Electrochemical Proton Reduction and Equilibrium Acidity (p K a ) in Aprotic Ionic Liquids: Protonated Amines and Sulfonamide Acids

. Many organic compounds contain acidic and/or basic groups that dictate their physical, chemical and biological properties. For this reason, the acid dissociation constant, K a , a quantitative measure of acid strength in solution, is a fundamentally important parameter in organic (synthetic) chemistry and related fields. In this study, the thermodynamics, kinetics and mechanisms of the proton reduction (hydrogen evolution) reaction at a platinum electrode have been investigated in the room temperature ionic liquid (IL) 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide, using a range of nitrogen (R x NH) acids as the proton source. The formal potential of the H +solvated /H 2 process (simulated by combining the classical Volmer and Tafel reactions) has been shown to be strongly dependent on the identity of the IL anion, making direct comparison of p K a data between ILs with different constituent anions impossible. Hydrogen evolution from weak nitrogen acids (protonated amines or sulfonamides) as the proton source is a diffusion controlled process which occurs in the potential region negative of the H +solvated /H 2 process. Simulations reveal that weak acid dissociation is limiting on the voltammetric timescale when p K a > 4, meaning proton reduction via a CE mechanism (where C is the acid dissociation step) cannot account for the experimentally observed mass-transport limited currents. Under these conditions, proton reduction must proceed via an alternate pathway, where the weak acid undergoes direct reduction at the platinum electrode surface. Finally, the p K a values for ten weak nitrogen acids have been calculated (5.2 ≤ p K a ≤ 19.5) from voltammetrically derived reversible half wave potentials ( E 1/2 ) and diffusion coefficients ( D ), highlighting the utility of voltammetry as a convenient and relatively straightforward method for quantifying equilibrium acidity.


