Determination of acidity constants of pyridines, imidazoles, and oximes by capillary electrophoresis

The acidity constant in the form of pKa is one of the most important physicochemical quantities. There are prediction tools available for calculating the pKa, but they only deliver precise calculated values for a relatively small set of chemicals. For complex structures with multiple functional groups in particular, the error in the predicted pKa is high due to the application domain of the corresponding models. Thus, we aim to enlarge the dataset of experimentally determined pKa values using capillary electrophoresis. We, therefore, selected various pyridines, imidazoles, and oximes to determine the pKa values using the internal standard approach and the classical method. Especially oximes were not investigated in the past, and predictions for them include larger errors. Thus, our experimentally determined values could contribute to an improved understanding of various functional groups impacting the pKa values and serve as additional datasets to develop improved pKa prediction tools.


INTRODUCTION
The acidity constant K a (usually expressed as pK a ) is one of the most relevant physicochemical quantities in pharmacology and environmental sciences, reflecting a chemical's acid-base equilibrium. The pK a value co-determines the state of dissociation of a chemical at a given pH. Thus, it impacts the migration times in capillary electrophoresis (CE) and is therefore essential for the separation technique. Recently, CE is often used to determine pK a values based on the effective electrophoretic mobility μ eff at a defined pH [1,2]. Besides the classical approach, where the whole range of pH values is covered during the measurements of μ eff , the internal standard (IS) method was established, requiring only two measurements at specific pH values in combination with an IS with a known and similar pK a value for univalent acids or bases [3][4][5][6]. The pH values are selected according to the ionic state of the chemical, which should be 100% ionized at the first pH and ∼50% ionized at the second pH.
The determination of pK a values by means of CE has gained strong importance in recent years, and many innovations have been achieved in addition to the expansion of datasets of experimentally determined pK a values. Some work focused on the determination of pK a values at the physiologically relevant temperature of 37 • C [7] and approaches to tackle sparingly soluble chemicals by the application of a methanol-water extrapolation [8]. Šolínová et al. even applied nonaqueous CE using methanol as solvent for the determination of pK a s of azahelicenes [9]. Furthermore, pressure assisted CE was used to determine pK a values [10]. Malý et al. developed the software AnglerFish to determine thermodynamic pK a s and limiting ionic mobilities using measured effective mobilities at a known buffer composition without the need for a constant ionic strength in the experiments [11]. This program was applied to the determination of thermodynamic pK a values of carborane-based inhibitors [12] and ampholytes [13].
Prediction of physicochemical properties is often done by applying quantitative structure-property relationship (QSPR) models. However, only a few models are available to predict the pK a values of chemicals [14,15]. The most commonly used ones are the models of the software tools JChem [16] and ACD [17]. Compared to other physicochemical quantities like the octanol-water partition coefficient or the solubility, the number of freely available tools for the prediction is relatively small. This is because QSPR models generally are designed to predict one end point, whereas a chemical might have several micro pK a values according to its functional groups leading to multiple macro pK a s.
Our aim was to determine experimental pK a values by applying the IS method. In addition, we used the classical approach for chemicals, where determination by the IS method was limited. We selected pyridines, imidazoles, and oximes with no experimental pK a values available for the experimental determination. Only few oximes have been characterized to date; thus, calculation methods often fail to predict valuable pK a s for this compound class. Our experimental determined pK a values should contribute to the development of novel prediction models and extend the application domain of future calculation tools.

THEORY
There are two methods employed in the measurement of pK a values in this work. The mainly used IS method is supplemented by measurements via the classical CE-method whenever the examined pH range requires it.

Classical CE-method
Using the classical CE-method for obtaining the pK a values, analytes are measured at a wide spectrum of pH values in the presence of an electroneutral chemical, a marker of electroosmotic flow (EOF), to determine the EOF mobility. The effective mobility μ eff can be calculated directly from the migration times of the analyte and the EOF marker via the following equation: where L T and L D are the total and the effective capillary length, respectively, V the separation voltage, t m the migration time of the analyte, and t 0 the migration time of the EOF marker. Plotting the effective mobilities obtained against their respective pH values renders a curve displaying the pK a value at its point of inflection.

