Voltammetric Characterization of the Lability of Weak Acids Involved in the Hydrogen Evolution as Proton Donors

Linear sweep voltammetry data, obtained for hydrogen evolution on a copper electrode were used to estimate the lability of weak monoprotic acids as proton donors. Analysis of differential equations involving diffusion and kinetic terms shows that the total mass transport of proton donors and acceptors does not depend on the kinetics of chemical steps. Their surface concentrations as functions of the electrode potential can be easily obtained by convolution of experimental voltammograms and used in further analysis. The results show that acetic and glycolic acids are sufﬁciently labile, whereas the dissociation of the carboxylic group in gluconic acid is kinetically inhibited. The zwitterions formed in glycine solutions cannot be regarded as labile proton donors due to the inertness of the protonated amino group. Transforms necessary for constructing linear Tafel plots are discussed. the the

Hydrogen evolution is one of the oldest targets of electrochemical research. The first fundamental laws of electrochemistry were established on the basis of investigations of this object. Despite the significant progress made in identifying features of the kinetics and mechanism of this process, interest in this area is preserved. This is due to various reasons. First, hydrogen is an important utility for numerous applications in multiple industries including its use as a promising source of energy in the future. Though hydrogen plants are designed to serve heavy duties, portable hydrogen generators also have demand. As an example, we mention that they are promising in the automotive industry, because electrochemically generated H 2 gas can help burn diesel fuel more efficiently.
Hydrogen evolution often attends the electrodeposition of metals as a side reaction, which should be taken into account when the main process is studied. Most often the onset of the hydrogen evolution is followed by a progressive rise of the voltammogram. However, current maxima are observed when the plating solutions contain such ligands as hydroxy acids, which can generate hydrated protons (H 3 O + ions) establishing the conditions for the CE mechanism (chemical + electrochemical step). Then, hydronium ions are formed additionally in a chemical reaction that precedes the electron transfer.
Since coupled CE processes are commonly encountered in various processes, including electrodeposition of metals from complex electrolytes, 1 there is a growing need for a deeper understanding of their regularities. The data obtained by us for electroreduction of metal complexes 1 and for hydrogen evolution 2-5 make it possible to conclude that the strategy of quantitative processing and interpretation of the experimental results is closely related to the assessment of the lability of the electrochemical system.
Theoretical developments of often used linear sweep voltammetry (LSV) have been widely covered in the literature, their generalization can be found, e.g. in monographs. 6,7 In general, the response of the system to LSV perturbation usually contains current peaks that can be either defined very clearly or manifested very weakly. This largely depends on the relations between the kinetic and diffusion characteristics or, as it is often said, on the lability of the system.
Analytical expressions for LS voltammograms, as well as for lability criteria, are available, unless electrode reactions are not too complex and are coupled by the chemical step of the first (or pseudo first) order. They contain kinetic terms, whose values are rather rare in the literature as compared with those of equilibrium constants. Therefore, there is a need to find other ways to assess lability, based on z E-mail: arvydass@ktl.mii.lt the available data. From this point of view, the simplest solutions of weak acids can be not only an independent object of research, but also serve for experimental verification of certain regularities following from theoretical models.
The present article deals with this problem of estimation of system lability. Further, taking into account the results obtained, adequate methods of analysis of experimental data are considered with a view to determining the kinetic parameters of the charge transfer step. LSV data on hydrogen evolution in solutions of simple monoprotic acids are used for this purpose.

Theoretical Notes
Let us suppose that the hydrogen evolution proceeds in the solution of a weak acid H M A. Its stepwise dissociation can be represented in a general way as follows: The index j means the serial number of a proton released from the acid molecule; it takes integer values from 1 to M. The rates of recombination (w j ) and dissociation (w −j ) of species participating in the reversible process 1 are characterized by the corresponding rate constants (k j and k −j , respectively): To simplify the records, hereinafter the charges of anions are omitted. When the hydrogen evolution proceeds, all these species take part in mass transfer, as well as OH − ions, which interact simultaneously with hydrated protons: The rates of the forward and reverse processes are, respectively: In the presence of supporting electrolyte, when migration effects can be neglected, differential equations for planar diffusion of H + ions Journal of The Electrochemical Society, 165 (15) J3186-J3191 (2018) J3187 and proton-containing species take the form: In the above records, the kinetic terms (w j or w −j ) are equal to zero at j < 1 and j > N. The mass transfer equation should also be written for OH − ions When kinetic characteristics of chemical stages are known, the evaluation of their role does not present fundamental difficulties. One can, for example, use a set of the above differential equations, which, supplemented by proper initial and boundary conditions, make it possible to determine the surface concentrations of all species, including those that take part in the charge transfer step. The latter concentrations should be inserted into the kinetic equation formulated in accordance with the assumptive mechanism of the electrochemical process. Eventually, it is possible to simulate voltammograms, which can be compared with the corresponding experimental data and/or used in fitting procedures.
