Extrathermodynamic Assumptions Research Articles

The Unified Redox Scale for All Solvents: Consistency and Gibbs Transfer Energies of Electrolytes from their Constituent Single Ions.

We have devised the unified redox scale Eabs H2O , which is valid for all solvents. The necessary single ion Gibbs transfer energy between two different solvents, which only can be determined with extra-thermodynamic assumptions so far, must clearly satisfy two essential conditions: First, the sum of the independent cation and anion values must give the Gibbs transfer energy of the salt they form. The latter is an observable and measurable without extra-thermodynamic assumptions. Second, the values must be consistent for different solvent combinations. With this work, potentiometric measurements on silver ions and on chloride ions show that both conditions are fulfilled using a salt bridge filled with the ionic liquid [N2225 ][NTf2 ]: if compared to the values resulting from known pKL values, the silver and chloride single ion magnitudes combine within a uncertainty of 1.5 kJ mol-1 to the directly measurable transfer magnitudes of the salt AgCl from water to the solvents acetonitrile, propylene carbonate, dimethylformamide, ethanol, and methanol. The resulting values are used to further develop the consistent unified redox potential scale Eabs H2O that now allows to assess and compare redox potentials in and over six different solvents. We elaborate on its implications.

Bruce-Vincent transference numbers from molecular dynamics simulations.

Transference number is a key design parameter for electrolyte materials used in electrochemical energy storage systems. However, the determination of the true transference number from experiments is rather demanding. On the other hand, the Bruce-Vincent method is widely used in the lab to approximately measure transference numbers of polymer electrolytes, which becomes exact in the limit of infinite dilution. Therefore, theoretical formulations to treat the Bruce-Vincent transference number and the true transference number on an equal footing are clearly needed. Here, we show how the Bruce-Vincent transference number for concentrated electrolyte solutions can be derived in terms of the Onsager coefficients, without involving any extrathermodynamic assumptions. By demonstrating it for the case of poly(ethylene oxide)-lithium bis(trifluoromethane)sulfonimide system, this work opens the door to calibrating molecular dynamics (MD) simulations via reproducing the Bruce-Vincent transference number and using MD simulations as a predictive tool for determining the true transference number.

Feasibility of multifunction calibration of H+-responsive glass electrodes in seawater (IUPAC Technical Report)

Abstract Seawater pH values are of the highest relevance in marine chemistry studies, not only through being acidity indicators but also due to the control provided by H+(aq) over the various simultaneous equilibria occurring in seawater. Although the concept of p H = − l g a H + = − lg ( m H + γ H + / m 0 ) $\mathrm{p}\mathrm{H}=-\mathrm{l}\mathrm{g}{\mathit{a}}_{{\mathrm{H}}^{+}}=-\mathrm{lg}\left({\mathit{m}}_{{\mathrm{H}}^{+}}{\mathit{\gamma }}_{{\mathrm{H}}^{+}}/{\mathit{m}}^{0}\right)$ , where m H + ${m}_{{\text{H}}^{+}}$ is the relative (molality basis) activity, γ H + ${\gamma }_{{\text{H}}^{+}}$ is the molal activity coefficient of the hydrogen ion H+ at molality m H + ${m}_{{\text{H}}^{+}}$ , and m 0 is the standard molality, was introduced in 1910 and reaffirmed on successive occasions by relevant bodies, different conceptual definitions and alternative measurement procedures have been adopted and are in use by some, namely among oceanographers, often leading to confusion. This leads to major difficulties with the use of data, e.g., on what concerns comparison of results in space and time. Primary pH values, the highest quality level in terms of the metrological chain, have been assigned to primary reference pH buffer solutions of low ionic strength, by a primary method based on measurements of the Harned cell potential in association with the Nernst equation, as well as on the adoption of extra-thermodynamic model assumptions for electrolyte solutions. Although equivalent types of recommendations dealing with standards and procedures based on metrological traceability are still lacking for higher ionic strength media, as it is in the case of seawater, reference Tris–Tris·HCl buffer solutions in artificial seawater have been suggested for use in the calibration of pH meter systems. In this work, Tris–Tris·HCl buffer saline solutions of three different molality ratios mTris:mTris.HCl, m/mol kg−1 H2O, have been assigned reference values for free p H = − lg a H + $\mathrm{p}\mathrm{H}=-\mathrm{lg}\,{a}_{{\text{H}}^{+}}$ and total pH T = − lg ( m H + * / m 0 ) ${\mathrm{pH}}^{\mathrm{T}}=-\text{lg}\left({m}_{{\text{H}}^{+}}^{\text{{\ast}}}/{m}^{0}\right)$ , where m 0 = 1 mol kg−1 and m H + * = lim m → m SW [ m ( H + ) + m ( HSO 4 − ) ] ${m}_{{\text{H}}^{+}}^{\text{{\ast}}}=\underset{m\to {m}_{\text{SW}}}{\mathrm{lim}}\left[m\left({\mathrm{H}}^{\mathrm{+}}\right)+m\left({\mathrm{HSO}}_{4}^{\mathbf{-}}\right)\right]$ . Multi-point calibration of pH meters in terms of either pH or pHT is thus possible and supports measurement of their respective values under routine conditions at a high metrological level.

