Co-electrolysis of CO2 and glycerol as a pathway to carbon chemicals with improved technoeconomics due to low electricity consumption.Nat. Energy. 2019; 4: 466-474Crossref Scopus (177) Google Scholar However, these technoeconomic analyses remain focused on specific reactions without investigating the physical basis for the preference of driving force in a general manner. While many of the choices in the driving forces for chemical reactions are determined by factors such as kinetics, cost, and safety, research and development often begins before estimates of these specific parameters are known. Accordingly, an intermediate-level framework for comparing driving forces based on available physical parameters is missing; specifically, one that is simple and intuitive, yet also quantitative and dependable across a wide range of chemical reactions. We address the question of how to compare and discriminate between energy sources for driving chemical reactions via a theoretical framework built around reaction thermodynamics. Efficiency and thermodynamic limits on extraction of useful work have been studied for centuries (e.g., with the Carnot engine),17Carnot, S. (1824) Réflexions Sur La Puissance Motrice du Feu et Sur Les Machines Propres a Développer Cette Puissance (Paris).Google Scholar,18Smeaton J. XVIII. An experimental enquiry concerning the natural powers of water and wind to turn mils, and other machines, depending on a circular motion.Philos. Trans. R. Soc. Lond. 1759; 51: 100-174Google Scholar and more recent work has slowly relaxed ideal constraints to add in real-world practicalities via developments in fields such as endoreversible thermodynamics and finite-time thermodynamics.19Hoffmann K.H. An introduction to endoreversible thermodynamics.Proceedings of the International Conference and Summer School on Thermal Theories of CONTINUA: Survey and Developments. 86. 2008: 1-18Google Scholar,20Andresen B. Berry R.S. Nitzan A. Salamon P. Thermodynamics in finite time. I. The step-Carnot cycle.Phys. Rev. A. 1977; 15: 2086-2093Crossref Scopus (152) Google Scholar However, these theories are often built to describe the extraction of energy from a chemical reaction, e.g., in a combustion engine, and they often still require significant knowledge of specific process parameters such as heat transfer coefficients, compressor efficiencies, thermodynamic paths, etc.21Sieniutycz S. Jeżowski J. Energy limits for thermal engines and heat pumps at steady states.in: Energy Optimization in Process Systems and Fuel Cells. Elsevier, 2018: 81-119Crossref Google Scholar In this work, we construct a universal equation to describe and analyze the thermodynamics of chemical reactions driven by temperature, pressure, and voltage. We have focused on these driving forces due to their prevalence in chemical synthesis, although the analysis can be extended to the direct use of photons or mechanochemical methods. We compare heat, mechanical work, and electrical work as energy inputs to a chemical system and find that an ideal, lossless model of energy comparison provides a physical basis for our non-dimensional thermodynamic parameter analysis. After constructing a universal equation, we then introduce a facile visualization method for comparing chemical reactions, with a focus on redox reactions (voltage is generally not an option for non-redox reactions) and show a clear divide between chemical reactions traditionally driven by elevated temperatures and pressures in industry and reactions that rely on electrical voltage. Our approach provides a simple, universal framework with a thermodynamic basis to compare and justify using temperature, pressure, or voltage as a driving force for a chemical reaction, and our analysis can be leveraged by researchers in a broad range of fields to help determine the important systems-level choice of thermodynamic driving force. We are interested in comparing the effects of temperature, pressure, and voltage as driving forces for shifting the equilibrium of a chemical reaction. Accordingly, we start with a chemical reaction that has some defined stoichiometry given by:∑iνiAi=0,(Equation 1) where νi are the stoichiometric coefficients for chemical species Ai. Chemical equilibrium at constant temperature (T), pressure (P), and voltage (E) provides the constraint:∑iνiμi(T,P,E)=0,(Equation 2) where μi are the species electrochemical potentials. Assuming that the system is an ideal mixture of gases and that ΔCP,rxn≡∑iνiCP,i=0, the equilibrium constant, K, is a simple function of thermodynamic variables (Derivation S1)22Inzelt G. Crossing the bridge between thermodynamics and electrochemistry. From the potential of the cell reaction to the electrode potential.ChemTexts. 