Introduction
2][3][4][5] The acid dissociation constant (Ka) of a Brønsted acid, HA, formally defined as follows, is a quantitative measure of acid strength: Although the acid is taken to be a neutral species (HA) in Eq. 1, the following equation is equally valid for a cationic acid species, BH + (i.e., a protonated neutral base, B): The concept of Brønsted acidity/basicity is well established in aqueous media 6 , where water, an amphoteric species, can act as a Brønsted base and accept a proton: or as a Brønsted acid and donate a proton: A − (or B) + H 2 O(acid) ⇌ HA (or BH + ) + OH − From Eq. 3, it is clear that the hydronium ion (also known as a hydrated/solvated proton), H3O + , which behaves as if it has a pKa of -1.74 (where pKa = -log10Ka), is the strongest acid that can exist in aqueous solution.The process shown in Eq. 3 effectively 'levels' the acidity of all strong acids (pKa < -1.74) in aqueous media and is the origin of the aqueous pKa scale. 7,8 y organic compounds contain acidic and/or basic groups that dictate their physical, chemical and biological properties.Indeed, bond transformations in solution frequently involve the cleavage or formation of 'R-H' bonds.0][11] The equilibrium acidity (pKa) is a solvent dependent parameter, being influenced by the ability of the solvent to solvate each of the species outlined in Eqs. 1 (HA, H + and A -) or 2 (BH + , H + and B).It follows that solvent acidity/basicity, dielectric properties and ability to donate/accept hydrogen bonds can all influence the pKa of an acid in solution. 11,12 lthough pKa data is most readily available in water 13,14 , pKa scales have been established in a range of non-aqueous solvents, including acetonitrile 15 , dimethylsulfoxide 11,16,17 and 1,2-dichloroethane 15 .A variety of methods 18 have been employed to quantify equilibrium acidities in conventional media, including potentiometry 19 , spectrophotometry 11,20 and voltammetry 12,16,17 .
Air/water stable non-haloaluminate room temperature ionic liquids (ILs) have shown promise as replacements for volatile molecular solvents (such as those listed above) in a range of applications. 21ILs are typically composed of a bulky organic cation and an inorganic anion with extensive charge delocalization.They are often referred to as 'designer solvents' because their physicochemical properties can be 'tuned' to an extent by changing their constituent cation and/or anion. 22,23 elatively strong electrostatic (cohesive) forces operate within ILs, which means they often tend to be highly viscous and non-volatile. 24Protons released from the dissociation of a Brønsted acid in an IL must associate with (or be 'solvated' by) the most basic component of the IL, most commonly the anion (A IL − ): where HAIL is the strongest acid that may exist in a given IL.HAIL effectively levels the acidity of strong acids in IL media, comparable to H3O + in aqueous media.In other words, HAIL is origin of the pKa scale in IL media and for this reason pKa data are not directly comparable between ILs with different constituent anions. 7,9,10 Fom this point forward, 'H + ' refers to the 'solvated' proton species and is equivalent to HAIL in the context of ILs.Unfortunately, absolute pKa data for weak acids in ILs are scarcely available. 7,9,10 Ian be shown 7,12,25 that the difference in the formal potential (E 0' ) of the HA/H2 or BH + /H2 couple and the H + /H2 couple is proportional to the equilibrium acidity of HA or BH + (i.e., ΔE 0' ∝ pKa).Therefore, in this study, we will employ electrochemical methods such as cyclic voltammetry 25 to probe the thermodynamics, kinetics and mechanisms of the H + /H2 and HA/H2 (or BH + /H2) processes.The proton overall reduction reaction (or hydrogen evolution reaction, HER) is a conceptually simple process, involving the transfer of one electron per proton [26][27][28][29][30][31] : However, this reaction is subject to significant kinetic barriers, requiring an electrocatalyst to proceed at an economically viable rate. 32The HER has been most extensively studied in acidic aqueous media, where it is postulated to proceed via a combination of the following three elementary reactions 27,29,32 : 2H ads → H 2 where Hads is a chemisorbed hydrogen atom and Eqs. 7, 8 and 9 are known as the Volmer, Tafel and Heyrovsky reactions, respectively. 27In a previous publication 33 , we investigated the proton reduction reaction at a platinum electrode in a range of bis(trifluoromethanesulfonyl)imide ILs using H[NTf2] as the proton source (i.e., the H + /H2 process).Our results indicated that the Volmer reaction (Eq.7) is the rate determining step for the HER in the IL media and that E 0' (H + /H2) is essentially insensitive to the identity of the IL cation.
Surprisingly, detailed studies available on the proton reduction process from weak acids in IL media are scarce.Doherty et al. 7 have investigated the proton reduction process from five protonated amines (i.e., the BH + /H2 couple) at a platinum electrode in a range of ILs.The BH + /H2 process is quasi-reversible and occurs at potentials negative of the H + /H2 process.By assuming ΔE 0' ≈ ΔE1/2 (where E1/2 is the reversible half-wave potential), an approximation which introduces considerable systematic error into the determination of pKa (vide infra), the authors estimated the pKa value directly from a transient cyclic voltammogram and found that the strength of a given acid depends strongly on the constituent anion of the IL.
In this paper, the thermodynamics, kinetics and mechanisms of the proton reduction (hydrogen evolution) reaction at a platinum electrode have been investigated in the room temperature ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide using ten nitrogen acids (protonated amines or sulfonamides, structures shown in Table 1) that cover a wide range of acidities as the proton source.The proton reduction process has been characterized predominantly using cyclic voltammetry with computational simulation.We also present a relatively straightforward method for calculating the pKa of weak acids in IL media, based on a combination of cyclic voltammetry and chronoamperometry.A companion study has also been undertaken using a range of oxyacids (phenols, carboxylic acids or sulfonic acids), which will be presented elsewhere.