The Influence of Distant Boundaries on the Solvation of Charged Particles

The long-ranged nature of the Coulomb potential requires a proper accounting for the influence of even distant electrostatic boundaries in the determination of the solvation free energy of a charged solute. We introduce an exact rewriting of the free energy change upon charging a solute that explicitly isolates the contribution from these boundaries and quantifies the impact of the different boundaries on the free energy. We demonstrate the importance and advantages of appropriately referencing the electrostatic potential to that of the vacuum through the study of several simple model charge distributions, for which we can isolate an analytic contribution from the boundaries that can be readily evaluated in computer simulations of molecular systems. Finally, we highlight that the constant potential of the bulk dielectric phase - the Bethe potential - cannot contribute to the solvation thermodynamics of a single charged solute when the charge distributions of the solvent and solute do not overlap in relevant configurations. But when the charge distribution of a single solute can overlap with the intramolecular charge distribution of solvent molecules, as is the case in electron holography, for example, the Bethe potential is needed when comparing to experiment. Our work may also provide insight into the validity of "extra thermodynamic assumptions" traditionally made during the experimental determination of single ion solvation free energies.

Ion-Hydroxyl Interactions: From High-Level Quantum Benchmarks to Transferable Polarizable Force Fields.

Ion descriptors in molecular mechanics models are calibrated against reference data on ion-water interactions. It is then typically assumed that these descriptors will also satisfactorily describe interactions of ions with other functional groups, such as those present in biomolecules. However, several studies now demonstrate that this transferability assumption produces, in many different cases, large errors. Here we address this issue in a representative polarizable model and focus on transferability of cationic interactions from water to a series of alcohols. Both water and alcohols use hydroxyls for ion-coordination, and, therefore, this set of molecules constitutes the simplest possible case of transferability. We obtain gas phase reference data systematically from "gold-standard" quantum Monte Carlo and CCSD(T) methods, followed by benchmarked vdW-corrected DFT. We learn that the original polarizable model yields large gas phase water → alcohol transferability errors - the RMS and maximum errors are 2.3 and 5.1 kcal/mol, respectively. These errors are, nevertheless, systematic in that ion-alcohol interactions are overstabilized, and systematic errors typically imply that some essential physics is either missing or misrepresented. A comprehensive analysis shows that when both low- and high-field responses of ligand dipole polarization are described accurately, then transferability improves significantly - the RMS and maximum errors in the gas phase reduce, respectively, to 0.9 and 2.5 kcal/mol. Additionally, predictions of condensed phase transfer free energies also improve. Nevertheless, within the limits of the extrathermodynamic assumptions necessary to separate experimental estimates of salt dissolution into constituent cationic and anionic contributions, we note that the error in the condensed phase is systematic, which we attribute, at least, partially to the parametrization in long-range electrostatics. Overall, this work demonstrates a rational approach to boosting transferability of ionic interactions that will be applicable broadly to improving other polarizable and nonpolarizable models.