2015; 1: 1-11Crossref Scopus (12) Google Scholar, 23Keszei E. Chemical Thermodynamics: An Introduction.Twelfth Edition. Springer, 2011Google Scholar, 24Clarke E.C.W. Glew D.N. Evaluation of thermodynamic functions from equilibrium constants.Trans. Faraday Soc. 1966; 62: 539-547Crossref Scopus (555) Google Scholar:logeK=-ΔGrxnT,P,ERT=-ΔHrxn0RT-ne-FERT-ΔnrxnlogePP0+ΔSrxn0R,(Equation 3) where ΔHrxn0 and ΔSrxn0 are the enthalpy and entropy of reaction, respectively, at ambient conditions (namely no applied voltage, T=T0=298.15 K, and P=P0=1 bar), R is the ideal gas constant, ne− is the minimum number of electrons necessarily transferred in the overall reaction (Derivation S1), and Δnrxn≡∑i∈gasνi. Although we assume for simplicity that all of our components are gases (with a few exceptions for pure liquids and solids), the extension to liquids, dissolved species, and solids is not difficult to incorporate when going through the full derivation (Derivation S1). Equation 3 is a familiar description of the equilibrium constant with one major difference: we have defined K≡∏i∈gasyiνi, with yi being the mole fraction of each component in the gas phase, instead of the more traditional K=∏ipiνi, where pi is the partial pressure of a species (i.e., the activity of an ideal gas).25Bockris J.O. Comprehensive Treatise of Electrochemistry Vol. 3: Electrochemical Energy Conversion and Storage.First Edition. Springer, 1981Google Scholar In this work, the equilibrium constant is defined by Equation 3 instead of the traditional definition so that pressure will be explicitly included in the expression. Through Equation 3 and proper stoichiometry normalization, we can better compare reaction equilibriums based on a more consistent relationship between mole fractions and K that is not present when K is written in terms of activity (e.g., partial pressures) instead of mole fractions. The practically relevant quantity for describing a chemical reaction is conversion, not the equilibrium constant. However, conversion will be dependent on the exact reaction equation and not a universal function. To keep the analysis general, the equilibrium constant, K, will be used as a proxy for conversion since conversion is a strictly increasing, sigmoidal function of K ranging from 0 to 1 (Derivation S2). Unfortunately, the expression for the equilibrium constant given by Equation 3 does not allow for facile comparison of temperature, pressure, and voltage in its current form since the quantities ΔHrxn0, ΔSrxn0, Δnrxn, and ne− are reaction-specific, preventing a general analysis of chemical reaction equilibrium. To facilitate a comparison, the equilibrium constant expression can be non-dimensionalized to remove any specifics about the chemical reaction. Non-dimensionalization is a useful tool for solving differential equations in certain limits and for quickly determining characteristic properties of a system such as time and length; for these reasons it finds wide use across the fields of chemical engineering, physics, fluid dynamics, etc.26Hecksher T. Insights through dimensions.Nat. Phys. 2017; 13: 1026Crossref Scopus (2) Google Scholar In the case of a chemical reaction, non-dimensionalization combines the reaction-specific details of the system with the reaction operating conditions to create new variables that are reaction-independent and scale simply with the thermodynamic driving forces of interest (Figure 1; Derivation S3). Traditional non-dimensionalization, e.g., of reaction-diffusion systems, relies on the structure of a differential equation to provide the non-dimensional groupings; an algebraic equation such as Equation 3 does not have equivalently straightforward non-dimensional groupings, and non-dimensionalization must instead rely on underlying physical intuition. Equation 3 can be non-dimensionalized to achieve a universal expression for how thermal, mechanical, and electrical energy shift the chemical equilibrium through non-dimensional temperature (T→Θ), pressure (P→Π), and voltage (E→Ψ):Θ≡RTloge10ΔHrxn0,Π≡Δnrxnlog10PP0,Ψ≡ne−FEΔHrxn0,σ≡ΔSrxnRloge10,log10K=−1Θ−ΨΘ−Π+σ.(Equation 4) Note that we have chosen to use Θ∝T instead of a potentially “natural” quantity Θ∝1/T so that changes in Θ are more intuitively interpretable.27Meixner J. Coldness and temperature.Arch. Rational Mech. Anal. 1975; 57: 281-290Crossref Scopus (15) Google Scholar One of the advantages of Equation 4 is that all reactions collapse onto simple plots that show the equilibrium constant, a proxy for reaction conversion, as a function of non-dimensional thermodynamic driving forces (Figure 2). This visualization reveals that crossing equilibrium contours with pressure requires a larger relative increase in thermodynamic driving force than crossing equilibrium contours with temperature or voltage (further supporting analysis of contours and derivatives provided in Derivation S4). This discrepancy is magnified by the fact that the scaling of Π is logarithmic with pressure whereas the scalings of Θ and Ψ are linear with temperature and voltage, respectively. So far, the analysis has relied on the mathematical form of our non-dimensional