Experimental Section
Reagents.and sealed in a fritted (Vycor glass frit) glass tube served as the pseudo reference electrode.
The pseudo reference electrode potential was calibrated against the formal potential of the IUPAC recommended Fc/Fc + process 35 in the electrolyte of interest, taking into careful consideration the difference in the diffusion coefficients of Fc and Fc + . 27,36  Pt macrodisk with a nominal diameter of 1.6 mm was purchased from BASi (Bioanalytical Systems, USA) and the Pt microdisk with a nominal diameter of 20 µm was purchased from Metrohm (Switzerland).The Pt macrodisk electrode was activated by polishing with successively smaller (1 and 0.3 µm) aqueous alumina slurries (Kemet, UK) on a clean polishing cloth (Buehler, USA).Adherent alumina was removed by sonication in de-ionized water.The Pt microdisk electrode was activated by polishing with an aqueous slurry of 0.3 µm alumina and rinsed thoroughly with de-ionized water.The working electrode was preconditioned prior to sweeping by anodic polarization at 1.5 to 2.2 V vs. Fc/Fc + for ≤ 10 ms as has been previously reported. 33The active electrode area (A) of each of the electrodes was calibrated with convolution voltammetry [37][38][39] , using the oxidation of a Fc solution of known concentration (2.0 mM in acetonitrile containing 0.10 M [NBu4][PF6]) and adopting a diffusion coefficient of 2.4 × 10 −5 cm 2 s −1 , as published under these conditions. 25scosity was measured using the falling ball method with an Anton Paar Automated Microviscometer (AMVn).Density was measured with an Anton Paar DMA 4500M Density Meter.
Data treatment and processing.The algorithm used to calculate the convolved currents is the same as used previously. 38Derivative cyclic voltammograms (i.e., 1 st order derivative of current or 2 nd order derivative of charge) were constructed by differentiating experimental current data with respect to time using the differentiate function available in OriginPro 9.0 software.Savitzky-Golay data smoothing (polynomial order 2) was performed prior to estimating the derivative peak potentials.The diffusion coefficients (D) of H + , BH + and HA were estimated from chronoamperometric (I−t) decay curves obtained at a microdisk electrode using the Shoup and Szabo 40 method, as reported elsewhere. 33,36 he diffusion coefficient (D) of H2 was estimated from the second (oxidative) step of a double-step chronoamperogram using numerical simulation as has been previously described. 41The sample time used in all chronoamperometric experiments was 0.01 s.Voltammetric simulations were undertaken using the DigiElch software package (v.7F, Elchsoft, Germany).The pKa of 2,4-dichloropyridine was estimated using the MarvinSketch software package (v.14.12.15.0,Chemaxon).V vs. Fc/Fc + ), as was highlighted in a previous publication. 33Shown in Figure 1a is a cyclic voltammogram obtained from the reduction of H[NTf2] at a platinum macrodisk electrode in

Electroreduction of 'solvated' H + in [C2mim
. This is a one electron per proton process, which occurs in the potential region just negative of the Fc/Fc + process, producing molecular hydrogen (H2) as per Eq. 6. 27,28,33 The voltammetric peak-to-peak separation (ΔEp) increases with increasing scan rate, with values of 72.2, 82.2 and 92.3 mV at 100, 250 and 500 mV s -1 , respectively (see Figure S1), indicating that the H[NTf2]/H2 process is quasi-reversible (Ru is expected to negligible, see Experimental Section).In a previous publication 33 , we demonstrated that H[NTf2] is not dissociated when dissolved in ILs containing the [NTf2] -anion (i.e., the protons diffuse as comparable to H3O + in aqueous media.Since H[NTf2] is the strongest acid that can exist in , the H[NTf2]/H2 process shown in Figure 1a will serve as the equilibrium acidity scale reference point in this medium. 8own in Figure 1b In other words, H[NTf2] behaves as a 'strong acid' in [C2mim][OTf], undergoing complete dissociation to form H[OTf] and [NTf2] -.Consequently, the H[OTf]/H2 couple is responsible for the proton reduction process observed in Figure 1c.The higher proton affinity of [OTf] - compared to [NTf2] -is thought to be due to the smaller size and more localized negative charge density of the former. 9,10 onversely, it would be expected that H[OTf] behaves as a 'weak acid' in [NTf2] -ILs, which was found to be the case in our companion study. 34 2.