Note that there is no need for a preliminary assessment of the system lability in this case. However, if this feature is of special interest, simulated concentration profiles can be used to reveal the region of the diffusion layer in which deviations from the equilibrium distribution are observed. In this regard, we refer the reader to our article, 8 which details the use of concentration profiles as lability indicators.
Certain key ideas, which contribute to the understanding of the processes under discussion, could be also obtained from the results of such simulations. Though most general approaches cover a wide range of options, 6,7 they do not contain desirable details. In this connection, it seemed to us expedient to make calculations using the differential equations with the limited set of diffusion and kinetic characteristics and considering only those that are most typical of the systems discussed here. The data were obtained without limitations in reaction order at c H = 0.01 M, c A = 0.02 M and different kinetics of chemical step. The values of other parameters (stability constant K 1 = k 1 /k −1 , diffusion coefficient D, exchange current density i 0 and cathodic charge transfer coefficient α c ) were maintained constant. Since the formation of water is extremely rapid, it was assumed that the concentration of OH − ions is determined by the ionic product of water.
The cathodic current decreases with decreasing pre-reaction rate as well and the peak potential E p is shifted toward smaller cathodic overvoltages, i.e. to more positive potentials ( Figure 1). In accordance with the data published earlier, 6,7 two limiting cases are realized that correspond to relatively high or rather low rates of chemical steps (lines 1 and 2 in Figure 2). In both cases, the dependencies of current peaks i p vs.
√ v are linear and obey the relationship that was derived for a simple irreversible redox process. 9 It is not difficult to verify that in the first case (labile systems), the total concentration c H should be substituted for c (line 1) and in the second limiting case (inert systems) the equilibrium bulk concentration of the electrochemically active particle should be used, i.e. c = [H + ] (line 2). The behavior of peak potentials E p is shown in Figure 3. Again, in the case of sufficiently rapid (k −1 > 100 s −1 ) or very slow (k −1 < 0.1 s −1 ) chemical step the slopes of linear E p − log v dependences are in agreement with the theoretical relation derived for simple redox  √ v obtained at different kinetics of the preceding chemical step. The data are located between two straight lines corresponding to perfectly labile (line 1) and particularly inert (line 2) systems.
It can be also seen from this figure how the potential sweep rate can affect the system lability at moderate k −1 = 1 s −1 . At low v, the system is rather labile and the process in it is controlled mainly by diffusion. However, at high v, the chemical stage does not necessarily guarantee a high rate of the process, which goes over into kinetic regime. The situation is different when the kinetics of the chemical stages is unknown. Then we have to look for other ways of estimating local concentrations. If, for example, the chemical stages are sufficiently fast (the system has sufficient lability), the relationship between local concentrations can be expressed in terms of the constants of the corresponding equilibria. In this case, one assumption becomes possible, which enables one to simplify the solution of the problem.
It was accepted above that diffusion coefficients of all the species are the same. However, it is well known that H + and OH − ions distinguish themselves from others by their greater mobility, which is determined by the so-called structural diffusion (Grotthuss mechanism). Let us consider the labile system with fast chemical interactions resulting in the equilibrium distribution of species in the diffusion layer. If the certain species has an increased mobility (higher individual diffusion coefficients D j ), then, with diffusion mass transport going on, their excess should appear in a certain region of the solution, causing the respective shifts of chemical equilibria. As a result, some of more mobile particles will react with other components. Formally the same result could be obtained by assigning the lower D j to these species. If we consider the particles of the reduced mobility, on the contrary, their D j should be increased. Thus, the mechanism, which allows one and the same effective D to be assigned to all the particles, appears in the labile systems. This mechanism was studied in more detail by Kačena and Matoušek; 11 similar conclusions were also drawn in investigating combined H + and HSO − 4 diffusion. 12,13 It is suggested that the effective D can be expressed in terms of individual D i as the sum of products x i D i , where x i is a molar fraction of the respective species. Consequently, the value of D depends on the composition of the solution. Note, while the concept of the effective D seems to be quite acceptable in the case of labile systems, its use for inert systems remains questionable.