IS method
The effective mobility is a function of the pH, which includes the acidity constant and actual ionic mobility of the protonated or deprotonated species as parameters. These are determined by nonlinear regression analysis of the dependence of effective mobility on pH of the background electrolyte. At the point of partial protonation of the analyte, μ eff of a monoprotic neutral acid (HA) can be expressed via the pH of the electrolyte in the capillary, the mixed acidity constant p ′ a , and the mobility of the deprotonated species A − [6,18]: The relationship between the mixed acidity constant p ′ a and pK a is determined by the following equation [19,20]: For monoprotic neutral bases (B), μ eff is expressed as follows: In the case of polyprotic bases containing two pK a values, the effective mobility would be [20] ef f = BH 2 2+ 10 p ′ a1 −pH + BH + 10 p ′ a1 −pH + 10 pH−p ′ a2 + 1 The activity coefficient γ in Equations (3) and (5) depends on the ionic strength of the solution I and is generally estimated using the Debye-Hückel equation: where A and B depend on the relative permittivity and temperature of the solution (A = 0.509 and B = 0.33, in water at 25 • C), whereas z specifies the charge number of the ion and a its hydrated diameter. For analytes and ISs with similar properties at similar conditions, the activity coefficient can be assumed as identical.
To calculate the p ′ a , the following equations can be rearranged to yield: and The quotient Q denotes the relationship between the limiting mobility of the fully deprotonated (or protonated) species and the effective mobility of any given analyte. The effective mobilities of IS and test chemical can be directly calculated from the total and the effective capillary lengths, the separation voltage, the migration time of the analyte, and the migration time of the EOF marker according to Equation (1).
As Equations (8) and (9) are equally used for the analyte as well as the ISs, they can be subtracted and yield the following equation for acids: As seen in Equation (5), p ′ a and pK a only differ by the activity constant, here identical for analyte and IS. Thus, the activity constants can be seen to cancel each other out after subtraction: By rearranging the equation, the pK a can be directly obtained from p a, AN = p a, IS + log AN − log IS (12) Similarly, the acidity constants of monoprotic bases are calculated via the following equation: p a, AN = p a, IS − log AN + log IS (13)

CE measurements
Experiments were performed using the Agilent G7100A CE system equipped with a diode-array spectrophotometric detector. The fused-silica capillaries used are available from Agilent, with an inner diameter of 50 µm, an outer diameter of 375 µm, a total length of 48.5 cm and an effective length of 40 cm (IS method), or a total length of 33 cm and an effective length of 24.5 cm (classical method). The capillary temperature was kept at 25.0 • C. Before use, the capillaries were conditioned with a 0.1 M solution of NaOH for 5 min, flushed with water for 10 min and running buffer for 20 min. The analytes were, respectively, injected hydrodynamically at 50 mbar for 5 s, followed by an injection of running buffer at 50 mbar for 5 s. The separation voltage was 20 kV with measurements between 10 and 120 min. Between two measurements, the capillary was flushed with running buffer for 50 s with 50 mbar. When changing buffers, the capillary was flushed with water for 10 min (1 bar) and the new buffer for 20 min (1 bar). Additionally, we checked for hysteresis effects before the first measurements at each selected pH. At the end of a working session, the capillary was flushed with water for 10 min and subsequently with air for 10 min. We measured three replicates for each pH applied. Detection was performed using a DAD at 214, 230, and 254 nm.

Chemicals and solvents
The chemicals used can be found in Table S1. Several running buffers in a pH range between 1.8 and 12.0 were prepared at an ionic strength of 0.05 M. Table S2 shows the respective buffers and the corresponding pH values. For obtaining the desired pH values, 50 mL of stock solutions were prepared at 0.1 M and then mixed with the respective appropriate amount of 0.5 M HCl or NaOH. The solutions were then diluted up to 100 mL and filtered through a 0.2 µm pore size nylon filter (Labsolute). TA B L E 1 Validation chemicals with CAS number, the experimental pK a values, and standard deviations (SD) determined via the internal standard (IS) or classical (C) method as well as the pK a values found in the literature with the corresponding references. Atenolol 29122-68-7 9.71 0.08 9.60 0.04 9.68; 9.6; 9.54 [27]; 9.6 [28] a Declared as insecure value in Ref. [22].
The ISs as well as analytes were prepared as solutions of 0.1 mg/mL in a mixture of methanol/water (v/v: 1/1). As an EOF marker, 0.4% (v/v) of DMSO, benzyl alcohol, and acetone were added, respectively. The solutions were filtered using a 0.45 µm pore size nylon filter (Labsolute).

Data processing and prediction of pK a values
To correct the total and effective length for the plug length of the BGE, we used the tool zeecalc [21]. The pK a values of the corresponding acids and bases were calculated using SMILES representations of the chemicals with JChem for Excel v. 20.6.0.618 [16] and the classic model of ACD/Percepta [17]. Data obtained from applying the classical method for pK a determination were plotted in OriginPro 2023 version 10.0.0.154 and fitted to Equation (4) for monoprotic bases and to Equation (6) for diprotic bases.