Simulation of the electroreduction of 'solvated' H + in [C2mim][NTf2] and [C2mim][OTf]
. Also shown in Figure 1 are simulations of the cyclic voltammograms.A number of mechanisms were considered 33 and the following was found to be consistent with the experimental data under a wide range of experimental conditions: where E 0' (H + /H * ),  s app and α are the formal potential of the H + /H * couple, apparent standard heterogeneous electron-transfer rate constant (vide infra) and charge transfer coefficient respectively.Additionally, Eq. 12 has been treated as a homogeneous process with arbitrarily defined dimerization equilibrium constant (Kdim) and dimerization rate constant (kdim) values.
Here, H + denotes a 'solvated' proton, referring to the strongest acid which can exist in a given medium, which in the current context is equivalent to HAIL.The reactions given in Eqs.11 and 12 correspond to the Volmer and Tafel equations respectively (see Eqs. 7 and 8).Although in reality H * is likely to be a surface confined species 29,31 , it has been treated as solution based (diffusing) species in the simulations, as justified in a previous publication. 33One consequence of treatment of the mechanism in this manner is that the process shown in Eq. 12 has no physical significance and the following parameters:  s app , Kdim, kdim and  H * are not quantitatively meaningful. 16For this reason, ks has been given the superscript 'app' to signify that it is the 'apparent' heterogeneous rate constant used in the simulations.
In all simulations, it was taken that  H * = 10 -10 cm 2 s -1 , Kdim = 10 4 , kdim = 10 16 M -1 s -1 , uncompensated resistance (Ru) = 0 Ω and double layer capacitance (Cdl) = 0 F. The E 0' value used in the simulations corresponds to the fictitious H + /H * couple and is related to E 0' (H + /H2) as follows: where R is the gas constant, F is Faraday's constant and T is temperature.The parameters derived by simulation of the experimental data are outlined in As shown in Figures S1 to S3, excellent fits between the experimental and simulated voltammograms are achieved over a wide range of scan rates when using the simulation parameters outlined in Table 2.As was highlighted in a previous publication 33 , the main discrepancy between the experimental and simulated data is in the hydrogen underpotential deposition (UPD) region, prior to the main (solution based) reduction process. 9The formal potential of the H + /H2 process in [C2mim][NTf2] is -0.026V vs. Fc/Fc + , compared to -0.342  mV negative of the H[NTf2]/H2 process (see Figure 1a), corresponding to the first and second deprotonation, respectively.Hydrogen UPD can be seen prior to the first proton reduction process at high scan rates; this was found to be the case with all of the acids investigated in this work.ΔEp for the process corresponding to the first deprotonation increases substantially with scan rate, with values of 142, 170 and 250 mV at 50, 100 and 250 mV s -1 , respectively.By contrast, ΔEp for the process corresponding to the second deprotonation increases to a lesser extent with scan rate, with values of 87.9, 93.8 and 108 mV at 50, 100 and 250 mV s -1 , respectively.These results qualitatively indicate that hydrogen evolution from monoprotonated [oPD-H] + is more kinetically facile than from diprotonated [oPD-H2] 2+ in this media, suggesting that the charge of the weak acid may influence the heterogeneous electron transfer kinetics of the proton reduction process.
Cyclic voltammograms obtained from two neutral sulfonamide acids, SACC and DBSA, are shown in Figure 3a and b, respectively.Proton reduction from SACC (see Figure 3a) occurs in the same potential region as