Bearing in mind the foregoing, we point out that very simple expressions containing no kinetic terms follow from the linear combination of the above differential equations: where c A is the total concentration of species containing ion A, i.e.
and c H is the quantity involving concentrations of proton donors (positive sign) and acceptors (negative sign): [ 15] In contrast to the concentration c A , which has an obvious physical meaning, the quantity c H is somewhat made-up. It was suggested for quantitative description of mass transport in the systems involving such components as protonated ligands or hydroxo-complexes. 1 In the case of solutions containing monoprotic acid HA, the last two equations take very simple form: . [17] Equation 13 supplemented by the proper initial and boundary conditions 3 has an analytical solution [18] where subscripts b and s denote bulk and surface concentrations respectively, the variable t in the time-dependent current density i(t) is replaced by the auxiliary variable (t − u). The function ψ(u) takes into account the existence of δ-thick diffusion layer; in the case of semi-infinite diffusion, ψ(u) = 1.
We would like to draw attention to a number of important features concerning the above relationships. First, the same Equations 12 and 13 are also obtained for more complex systems containing mixtures of acids. In this case, Equations 14 and 15 must be transformed in accordance with the composition of the solutions used. Further, the derivation of Equation 18 is not associated with any preliminary assumption about the nature of the electrochemically active species; it can be used at different mechanisms of the process. Finally, since Eq. 18 contains no kinetic characteristics of chemical steps, it is suitable for estimating the total surface concentration both in labile and inert systems.

Experimental
Solutions were prepared using deionized water, sodium acetate, sodium gluconate, aminoacetic acid (glycine) (all Sigma-Aldrich, 99% pure) and hydroxyacetic (glycolic) acid (Reakhim, Russia). 0.3 M sodium perchlorate (Fluka, > 98%) was used as a supporting electrolyte. Specified values of pH were adjusted by addition of HClO 4 or NaOH. Solutions were deaerated before experiments with an argon stream for over 0.5 h. Measurements were carried out using platinum and copper electrodes. To prepare the working electrodes, a 1 cm 2 platinum disc was coated with 5-7 μm thick copper in a solution containing (g dm -3 ): CuSO 4 · 5H 2 O -250, H 2 SO 4 -50. A polycrystalline layer with well-exhibited crystallographic edges and faces was formed. Detailed characteristics of surface morphology are given elsewhere. 14 LSV measurements were performed using a potentiostat/galvanostat REF 600 from Gamry Instruments. Voltammograms were recorded at a potential sweep rate v ranging from 0.01 to 0.2 V s −1 . In all cases, cathodic scans were applied, starting with the open-circuit potential. The electrode potential was measured in reference to the Ag | AgCl | KCl(sat) electrode and was converted to the standard hydrogen scale. All experiments were performed at 20 • C.

Results and Discussion
Four simple monoprotic carboxylic acids were selected for research. Acetic acid CH 3 -COOH solutions are the most studied object that can be used for experimental verification of the regularities of theoretical models. Two derivatives -hydroxyacetic (glycolic) acid HO-CH 2 -COOH and aminoacetic acid (glycine) H 2 N-CH 2 -COOHare slightly stronger due to the electron-withdrawing power of the terminal groups. Unlike the previous ones, gluconic acid HO-CH 2 -(CH-OH) 4 -COOH has a substantially longer hydrocarbon chain. Its deprotonated OH groups are capable of forming strong coordination bonds only in alkaline media. Therefore, in weakly acidic solutions, gluconic acid, like the rest, is considered to be monoprotic.
The set of parameters used in the present investigation is listed in Table I. Equilibrium characteristics (the values of K 1 = 1/K a ) are widely represented in various databases and can be simply selected as most appropriate to the composition and ionic strength of the solutions used. Diffusion characteristics 15-21 given mainly for 25 • C, as well as rate constants available in literature [20][21][22][23] are also reported.