On the Assumption-Free Determination of Single-Ion Gibbs Energies of Transfer

Since about 100 years, the quest on the determination of Gibbs energies of transfer of single-ions exists. While some consider that the chemical potential of single-ions is physically senseless, other determined Gibbs solvation energies or Gibbs transfer energies of single-ions with the help of extra-thermodynamic assumptions (e.g. TATB-assumption, ferrocene-assumption and others), thereby introducing an error of the respective quantity of insufficiently assessable magnitude.[1] We suggest a procedure for the thermodynamically rigorous, experimental determination of the Gibbs energy of transfer of single-ions Δtr G°(i, S1--> S2). The method is based on potential difference measurements between two electrochemical half-cells with different solvents (solvation cells) connected by an ideal ionic liquid salt bridge (ILSB).[2] We point out the specific requirements for the IL with regard to the procedure, thus ensuring that those parts of liquid junction potentials (LJP) at both ends of the ILSB cancel which depend on the redox system used. The remaining parts of the LJPs can be determined by separate electromotive force measurements, the knowledge of the ionic transference numbers and Gibbs energies of transfer of the used salts is mandatory. No extra-thermodynamic assumptions are necessary for this procedure. The accuracy of the target quantity is an inherent part of the measurements and depends, amongst others, on the ideality of the IL used. We present results concerning the crucial steps a) and b) of the methodology exemplarily for Ag+ and Cl− with S1 being water and S2 being acetonitrile as an important intermediate goal to evaluate our concept for the assumption-free determination of single-ion Gibbs transfer energies Δtr G°(i, S1--> S2).[3] The used IL, [N2225]+[NTf2]−, shows nearly ideal behavior, that is, nearly identical diffusion of anion and cation, in the pure IL, but also in water and acetonitrile solution. Electromotive force measurements of solvation cells between S1 and S2 demonstrate Nernstian behavior for Ag+ concentration cells and constant like cell potentials for solutions with five tested Ag+ counterions. The Gibbs transfer energies can be utilized to collect data for the unified scales of acidity pHabs and reducity and peabs and for their two dimensional plot, the Protoeletric Potential Map (PPM), enabling the possibility to easily compare acidities and redox potentials between different media.[4] Literature:[1] P. Hünenberger, M. Reif, Single-Ion Solvation. Experimental and Theoretical Approaches to Elusive Thermodynamic Quantities, The Royal Society of Chemistry, Cambridge, 2011.[2] V. Radtke, A. Ermantraut, D. Himmel, T. Koslowski, I. Leito, I. Krossing, Angew. Chem. Int. Ed. 2018, 57, 2344.[3] A. Ermantraut, V. Radtke, N. Gebel, D. Himmel, T. Koslowski, I. Leito, I. Krossing, Angew. Chem. Int. Ed. 2018, 57, 2348.[4] D. Himmel, V. Radtke, B. Butschke, I. Krossing, Angew. Chem. Int. Ed., 2018, doi:10.1002/anie.201709057.

The Ideal Ionic Liquid Salt Bridge for the Direct Determination of Gibbs Energies of Transfer of Single Ions, Part I: The Concept.

Described is a procedure for the thermodynamically rigorous, experimental determination of the Gibbs energy of transfer of single ions between solvents. The method is based on potential difference measurements between two electrochemical half cells with different solvents connected by an ideal ionic liquid salt bridge (ILSB). Discussed are the specific requirements for the IL with regard to the procedure, thus ensuring that the liquid junction potentials (LJP) at both ends of the ILSB are mostly canceled. The remaining parts of the LJPs can be determined by separate electromotive force measurements. No extra-thermodynamic assumptions are necessary for this procedure. The accuracy of the measurements depends, amongst others, on the ideality of the IL used, as shown in our companion paper Part II.

A new theoretical model – The ionic molar surface Gibbs free energy and its application

Three novel ether-functionalized ionic liquids (ILs) 1-ethyl-3-(2-methoxyethyl)-imidazolium acetate, [C22O1IM][OAc], 1-ethyl-3-(2-methoxyethyl)-imidazolium thiocyanate, [C22O1IM][SCN], 1-ethyl-3-(2-methoxyethyl)-imidazolium trifluoromethanesulfonate, [C22O1IM][TfO], and two ILs 1-ethyl-3-(2-methoxyethyl)-imidazolium dicyanamide, [C22O1IM][DCA], 1-ethyl-3-(2-methoxyethyl)-imidazolium bis(trifluoromethylsulfonyl)imide, [C22O1IM][NTF2] were prepared and characterized. Their density and surface tension were measured at T=(298.15–338.15)K. As a new theoretical model, the ionic molar surface Gibbs free energy, gi, was put forward. The ionic molar surface Gibbs free energy, g−, for [BF4]−, which was as reference ion, was obtained in terms of the extrathermodynamic assumptions so that the ionic molar surface Gibbs free energy, g+, of the corresponding cations, [Cnmim]+ (n=2–6), were determined. In terms of the g+ values of [Cnmim]+ (n=2–6), the g− values of 12 kinds of anions were determined and then the average g+ value of [C22O1IM]+ (9.52±0.21kJ·mol−1) was gotten. By using the values of these gi, the predicted values of molar surface Gibbs free energy, gest, and surface tension, γest, for [C22O1IM][X] (X=OAC, SCN, DCA, TfO, NTF2) and other 45 ionic liquids were estimated. In comparison, the predicted values correlated quite well with their matching experimental values.