Simulation of the proton reduction process from weak nitrogen acids in [C2mim][NTf2].
The overall proton reduction process from a weak acid is: where B/BH + correspond to a neutral base/conjugate cation acid and HA/A -correspond to a neutral acid/conjugate anion base.The two reactions described above are stoichiometrically equivalent and although the following discussion refers to the BH + /H2 couple, it is equally applicable to the HA/H2 couple.In order to simulate the BH + /H2 process, a CE mechanism was considered, whereby proton reduction via the mechanism described by Eqs.11 and 12 is preceded by dissociation of BH + : where kdissoc is the dissociation rate constant and kassoc is the association rate constant.In all simulations, kassoc was set to be 5 × 10 8 M -1 s -1 which is thought to the approximate the diffusion controlled limit for a bimolecular reaction in this viscous electrolyte. 39Additionally, in all simulations it was assumed that  B =  BH + and the parameters for Eqs.11 and 12 were taken from Table 2. Simulations were carried out for [dClPyr-H][NTf2] using the diffusivity and pKa values outlined in Table 3; the results are shown in Figure 4. Evidently, BH + reduction solely via the CE pathway cannot support a mass-transport controlled current, even at 50 mV s -1 .This is because kdissoc = Kakassoc and kassoc cannot exceed the diffusion controlled limit, which, in the present case means kdissoc ≈ 300 s -1 , making the reaction shown in Eq. 16 limiting on the voltammetric timescale.
Clearly, a parallel reaction pathway must be available to support the diffusion controlled currents observed experimentally.One possibility is that BH + undergoes direct reduction (DR mechanism) at the electrode surface without prior dissociation, giving rise to surface adsorbed H * as previously discussed: This reaction is conceptually analogous to the direct reduction of water at platinum in neutral or basic aqueous solution. 17Simulations were carried out by combining Eqs.11, 12, 16 and 17; the result is also shown in Figure 4.There is excellent agreement between the simulations and experimental data when the DR pathway (Eq.17) also is considered.Simulation-experiment comparisons for all of the investigated weak acids are included in the Supporting Information (Figures S3 to S13).The parameters derived by simulation of the experimental data are outlined in Table 3.As shown in Figures S3 to S13, excellent fits between the experimental and simulated voltammograms are achieved over a wide range of scan rates when using the simulation parameters outlined in Table 3. Once again, the main discrepancy between the experimental and simulated data is in the hydrogen UPD region. 16Fourteen orders of magnitude in acid strength (Ka) have been covered in this study, ranging from pKa = 5. ).This trend is not likely to be the result of a double layer effect 25 , which would predict that the apparent ks increases at increasingly negative potentials for cationic species (assuming all of the processes are negative of the point of zero charge).Since Eq. 17 is the rate determining step, one possible explanation for this trend is that activation energy (overpotential) required to break the N-H bond is related to the heterolytic bond dissociation energy, which is larger for the weaker acids (proportional to pKa). 16,17 lso evident from the data in Table 3, the proton reduction process from monocationic nitrogen acids is more kinetically facile (electrochemically reversible) than from dicationic or neutral nitrogen acids of comparable strength.Since [oPD-H] + and [oPD-H2] 2+ are structurally identical, the trend in  s app is most likely related to the charge of the respective acids.A similar comparison cannot be made between the monocationic protonated amine acids and neutral sulfonamide acids, because structural variations in the vicinity of the acidic proton on the parent acid may affect the kinetics of the Volmer-type reaction shown in Eq. 17.
Further simulations carried using the CE (see Eqs. 11, 12 and 16), DR (see Eqs. 12 and 17) or CE + DR pathways are included in the Supporting Information (Figures S14 to S18).
Setting kassoc to be the diffusion controlled value (5 × 10 8 M -1 s -1 ) and using a 'typical' set of simulation parameters for proton reduction in [C2mim][NTf2] (outlined in Table S1), it was found that proton reduction through the CE pathway could only attain a diffusion controlled current when pKa < 4. It was also found that proton reduction through the DR pathway becomes insignificant when pKa < 2. Although these are generalizations, as they strictly only apply under the conditions investigated (r0 = 0.0825 cm, ν = 500 mV s -1 ), they do provide valuable insight into how the preferred proton reduction pathway relates to the strength of the weak acid.In line with the simulations, we have shown in our companion study 34 that H[OTf] has a pKa of approximately 2 in [C2mim][NTf2], allowing proton reduction to proceed via the CE pathway.