Since the main experimental material discussed below refers to 0.04 M acid solutions at pH 3, we also present total concentrations of proton donors (see Equation 17) obtained from well-known material balance equations with the activity coefficient of hydronium ions equal to 0.7. Some features concerning glycine solutions are discussed below. Voltammograms display well-defined, even current peaks whose shape is actually the same for both platinum and copper electrodes despite the fact that these metals differently adsorb hydrogen with the only difference that the voltammograms for Pt are markedly (about 0.5 V) shifted to more positive potentials. This phenomenon indicates that the shape of voltammograms is specified, in a fundamental way, by the processes taking place in the near-electrode (diffusion) layer, but not at the interphase. Bearing this in mind, we provide further data obtained for copper electrode. Typical curves are presented in Figure 4. The height of current peaks is different for each acid and decreases in the same order as the total concentration of proton donors c H (see Table I). At the same time, i p varies linearly with √ v (inset in Figure 4). As already noted, before proceeding to the quantitative analysis of the experimental curves, it is necessary to estimate the degree of system lability. This is most easily done, if diffusion and kinetic characteristics of the system are known. The acetate system is in a favorable position in this respect. Comparison of kinetic parameters (Table I)  Since the kinetic constants for glycolic acid system were not available to us, we had to use only voltammetric data. Certain conclusions can be obtained from the analysis of surface concentrations obtained  [19] Hence, the fulfillment of condition 19 is an indispensable sign indicating a labile character of the system under the conditions applied. Another limiting case is possible in highly inert systems, where dissociation of the electrochemically inactive HA is considered to be very slow. Therefore, its surface concentration will vary slightly with i and all changes in c H will be caused by a decrease in the concentration of hydronium ions. Then, the condition 19 changes to [20] In view of the foregoing, lability estimates, based on the analysis of the c H values, are possible. The case of labile system is demonstrated in Figure 5. At sufficiently high cathodic polarizations (E < −1 V), the convoluted experimental voltammograms reach the plateau, where c H approaches the bulk concentration of proton donors (see Table I). A further increase in this quantity, observed at E < −1.2 V, arises from the discharge of water molecules. Similar results are also typical of acetate system. [2][3][4][5] The lability of systems opens up a relatively simple way of further analysis of the experimental data. When chemical interactions are sufficiently fast, the deviations from the equilibria in the diffusion layer can be considered to be insignificant. Then the interconnections between species concentrations can be expressed in terms of the corresponding equilibrium constants. Further, the surface distribution can be determined on the basis of common mass balance equations taking into account that a certain profile of c H is established in the diffusion layer, whereas the gradient of c A is absent due to the electrochemical inertness of anion-containing species. In other words, the c A quantity is constant throughout the system. The above procedures are required for determining kinetic parameters of the charge transfer process.
According to the simplest mechanism, which has been taken as a basis for the studies of the kinetics of dissociation of some monoprotic carboxylic acids, 20 the charge transfer H + + e → H ads can be considered as the rate-determining step. In this case, at sufficiently large cathodic overvoltages, η c , the kinetic equation takes the form: where These expressions describe the so-called normalized Tafel plots (NTP). Experimental voltammetric data can be transformed into linear NTPs when the current density is normalized with respect to the potential-dependent surface concentration [H + ] s . This procedure has been widely applied in various investigations including electroreduction of metal complexes 1 and hydrogen evolution. 1,3-5 NTPs close to linear were obtained for the acetate system even in such cases when voltammograms contained double current peaks. 5 Below (Figure 6), we present the NTP obtained for a sufficiently labile system containing glycolic acid. The data obtained at different potential sweep rates can be approximated by one general line. Its slope and intercept yields kinetic parameters listed in the figure. Note that the solutions were not saturated with hydrogen and the opencircuit potentials were more positive than the equilibrium potential E eq = −0.058 pH. Since the overvoltage was determined with respect to the theoretical E eq value, the exchange current density, obtained from the NTP intercept, is treated as effective.
Kinetic parameters of hydrogen evolution depend on various factors: the composition and acidity of the solution, the nature of the metal, the method of its preparation before measurements, the adopted mechanism of the process, the procedures used in processing and interpreting the experimental data, etc. A critical review of the literature data obtained for hydrogen evolution on Cu electrodes has shown 24 that reliable values of i 0 obtained at pH 0.0-1.0 fall within the range from 10 −7.5 to 10 −6 A cm −2 . Thus, a comparatively low value of i 0 (∼60 nA cm −2 ) was obtained for the Cu|HCl system under highpurity conditions. 25 This quantity was found to be tenfold higher for hydrogen evolution on polished copper in slightly acid H 3 BO 3 solutions saturated with, hydrogen. 26 It was assumed in this case that the Volmer reaction is the rate-determining step. The i 0 quantities of several μA cm −2 follow from the NTPs obtained for copper coatings in solutions of carboxylic acids containing 0.5 M K 2 SO 4 as a supporting electrolyte. 27 Such solutions contain HSO − 4 ions acting as additional proton donors. As can be seen from the above, the exchange current densities in perchlorate media are rather low. On the basis of the foregoing, we can conclude that there are no fundamental contradictions between the kinetic data obtained by us and published previously.