parameters. In practice, there are many alternative non-dimensional groupings with additional constant factors or functional forms that would change this analysis. However, these non-dimensional thermodynamic parameters (Figure 1) are not only convenient from a mathematical perspective but also represent physical groupings related to analogous work and energy fluxes, discussed below, such that conclusions drawn from analysis of the non-dimensional thermodynamic parameters are physically relevant. A direct comparison between temperature, pressure, and voltage is difficult since each driving force has different units. Even with our non-dimensional scalings, there is no reason to assume a priori that these non-dimensional parameters have any physical meaning and can be directly compared with each other. Instead, a metric for comparing driving forces on equal footing would be to compare work and energy exchanges of the system; this comparison will provide a physical basis for our non-dimensional parameters so that we can directly compare them. In practice, no general method to convert between thermodynamic parameters and work exists since heat and work are path functions. However, if the system does not have any energy losses, the overall, steady-state energy exchanges of the system must obey the law of energy conservation:WM+WE+Q=ΔHrxn0⋅z,(Equation 5) where z is the reaction conversion at equilibrium, a function of K and defined between 0 and 1. A more convenient form of Equation 5 results from non-dimensionalization of the work terms with the reaction enthalpy as the characteristic energy of the system (Derivation S5):ΩWM+ΩWE+ΩQ=z.(Equation 6) Ignoring the exact functional form of the work terms for now and assuming that the system is driven by either pressure or voltage individually, but not both simultaneously, the constraint imposed by Equation 6 has the geometric form of a plane in ΩWi-ΩQ space (Figure 3). Accordingly, for a system with no energy losses, any energy input will result in an equivalent change in conversion, regardless of the energy source. If additional information is available, such as the cost of electricity, efficiency of heat flux, compressor losses, etc., there are a multitude of thermodynamic and technoeconomic heuristics that can lead to a quantitative conclusion, but these are beyond the scope of this work. In the absence of more information, there are still important insights to glean from the functional forms of the work and heat inputs. In addition to the previous assumptions (ideal gas mixture and ΔCP,rxn=0), additional assumptions are necessary to convert from thermodynamic parameters to work and energy fluxes: (1) the reactor is isothermal, isobaric, and does not exchange mechanical work with the environment, and (2) the processes that bring the inputs to the operating conditions and bring the outputs back to ambient conditions have access to a single heat bath at some Tbath. Given these assumptions, as well as assuming unit efficiency of every process, the total energy and work exchanges with the overall system are functions of the previous thermodynamic parameters, the conversion, z=z(K), which is a function of the equilibrium constant, and the single non-dimensional thermal bath temperature, Θbath≡RTbathloge10ΔHrxn0, that is used to bring reactants to operating conditions and products to ambient conditions (Derivation S5)28Bazhin N.M. Mechanism of electric energy production in galvanic and concentration cells.J. Engin. Thermophys. 2011; 20: 302-307Crossref Scopus (4) Google Scholar, 29Bazhin N.M. Parmon V.N. Conversion of the chemical reaction energy into useful work in the Van’t Hoff equilibrium box.J. Chem. Educ. 2007; 84: 1053-1055Crossref Scopus (6) Google Scholar, 30Kowalewicz A. Fuel-cell: power for future.J. KONES. 2001; 8: 325-333PubMed Google Scholar, 31Panagiotopoulos A.Z. Essential Thermodynamics.First Edition. CreateSpace Independent Publishing Platform), 2011Google Scholar:ΩWE=−z(K)ΨΩWM=−z(K)ΘbathΠΩQ=z(K)(Ψ+ΘbathΠ+1)(Equation 7) Without additional practical information, our energy analysis is qualitative, and these equations by themselves do not reveal a preference for mechanical work, electrical work, or heat. However, these equations do provide justification for our previous analysis. We initially began our reaction analysis by non-dimensionalizing temperature, pressure, and voltage to remove any reaction-specific quantities from the equilibrium expression given in Equation 3. The chosen non-dimensionalizations are intuitive; although these parameter groupings are relatively common throughout the literature (e.g., Π is found in the Nernst equation and Ψ is related to the thermo-neutral voltage), the physical basis of these non-dimensional parameters (Θ, Π, and Ψ) on an energy basis has not been described. The energy analysis presented here, however, reveals that the non-dimensional electrical work (ΩWE) will scale directly