These simulations are in qualitative agreement with the studies by Evans et al. 16,17 on the reduction of weak acids in dimethylsulfoxide (kassoc ≈ 1 × 10 10 M -1 s -1 ), where the authors postulated that there is a transition from the CE pathway to the DR pathway when pKa > 6.  - , where H + is the strongest acid which can exist in a given medium (i.e., a 'solvated proton'), which in the current context is equivalent to H[NTf2].If it is assumed that activities are equal to molar concentrations, as justified by Doherty and coworkers 7 , the Nernst Equation for the H + /H2 couple is as follows: Here, the concentration rather than pressure-based standard state of H2 has been used.Proton reduction from a weak acid can be described by the process given in Eq. 14.Once again, if it is assumed that activities are equal to molar concentrations, the Nernst Equation for the BH + /H2 couple is as follows: If Eq. 18 is subtracted from Eq. 19, we get: so the pKa of an acid can be estimated if E 0' (H + /H2) and E 0' (BH + /H2) are known.Although E 0' (H + /H2) was previously estimated to be -0.026V using numerical simulation (see Table 2), it can be more conveniently calculated directly from a transient cyclic voltammogram (see Figure 1a) as follows.Under conditions where mass transport is governed solely by semiinfinite planar diffusion and H + is the only species initially present in solution, the following relationship between E 0' (H + /H2) and the reversible half wave potential, E1/2, can be derived from Eq. 18 using the diffusion layer method 17,25,30,44 : where the subscript 'b ' signifies 'bulk concentration'.E1/2 can be estimated from a transient cyclic voltammogram as follows: where Ep,ox and Ep,red are the oxidation and reduction peak potentials respectively. 17 2).Likewise, E 0' (BH + /H2) can be estimated using numerical simulation (see Table 3) or directly from a transient cyclic voltammogram using the following equation, derived from Eq. 19 using the diffusion layer method 17,25 : Again,  1/2 (BH + /H 2 ) can be estimated from a transient cyclic voltammogram using Eq.22.
The pKa values calculated for all of the nitrogen acids are summarized in Table 4.In addition, experimental and simulated cyclic voltammograms obtained from the full spectrum of nitrogen acids investigated in the work are shown in Figure 5.The pKa values estimated using numerical simulation are generally in excellent agreement with those determined directly from the cyclic voltammogram (CV) using Eqs.21, and 24.The largest deviation between the two methods is approximately 0.3 pKa units for the neutral sulfonamide acid, DBSA.This is not surprising, since Emid most closely approximates E1/2 (see Eq. 22) when heterogeneous kinetics are reversible and the charge transfer coefficient (α) is equal to 0.5; neither of these conditions are met in the case of DBSA (see Table 3).Also included in the table are pKa values calculated using Eqs.21 and 24 after estimating E1/2 from the derivative peak potentials of a derivative cyclic voltammogram (example shown in Figure S19).Although processing the data in this way (see Experimental Section) is unnecessary in the present case, it has been included here as a point of comparison because in our companion study on the reduction of oxyacids in [C2mim][NTf2], estimating E1/2 directly from the CV is complicated by the effects of homoassociation. 34In that study, we found that the differential response of the derivative cyclic voltammetry (DCV) technique resolved fine details that are not readily discernable on the normal cyclic voltammogram 45,46 , allowing E1/2 to estimated with greater accuracy.As expected, the pKa values calculated using DCV method are in excellent agreement with those determined directly with CV or with CV plus numerical simulation.
Where available, aqueous pKa values have also been included in Table 4.In all cases the nitrogen acids dissociate less readily in [C2mim][NTf2] than in water.This is not surprising, since [C2mim][NTf2] is a weak hydrogen bond donating/accepting solvent compared to water 47 and the [NTf2] -anion is very weakly basic due to extensive charge delocalization. 47,48 n addition, aprotic ILs are only considered to be 'moderately polar' solvents, with reported static dielectric constants being in the 10 to 20 range 49 , compared to 80.1 for water 50 .Nonetheless, there is a good correlation between the pKa (aq) and pKa (IL) data (see Figure S20) for the monocationic protonated amine acids, with pKa increasing in the order [dClPyr In order to apply this equation in practice, a containing H[NTf2] and pyridine in a 2:1 ratio was prepared and characterized voltammetrically, as is shown in Figure 6.There are two reduction processes observable with cyclic voltammetry (see Figure 6a); the more positive process corresponds to the H + /H2 couple and the more negative process corresponds to the [Pyr-H] + /H2 couple. 1/2 (H + /H 2 ) and  1/2 (BH + /H 2 ) can be readily estimated from the peak potentials labeled in Figure 6a using Eq.22.  BH + and  H + can be readily estimated by performing a potential step past each of the peaks (indicated in Figure 6a); chronoamperograms are shown in Figure 6b.The potential step to -0.323 V vs. Fc/Fc + corresponds to the masstransport controlled reduction of H + to H2 (see Eq. 6), and from this chronoamperogram,  H + was estimated to be 3.0 × 10 -7 cm 2 s -1 .The potential step to -1.023 V vs. Fc/Fc + corresponds to mass-transport controlled proton reduction from both H[NTf2] and [Pyr-H][NTf2];  BH + was estimated to be 3.6 × 10 -7 cm 2 s -1 from the chronoamperogram obtained by subtracting the I-t transient at -0.323 V vs. Fc/Fc + from the one at -1.023 V vs. Fc/Fc + .
Substituting the appropriate values into Eq.25, the pKa of pyridine was calculated to be 13.4,which is in excellent agreement with the previously determined values (see length on the imidazolium cation is expected to have a minimal impact on pKa 9,10 , so the large discrepancy between our value, 13.4, and their value, 10.5, is predominantly attributable to the method in which pKa was calculated from the voltammogram.In their work, the authors assumed ΔE1/2 ≈ ΔE 0' , neglecting the two additional logarithmic terms shown in Eq. 25. Although the first logarithmic term is somewhat negligible because   + ≅  BH + (see Table 3), the second term is significant when working at millimolar concentrations, equaling -0.1 V or +1.7 pKa units when [H + = [BH + ]b = 40 mM.Furthermore, the authors assumed that H [OTf]   behaves as a strong acid (i.e., undergoes 100% ionization) in [C4mim][NTf2]; we have shown in our companion study 34 that this is not likely to be the case.