Traceability of pH to the Mole

Free acidity of aqueous solutions was initially defined in 1909 by Søren Peter Lauritz Sørensen as pH = −lgcH+ (c/mol·dm−3 or m/mol·kg−1 of the free hydrogen ions in solution, H+) soon (1910) was changed to pH = paH+ = −lgaH+, integrating the new concepts of activity, ai and activity coefficient γi, for the ionic species i under concern, H+ in this case; it is ai = −lg(miγi). Since individual ions do not exist alone in solution, primary pH values cannot be assigned solely by experimental measurements, requiring extra thermodynamic model assumptions for the activity coefficient, γH+, which has put pH in a unique situation of not being fully traceable to the International System of Units (SI). Also the concept of activity is often not felt to be as perceptible as that of concentration which may present difficulties, namely with the interpretation of data. pH measurements on unknown samples rely on calibration of the measuring setup with adequate reference pH buffers. In this work, the assignment of pH values to buffers closely matching the samples, e.g., seawater, is revisited. An approach is presented to assess the quantity pmH+ = −lgmH+ profiting from the fact that, contrary to single ion activity coefficients, mean activity coefficients, can be assessed based on experimentally assessed quantities alone, γExp ±, thus ensuring traceability to the mole, the SI base unit for amount of substance. Compatibility between γExp ± and mean activity coefficient calculated by means of Pitzer model equations, γPtz ±, validates the model for its intended use.

Single-ion hydration thermodynamics from clusters to bulk solutions: Recent insights from molecular modeling

The importance of single-ion hydration thermodynamic properties for understanding the driving forces of aqueous electrolyte processes, along with the impossibility of their direct experimental measurement, have prompted a large number of experimental, theoretical, and computational studies aimed at separating the cation and anion contributions. Here we provide an overview of historical approaches based on extrathermodynamic assumptions and more recent computational studies of single-ion hydration in order to evaluate the approximations involved in these methods, quantify their accuracy, reliability, and limitations in the light of the latest developments. We also offer new insights into the factors that influence the accuracy of ion–water interaction models and our views on possible ways to fill this substantial knowledge gap in aqueous physical chemistry.

Meaning and Measurability of Single-Ion Activities, the Thermodynamic Foundations of pH, and the Gibbs Free Energy for the Transfer of Ions between Dissimilar Materials.

Considering the relationship between concentration and vapor pressure (or the relationship between concentration and fugacity) single-ion activity coefficients are definable in purely thermodynamic terms. The measurement process involves measuring a contact potential between a solution and an external electrode. Contact potentials are measurable by using thermodynamically reversible processes. Extrapolation of an equation to zero concentration and ionic strength enables determination of single-ion activity coefficients. Single-ion activities can be defined and measured without using any extra-thermodynamic assumptions, concepts, or measurements. This method could serve as a gold standard for the validation of extra-thermodynamic methods for determining single-ion activities. Furthermore, it places the concept of pH on a thermodynamically solid foundation. Contact potential measurements can also be used to determine the Gibbs free energy for the transfer of ions between dissimilar materials.

Electric Field of the Ocean Induced by Diffusion

The equations for gradient of electric field in seawater induced by gradients of salinity, temperature and pressure were developed by means of non-equilibrium thermodynamics. Extrathermodynamic assumptions and accepted chemical model of seawater permit to carry out numerical calculations of electric field caused by diffusion, thermodiffusion and barodiffusion for realistic hydrophysical structure of the ocean. It is shown that contribution of barodiffusion into electric field of the ocean is almost constant (about -3 × 10-7 V/M). This magnitude can be ignored in many cases because it is too small. However natural salinity and temperature gradients significantly impact into electric field of the ocean.