with non-dimensional voltage (Ψ), the non-dimensional mechanical work (ΩWM) will scale directly with non-dimensional pressure (Π), and the heat flux is a convolution of all the energy inputs but has a clear characteristic energy given by ΔHrxn0, which was used to non-dimensionalize temperature (Θ). Accordingly, although the previous analysis dealt with non-dimensional driving forces that were not, a priori, comparable, this energy analysis reveals that these non-dimensional quantities are reasonable proxies for work and energy exchanges and that our non-dimensional analysis has a strong physical basis. Direct comparisons of the non-dimensional thermodynamic parameters therefore correspond to comparisons of analogous energy and work exchanges, validating conclusions drawn from such direct comparisons. While the universal colormaps of Equation 4 are interesting on their own (Figure 2), contour lines of constant K for a specific reaction help visualize the thermodynamics of that reaction. This is the advantage of plotting the equilibrium constant in non-dimensional space: instead of qualitatively looking at endo- versus exothermicity or analyzing a specific reaction’s equilibrium constant at various temperatures, pressures, and voltages, we can quantitatively display the influence of these driving forces on a single set of axes since the thermodynamic landscapes for individual reactions all collapse onto a single plot in non-dimensional space (Figure 2). Two well-studied reactions are ammonia synthesis (Reaction 1, industrially known as the Haber-Bosch process):12N2+32H2→NH3 (Reaction 1) and water splitting (Reaction 2):H2O→H2+12O2 (Reaction 2) The constant K contours for these reactions can be plotted on the universal colormaps and compared (Figure 4).32Burgess, D. (2020). Thermochemical data. Thermochemical data. In NIST Chemistry WebBook, NIST Standard Reference Database Number 69, P. Linstrom and W. Mallard, eds., chapter Thermochem. National Institute of Standards and Technology Gaithersburg. (MD).Google Scholar Using the reaction thermodynamic properties, dimensional parameters (T, P, and E) are shown for each reaction on the secondary axes. In addition to helping visualize the equilibrium constants for these reactions in standard units, these secondary axes demonstrate that the non-dimensional axes span a sufficient range of operating conditions for most reactions. The key points to consider with these plots are: (1) the red dot represents ambient conditions, and the horizontal distance to Θ=0 is inversely proportional to the enthalpy of reaction; (2) the red vertical line attached to each ambient conditions point on the pressure-temperature plots (Figures 4A and 4C) represents an increase of an order of magnitude in pressure; (3) the vertical distance from the red dot to the solid pink line (K=1) on the voltage-temperature plots (Figures 4B and 4D) is the non-dimensional equilibrium potential of the reaction. For the case of ammonia synthesis (Figures 4A and 4B), the thermodynamic equilibrium favors full conversion of nitrogen and hydrogen to ammonia at ambient conditions; however, kinetics mandate the use of an elevated operating temperature and pressure. This reaction is an important example of the utility of thermodynamic analyses even for reactions where kinetics dictate operating conditions. The scaling of the axes (seen by the secondary axes) demonstrates that crossing equilibrium contours and moving around the thermodynamic equilibrium space with temperature and pressure are feasible at practical operating conditions for ammonia synthesis. In other words, at a temperature at which the kinetics are favorable for ammonia synthesis, the visualization demonstrates that pressure can allow us to easily move through thermodynamic equilibrium space; this is reflected in the fact that ammonia synthesis is commercially practiced at elevated pressures that enable higher equilibrium conversions. This is in contrast with water splitting (Figures 4C and 4D), for which the visualization clearly demonstrates that increasing pressure decreases conversion, and enormous temperatures are necessary to achieve meaningful equilibrium conversions. However, voltage remains a powerful tool, since approximately 1.2 V is sufficient to drive water splitting, a feasible amount compared with the high temperature or low pressure necessary otherwise. This analysis is currently limited to thermodynamic equilibrium considerations, while in reality temperature, pressure, and voltage also play a role in kinetics, cost, selectivity, and safety, all of which strongly influence the trade-offs between thermochemistry and electrochemistry. These other factors are beyond the scope of this analysis as we aim to describe broad trends in driving forces for chemical reactions using a thermodynamic framework. Even without knowledge of these other factors, a thermodynamic analysis reveals whether high