Voltammograms with well-defined current peaks are also typical of gluconate solutions. Transform of the experimental voltammo-grams according to Eq. 18 produces the c Ht dependences that are also similar to those obtained for acetate or glycolate solutions (see Figure 5). However, the height of plateau on this curve coincides with the bulk concentration of proton donors c H (Table I) when the apparent D = 3.4×10 −6 cm 2 s −1 . In contrast to the above systems, the D obtained is twice lower than D = 6.75×10 −6 cm 2 s −1 determined for gluconic acid and glucose by reasonable methods. 19,21 Even more low D = 1.5×10 −6 cm 2 s −1 was obtained in a similar manner for gluconate solutions containing sulfate as a supporting electrolyte. 27 It follows from Eq. 18 at D = 6.75×10 −6 cm 2 s −1 , that the surface concentration of proton donors c H, s ≈ 0.3 c H, b and does not approach zero. The result obtained seems to arise from the limited dissociation rate of gluconic acid, which becomes the controlling factor at high enough overvoltages. This conclusion is in line with the kinetic data given in Table I. The dissociation/recombination rates for gluconic acid are significantly (by ∼4 orders) lower as compared with those for the acetate system.
It was of interest to revise the voltammetric data in order to detect other indications of limited lability of the system. It turned out that the linear dependencies of i p vs.
√ v and E p vs. log v can be also constructed for the gluconate system. Moreover, NTPs, obtained ignoring kinetic limitations, can be approximated by a single general line at different potential sweep rates over a wide potential range. 3 Finally, it was also of interest to compare shapes of current peaks obtained for the acetate and gluconate systems. It turned out 3 that the peak regions of voltammograms, each normalized with respect to its individual i p , can be displaced along the potential axis so, that they would actually coincide. Consequently, the shape of the voltammogram also contains no signs for assessing the presence of slow chemical steps. Before proceeding to the analysis of the data obtained for the glycine system, it is necessary to discuss some of its distinctive features which are not characteristic of previous research objects. Glycine (HA) in aqueous solutions promotes formation of a zwitterion + H 3 N-CH 2 -COO -, which together with its protonated form + H 3 N-CH 2 -COOH (H 2 A + ) dominates in acid media. Both species are capable of splitting off one and two protons, respectively. On this basis, the total concentration of proton donors and acceptors might be expressed as follows: [23] As a result of a preliminary study of this system, 4 the question arose, whether all the species in Eq. 23 are labile. One can suggest by analogy with two previous systems that the carboxyl group dissociates relatively fast. Assuming further that the proton attached to the amino group is insufficiently mobile, the zwitterion LH should be excluded from consideration and the LH 2 species should be treated as the particle containing only one mobile proton, which is split off from the carboxyl group. As a result, we get for labile components that Equations 23 and 24 give rather differing results, e.g. 51.4 and 11.4 mM for 0.04 M glycine solution at pH 3 (see Table I).
We conducted additional experiments extending the range of the solution compositions. The results accumulated in the mentioned studies are summarized in Figure 7. The c H quantities obtained for different solutions by Eq. 24 are displayed by dotted lines. Plateaux of c H -E dependences agree with these values when D = (8.4±0.4)×10 −6 cm 2 s −1 is used. This value is close to D = 9.4×10 −5 cm 2 s −1 that has been estimated earlier. 18 The generalized experimental data confirm the conclusion 4 that protonated + H 3 N-CH 2 -COOH species can be treated as labile proton donors, whereas zwitterions + H 3 N-CH 2 -COOdo not fall into this category.
Proceeding from the latter assumption, we constructed NTPs using the method described above. It is evident from the presented example (inset in Figure 7) that the linear graph is not obtained. The reasons for such a result have yet to be clarified. It seems possible that the mechanism of the process in this system can exhibit a number of distinctions; therefore further research is needed to elucidate it.

Concluding Remarks
Methods for estimating the lability of weak acids, which are involved as proton donors in the electrochemical hydrogen evolution, have been considered. Simulations by differential equations including diffusion and kinetic terms show that, under the conditions of common linear sweep voltammetry, those acids whose dissociation rate constant k −1 exceeds 10 3 -10 4 s −1 might be classified as labile. In the absence of kinetic data of chemical stages, the system lability can be estimated using the data of the surface concentrations of proton donors and acceptors, which can be obtained by convolution of experimental voltammograms. It has been found that acetic or glycolic acid systems show labile behavior, while the dissociation of gluconic acid has certain kinetic limitations. Protonated glycine exhibits dual behavior: a fast split of the proton from the carboxyl group and a slow dissociation of the protonated amino group.