Solvent-Independent Electrode Potentials of Solids Undergoing Insertion Electrochemical Reactions: Part I. Theory

A formally solvent-independent redox system can be theoretically defined using the Lovric and Scholz modeling of the voltammetry of microparticles for ion-insertion solids. The proposed theory is based on the extra-thermodynamic assumptions that no net charge accumulates at the solid|electrolyte interface and the assumption that the structure of the solid and the ion binding remain unaffected by the solvent. Under voltammetric conditions, the corresponding redox potential can be estimated from voltammetric and chronoamperometric data assuming electrochemical reversibility and diffusive charge transport in the solution and solid phases, also taking into account ion partition (electrolyte/solid) and ion-binding equilibria.

Physicochemical Properties of Air and Water Stable Rhenium Ionic Liquids

Air and water stable ionic liquids (ILs) based on catalytic functional metal rhenium, [C(n)mim][ReO(4)](n = 2,4,5,6)(1-alkyl-3-methylimidazolium perrhenate), are designed and synthesized. Their density and surface tension are measured in the temperature range of 293.15-343.15 ± 0.05 K. Some physical-chemical properties of the ILs have been calculated or estimated by the empirical methods. The ion parachor is put forward and calculated by two extrathermodynamic assumptions. According to the interstice model, the thermal expansion coefficient of ILs [C(n)mim][ReO(4)], α, are calculated and in comparison with experimental values, their magnitude order is in good agreement.

Ionic Parachor and Its Application in Acetic Acid Ionic Liquid Homologue 1-Alkyl-3-methylimidazolium Acetate {[Cnmim][OAc](n = 2,3,4,5,6)}

Five acetic acid ionic liquids (AcAILs) [C(n)mim][OAc](n = 2,3,4,5,6) (1-alkyl-3-methylimidazolium acetate) were prepared by the neutralization method and characterized by (1)HNMR spectroscopy and differential scanning calorimetry (DSC). The values of their density and surface tension were measured at 298.15 ± 0.05 K. Since the AcAILs can strongly form hydrogen bonds with water, the small amounts of water are difficult to remove from the AcAILs by common methods. In order to eliminate the effect of the trace water, the standard addition method (SAM) was applied to these measurements. As a new concept, ionic parachor was put forward. [OAc](-) was seen as a reference ion, and its individual value of ionic parachor was determined in terms of two extrathermodynamic assumptions. Then, the values of ionic parachors of a number of anions, [NTf(2)](-), [Ala](-), [AlCl(4)](-), and [GaCl(4)](-), were obtained by using the value of the ionic parachor of the reference ion; the parachor and surface tension of the investigated ionic liquids in literature were estimated. In comparison, the estimated values correlate quite well with their matching experimental values.

Determination of Individual Gibbs Energies of Anion Transfer and Excess Gibbs Energies Using an Electrochemical Method Based on Insertion Electrochemistry of Solid Compounds

A method is presented to determine, individually and with minimal extra-thermodynamic assumptions, the Gibbs energy for anion transfer between two solvents using solid state electrochemistry of alkynyldiphosphine dinuclear Au(I) complexes (AuC2R)2PPh2C6H4PPh2 (L1, R = Fc; L2, R = C6H4Fc) and the heterometallic Au(I)–Cu(I) [{Au3Cu2(C2R)6}Au3(PPh2C6H4PPh2)3](PF6)2 (L3, R = Fc; L4, R = C6H4Fc) cluster complexes containing ferrocenyl units. These compounds exhibit a well-defined, essentially reversible solid-state oxidation in contact with different electrolytes, based on ferrocenyl-centered oxidation processes involving anion insertion. Voltammetric data can be used for a direct measurement of the free energy of ion transfer from one solvent to another using midpeak potentials in solutions of suitable salts in each one of the solvents separately or mixtures of the solvents. Excess Gibbs energy of solvation in solvent mixtures can also be directly measured using this procedure. Solvation data for different common inorganic oxoanions in water, MeOH, and MeCN and water–MeOH and water–MeCN mixtures are provided.