conversion is even physically possible, a prerequisite to engineering reactivity given operating conditions dictated by kinetics and other non-thermodynamic constraints. This continues to motivate the search for catalysts that are active at lower temperatures in the case of ammonia synthesis, while telling us not to search for thermochemical water splitting catalysts at ambient conditions due to thermodynamic restrictions. While these universal colormaps are useful for visualizing individual reactions, they are not ideal for comparing multiple reactions because they require unique constant K contours for each reaction, meaning that multiple reactions would quickly obscure each other. Instead, the axes can be redefined such that every reaction has the same K contours, facilitating direct comparison between different reactions. Instead of using the non-dimensional groups derived above as axes, in which each reaction has a distinct set of K contours, a simple variable transformation can collapse these to a single set of equilibrium K contours for all reactions (Figure 5). Specifically, the x axis is transformed to 1/Θ and the y axis is transformed to Ψ/Θ+Π−σ (Derivation S6). In general, we assume that in addition to temperature, either voltage or pressure is being used to drive the reaction, not both simultaneously, which results in either Π=0 or Ψ=0, respectively. As depicted, in these axes a change in pressure or voltage corresponds to a vertical movement relative to the reaction point and an increase (decrease) in T corresponds to a movement toward (away from) the point (0,Π−σ) (Figure 5A; Derivation S6). These new, composite axes allow for the direct comparison of chemical reactions since all reactions have the same K contours, with each reaction at ambient conditions represented by a single point:(x,y)rxnambient=(1Θambient,−σ)(Equation 8) =(ΔHrxn0RT0loge10,−ΔSrxn0Rloge10),where T0=298.15 K. For each reaction point at ambient conditions, the distance from the reaction point to x=0 is proportional to ΔHrxn0, the distance to y=0 is proportional to ΔSrxn0, and the distance to the solid black line (K=1, given by y=−x) is proportional to the dimensional equilibrium potential of the reaction (Figure 5B; Derivation S7). When multiple reactions are plotted on these axes, a clear divide appears between those that are conventionally driven thermochemically versus electrochemically (Figure 6). Reactions to the left of the K=1 line (y=−x) are already thermodynamically favorable at ambient conditions. Any adjustment to the reaction conditions (e.g., an increase in temperature to improve kinetics) must keep the reaction as far left as possible to maintain thermodynamic favorability. If the reaction point is near or to the right of the K=1 line (y=−x), then pressure or temperature can practically cross the equilibrium contours only if the reaction point is within a reasonable distance to the K=1 line. In particular, to use pressure to drive conversion, the vertical distance from the reaction point to the line y=−x must be within a couple of orders of magnitude of pressure (a version of Figure 6 with pressure effects depicted for each reaction is shown in Derivation S6). If the reaction point lies to the right of the K=1 line (y=−x), then the reaction can be driven to quantifiable conversion using just temperature when the horizontal distance from the reaction point to y=−x is sufficiently small and the reaction point does not lie in the top-right quadrant; in that quadrant, the ΔHrxn0 and ΔSrxn0 conspire to make the K=1 contour unreachable with temperature. The horizontal distance to y=−x is quantified by the temperature, Teq, when K(P=1 bar,T=Teq)=1, namely when Teq=ΔHrxn0/ΔSrxn0. Due to physical practicalities, the operating temperature should be within a factor of ca. 5 of the ambient temperature (∼1500 K, a choice which is further discussed in Derivation S8).33Weissermel K. Arpe H. Industrial Organic Chemistry.Fourth Edition. Wiley-VCH Verlag, 2003Crossref Google Scholar Mathematically, this translates to Teq/Tambient=1/(σΘambient)≤5. For a reaction point given by (x,y)rxnambient on these axes, the reaction can practically be driven by temperature alone when 1/(σΘambient)=−x/y≤5, approximately (green shading on Figure 6). Voltage, however, is particularly well suited to drive chemical reactions that are far from the K=1 line since even large values of Ψ/Θ generally correspond to voltages of order 1 V (Derivation S4). Thus, this visualization quantitatively supports our intuition, namely that reactions with large, positive values of ΔHrxn0 (highly endothermic) are generally better driven by voltage. In particular, reactions which require large excursions on these non-dimensional axes can generally only be done electrochemically (Figure 6, blue points). Those requiring small excursions on these axes can generally be done either electrochemically or thermochemically, and these reactions often