Conclusions
The thermodynamics, kinetics and mechanisms for the proton reduction (hydrogen evolution) reaction at a platinum electrode have been investigated in ionic liquid media using a range of nitrogen acids (protonated amines or sulfonamides) as the proton source.The formal potential of the H + /H2 process (where H + signifies a 'solvated proton' released from a strong acid) was found to be strongly dependent on the identity of the IL anion, making direct comparison of pKa data between ILs with different constituent anions impossible.Proton reduction from weak nitrogen acids (i.e., HA/H2 or BH + /H2) was found to be a diffusion controlled process which occurs in the potential region negative of the H + /H2 process (proportional to pKa).Numerical simulations, performed by combining the classical Volmer and Tafel reactions, revealed that weak acid dissociation is limiting on the voltammetric timescale when pKa > 4, meaning proton reduction via a CE mechanism cannot account for the experimentally observed mass-transport limited currents.A parallel direct reduction (DR) pathway was considered in addition to the CE pathway and using this mechanism, the proton reduction response from ten weak nitrogen acids covering 14 orders of magnitude in acid strength (5. the pKa values for each of the ten weak nitrogen acids were calculated using a straightforward formula, demonstrating the utility of voltammetry as a convenient method for calculating equilibrium acidities.

Figure 1 .
Figure 1.Comparison of the simulated (○) and experimental (-) concentration-normalized from a typical monoprotonated amine, [Pyr-H][NTf2], are shown in Figure 2a.Proton reduction from [Pyr-H] + gives rise to a one-electron per proton process at potentials approximately 700 mV negative of the H[NTf2]/H2 process (see Figure 1a).ΔEp increases with increasing scan rate, with values of 114, 120, 136 and 156 mV at 50, 100, 250 and 500 mV s - 1 , respectively, indicating that proton reduction from this weak acid is a quasi-reversible process.A diprotonated amine, [oPD-H2][NTf2]2, was also investigated; representative cyclic voltammograms are shown in Figure 2b.Proton reduction from [oPD-H2][NTf2]2 gives rise to two one-electron per proton processes in the potential regions approximately 200 mV and 550

Figure 4 .
Figure 4. Comparison of simulated and experimental (solid line) cyclic voltammograms of weak nitrogen acids in [C2mim][NTf2].The hydrogen evolution reaction is given in Eq. 6

Table 1 .
Names and structures of the protonated amines and sulfonamide acids (known collectively as nitrogen acids) investigated in this work.