Rational design of ion force fields based on thermodynamic solvation properties

Most aqueous biological and technological systems contain solvated ions. Atomistic explicit-water simulations of ionic solutions rely crucially on accurate ionic force fields, which contain most commonly two adjustable parameters: the Lennard-Jones diameter and the interaction strength. Assuming these parameters to be properly optimized, the plethora of parameters one finds in the literature for one and the same ion is surprising. In principle, the two parameters should be uniquely determined by matching two ionic properties obtained for a particular water model and within a given simulation protocol with the corresponding experimental observables. Traditionally, ion parameters were chosen in a somewhat unsystematic way to reproduce the solvation free energy and to give the correct ion size when compared with scattering results. Which experimental observable one chooses to reproduce should in principle depend on the context within which the ionic force field is going to be used. In the present work we suggest to use the solvation free energy in conjunction with the solvation entropy to construct thermodynamically sound force fields for the alkali and halide ions for the simulation of ion-specific effects in aqueous environment. To that end we determine the solvation free energy and entropy of both cations and anions in the entire relevant parameter space. As an independent check on the quality of the resulting force fields we also determine the effective ionic radius from the first peak of the radial ion-water distribution function. Several difficulties during parameter optimization are discussed in detail. (i) Single-ion solvation depends decisively on water-air surface properties, which experimentally becomes relevant when introducing extrathermodynamic assumptions on the hydronium (H(3)O(+)) solvation energy. Fitting ion pairs circumvents this problem but leaves the parameters of one reference ion (here we choose chloride) undetermined. (ii) For the halides the problem is almost underdetermined, i.e., there is a whole set of degenerate parameters that equally well describe, e.g., chloride and bromide ions. (iii) For the heavy cations the problem is overdetermined, i.e., no combination of Lennard-Jones parameters is able to reproduce simultaneously energy and entropy of solvation. We discuss various possibilities to deal with these problems and finally present an optimized force field for the halide anions that reproduces the free energy and the entropy of solvation. For the alkali metal cations there is no unambiguous choice of parameters. Therefore, we give three different parameter sets for every ion with a small, intermediate, or large Lennard-Jones interaction strength, where the Lennard-Jones diameters are optimized to reproduce the solvation free energy. The ionic radius is reproduced with acceptable accuracy by this optimization strategy, meaning that the proposed force fields are reliable beyond the target observables (i.e., free energy and entropy of solvation).

Basicities of Aquo + Alcoholic (Mono-ol) mixtures

Gibbs energies of transfer of H+ion [ΔG0t(w→s)(H+)] from water (w) to different aquo + alcoholic mixtures (s) were calculated using no extrathermodynamic assumptions. ΔG0t(w→s)(H+) values with and without interactions are given.ΔG0t(w→s)(H+) values (without interaction terms) compare well with the selected values of ΔG0t(w→s)(H+) in different aquo + alcoholic mixtures recommended by Marcus from compilations of data reported by various workers using different extrathermodynamic assumptions. Suitable conversion was made to bring the data into the range of the TATB scale.ΔG0t(w→s)(H+) values in binary mixtures (without interaction terms) are lower and qualitatively to some extent close to the values reported in the literature at least at low percentages.The results show that ΔG0solv(H+) and ΔG0t(w→s)(H+) values are increasingly positivei.e.less basic as the mass% of organic solvents increases and the sequence of basicities are in the orderi.e.the organic solvent and solvent mixtures are less basic than water contrary to the prevalent conceptions. The main factor appears to be the number of O-atoms with lone-pair of electrons responsible for H+acceptance, H-bonding and other structural modifications of the solvent mixtures. Obviously, the lower the molar mass of the organic solvent, the greater will be the basicity of the solvent and solvent mixtures.

A critique of a thermodynamic description of hydrophobic aggregation in aqueous solution

The conclusions recently summarised by A. Marmur [J. Am. Chem. Soc. 122 (2000) 2120] concerning hydrophobic aggregation of solutes in aqueous solution are examined. The thermodynamic analysis is critically reviewed and the impact of implicit extrathermodynamic assumptions discussed. These assumptions are questioned and shown to lead to a model for hydrophobic aggregation which is flawed.

Effect of the energy of zero vibrations and the entropy of reagents on the kinetic isotopic effect of the hydrogen evolution reaction

The effect the difference in zero energies and entropies of isotopic forms of reagents has on the difference in free energies of the elementary act of discharge of a hydronium ion for an initial equilibrium configuration of a reaction complex and equilibrium (ground) energy levels is considered. The analysis is performed for conditions of constancy of potential and constancy of overvoltage: only in the latter case one does not have to resort to extrathermodynamic assumptions. It is shown that differences in entropies of isotopic forms play a substantial role