are driven with temperature and pressure due to industrial expertise and convenience (Figure 6, pink points). For reactions that could be driven either thermochemically or electrochemically, reaction-specific properties such as kinetics and selectivity must be taken into account when choosing a driving force, as well. Beyond the influence of temperature, pressure, and voltage on the chemical equilibrium, system design choices can also shift the reaction equilibrium. For example, removal of products from the reactor can shift the equilibrium away from reactants (Le Chatelier’s principle). Multi-step chemical looping strategies can operate at lower temperatures, which is leveraged in solar thermal water splitting and solar thermal carbon dioxide reduction to drive these reactions at temperatures less than 1,500 K. These multi-step reactions are outside the scope of our present analysis, but it can be extended to understand these systems as well (Derivation S8).34Hao Y. Yang C.-K. Haile S.M. Ceria-zirconia solid solutions (CE1-xZrxO2-δ, x ≤ 0.2) for solar thermochemical water splitting: a thermodynamic study.Chem. Mater. 2014; 26: 6073-6082Crossref Scopus (134) Google Scholar,35Furler P. Scheffe J. Gorbar M. Moes L. Vogt U. Steinfeld A. Solar thermochemical CO2 splitting utilizing a reticulated porous ceria redox system.Energy Fuels. 2012; 26: 7051-7059Crossref Scopus (283) Google Scholar Note that throughout our analysis we restrict ourselves to redox reactions for synthesizing chemicals and do not address reactions where energy is extracted (e.g., via a combustion engine or a fuel cell). On these proposed axes (Figure 5), the thermodynamic equilibrium conversion at ambient conditions is readily determined for any reaction by generating a single point (x,y). Unlike binary descriptors for a chemical reaction such as endo- versus exothermic or sign of ΔGrxn (Derivation S9), the points representing each reaction can be easily shifted to account for non-ambient conditions (e.g., operating conditions). Additionally, these points inherently encompass multiple discriminating properties of a chemical reaction. First, we can use these points to determine if temperature or pressure can individually drive a reaction to high conversion via the x and y values (see Derivation S6 for more details). Second, we can determine if, at practical operating conditions (e.g., elevated temperatures), other driving forces such as pressure can result in high equilibrium conversion. Last, we can visually discriminate when voltage is necessary for high conversion, recognizing that for cases where temperature, pressure, or voltage all exhibit high fidelity as driving forces for a chemical reaction, significant practical maturity in the use of temperature and pressure as driving forces for a wide range of chemical reactions may favor their usage. In addition to allowing direct comparison of chemical reactions, these axes also enable facile addition and subtraction of reactions. For example, both water splitting (blue diamond) and ammonia synthesis (pink diamond) are represented, but the sum of these two reactions, converting water and nitrogen to ammonia and oxygen, is also shown (blue circle) and has (x,y) coordinates that are simply the sum of the two individual reaction points (Figure 6). This is a manifestation of Hess’s Law, namely that the total enthalpy change for a reaction given by multiple steps is the sum of all enthalpy changes of the individual steps. Combining reactions on these axes to generate new reactions is therefore simple and enables quick visual analysis of how multiple reactions can work together from a thermodynamic perspective. This additive property of these axes makes it clear why using water as a source of hydrogen or oxygen can be difficult with pressure and temperature but is feasible with voltage as a driving force; since the water splitting point is so far from the vertical axis (very endothermic), the specific reaction where we want to replace hydrogen or oxygen would need to be equally far on the opposite side of x=0 to be thermochemically feasible using water as a reactant. Beginning with the question: “why should a given chemical reaction be driven preferentially with temperature (thermal energy), pressure (mechanical energy), or voltage (electrical energy)?” we developed a non-dimensional, reaction-independent expression for chemical equilibrium as a function of thermodynamic driving forces. We then analyzed the thermodynamics for multiple industrial and lab-scale chemical reactions that rely on different combinations of temperature, pressure, and voltage as driving forces and compared them visually on the same axes, finding a clear discrimination between electrochemically and thermochemically driven reactions. Converting from temperature, pressure, and voltage to heat and work fluxes reveals that our analysis has a strong physical basis in work and energy exchanges.