Table 2 .
33so highlighted in a previous publication33, the Volmer reaction (Eq.11) is the rate determining step for the HER on Pt in the investigated ILs, where the second step (Eq.12) is simply required to fulfill the stoichiometry requirements of the overall process (see Eq. 6).It is also worth noting that degradation of the voltammetric response caused by slowing heterogeneous electron transfer kinetics with potential cycling33, occurred more rapidly in [C2mim][OTf] than in [C2mim][NTf2] suggesting that that electrode 'deactivation' is intrinsically linked to the IL anion.Parameters extracted from the comparison of experimental cyclic voltammetric data for the electroreduction of 'solvated' H + in [C2mim][NTf2] or [C2mim][OTf] and simulated data, based on the mechanism described by Eqs.11 and 12.

Proton reduction from weak nitrogen acids in [C2mim][NTf2].
Further studies were focused on the proton reduction process from a range of weak nitrogen acids (i.e., BH + /H2 or HA/H2 couple) in [C2mim][NTf2].The name and structure of all of the nitrogen acids investigated were previously shown in Table1.The electrode was activated prior to sweeping by oxidative pretreatment as discussed above.Representative cyclic voltammograms obtained

Table 3 .
Parameters extracted from the comparison of experimental cyclic voltammetric data for the proton reduction process from ten weak nitrogen acids in [C2mim][NTf2] and simulated data, based on the mechanism described by Eqs.11, 12, 16 and 17.
. The simulations were carried out using the CE mechanism only (dashed line, see Eqs. 11, 12 and 16) or the CE + DR mechanism (dotted line, see Eqs. 11, 12, 16 and 17).Simulation parameters are available in Table 2 (CE) or Table 3 (CE + DR).
H + and  H 2 can be estimated experimentally using double step chronoamperometry, as outlined in the Experimental Section.H 2 / H + is approximately equal to 100 (in a range of ILs33) and [H + ]b is typically 0.02 to 0.05 M, meaning both of the logarithmic terms in Eq.21 are significant.
Once again, the derivation of Eq. 23 assumes mass transport to the electrode surface is governed solely by semi-infinite planar diffusion and BH + is the only species initially present in solution.Although  BH + and  H 2 can be estimated using double step chronoamperometry,  B cannot be readily estimated by electrochemical methods.If it is assumed that  B =  BH + ,

Table 4 .
pKa (IL) values calculated in this work and pKa (aq) values obtained from the literature for a range weak nitrogen acids.
34similar observation was made with neutral oxyacids and has been explored in further detail in our companion study.34Finally,by combining Eqs. 20, 21 and 24, the following relationship can be derived: The neutral sulfonamide acid, SACC, is the outlier in the pKa (aq) vs. pKa (IL) trend, having a considerably higher pKa (IL) value than expected relative to the cationic protonated amine acids.

Table 4
7y adding B directly to a HAIL/IL mixture.It should be noted that a similar set of experiments have been previously reported by Doherty and co-workers7, where they calculated the pKa value of [Pyr-H] + to be 10.5 in [C4mim][NTf2].Changing the alkyl chain numerical simulation is not required; (b) only a single solution containing a 2:1 mixture of HAIL and B is required and; (c) preparation of [BH][AIL] is not required, the solution can be prepared simply 2 < pKa < 19.5) was successfully simulated.All of the investigated nitrogen acids dissociated to a much lesser extent in [C2mim][NTf2] compared to water, indicating that the H + solvating ability of the former solvent is considerably weaker than the latter.Finally, after estimating E1/2(HA/H2) -E1/2(H + /H2) or E1/2(BH + /H2) -E1/2(H + /H2) from a transient cyclic voltammogram and  HA / H + or  BH + / H + from a microdisk electrode chronoamperogram,