Method validation
In order to validate and compare the two methods used in this work, six chemicals with known pK a values ranging from 2.5 to 9.6 were selected for pK a determination.  [6]. For the IS method, between two and five ISs were used for every test compound. The IS chemicals were selected to have pK a values of the same character (acidic or basic) as the tested chemicals and to deviate from the predicted pK a s by no more than ±1. In cases of substantial differences between predictions and measurements, new IS substances were selected.

Determination of pK a values for pyridines, imidazoles, and oximes
Three classes of compounds with a wide array of substitution patterns and thus a wide range of hitherto unknown pK a values were selected as test substances: pyridines ( Table 2 and Table S3-1), imidazoles (Table 3 and Table  S3-2), and oximes (Table 4 and Table S3-3).
For the compounds 4-(4-nitrobenzyl)pyridine, 4vinylpyridine, 2-methylpyridine, 2-N-hexylpyridine, imidazo(1,2-a)pyridine, 3-(methylaminomethyl)pyridine, and 4-methylaminopyridine, the IS method was employed. Here, two to five IS at pK a values close to those of the test analytes (±1) have been selected, respectively, and measured together as a mixture at a pH closest to those pK a values in order to obtain μ eff . In a second step, the mobilities of the fully protonated species were measured at a pH 2 units below those values. The influence of derivatization can be most clearly observed in the wide range of pK a values determined for the pyridines (Figure S5-1). Pyridine itself has pK a of 5.28 [3], whereas a value of 9.43 can be TA B L E 2 Pyridines with CAS number, the experimental pK a values, standard deviation (SD), method (M), and the predicted pK a values. Abbreviation: IS, internal standard. a Second and third pK a value predicted to be 13.28 and 16.88 (ACD) and 12.32 and 15.32 (JChem) but could not be experimentally determined. b Second pK a value predicted to be 13.00 (ACD) and 12.67 (JChem) but could not be experimentally determined. c Second pK a value predicted to be 11.41 (ACD) and 11.51 (JChem) but could not be experimentally determined. d Second pK a value predicted to be 13.82 (ACD) and 15.45 (JChem) but could not be experimentally determined. measured for 4-methylaminopyridine due to a strong positive mesomeric effect (+M). Similarly, the substituents in 4-(4-nitrobenzyl)pyridine, 4vinylpyridine, 2-methylpyridine, and 2-N-hexylpyridine raise the respective pK a values due to the positive inductive effect (+I), whereas the negative inductive effect (−I) of the silyl, halogen, and carbonyl groups in 3-(trimethylsilylethynyl)pyridine, 2,6bis(bromomethyl)pyridine, 4-(trifluoromethyl)pyridine, 4-(difluoromethyl)pyridine 3-acetylpyridine, 4acetylpyridine, and methyl-3-pyridinecarboxylate lowers their pK a values considerably.
The same procedure has been applied to the imidazoles (Table 3, Figure S5-2), where pK a values for all nine analytes could be determined via the IS method. In each case, we were able to determine the basic pK a , but the corresponding acidic pK a of the imidazole structure was out of the range available for experimental determination. Again, TA B L E 4 Oximes with CAS number, the experimental pK a values, standard deviation (SD), method (M), and the predicted pK a values. Abbreviation: IS, internal standard. a Second pK a value predicted to be 12.82 (ACD) and 15.97 (JChem) but could not be experimentally determined. JChem includes a third pK a prediction of 1.11, which could not be experimentally determined. b Second pK a value predicted to be 2.85 (JChem) but could not be experimentally determined. c Second pK a value predicted to be 13.52 (ACD) and 9.01 (JChem) but could not be experimentally determined. d Second and third pK a value predicted to be −1.65 and 1.32 (ACD) and 0.77 and 2.43 (JChem) but could not be experimentally determined. e Second and third pK a value predicted to be 2.95 and 13.43 (ACD) and 2.43 and 9.16 (JChem) but could not be experimentally determined. f Second pK a value predicted to be 13.69 (ACD) and 9.36 (JChem) but could not be experimentally determined.
a trend can be observed in the pK a values. The −I effect of the OH group of 1-(4-hydroxyphenyl)imidazole leads to a lower pK a compared to 1-(4-methoxyphenyl)imidazole (still with a −I effect). However, for the N substituents of the chemicals 1H-imidazole-1-propanamine, 1-(tertbutyldimethylsilyl)imidazole, 1-(trimethylsilyl)imidazole, and imidazole-1-ethanol, only a small impact is observed in the corresponding pK a values. We were able to determine two distinct pK a values for the compounds 1-(4-hydroxyphenyl)imidazole and 1H-imidazole-1propanamine, respectively. 1-(4-Hydroxyphenyl)imidazole displays an additional acidic pK a of 9.13 for its OH group, whereas the NH 2 group in the side chain of 1H-imidazole-1-propanamine has a basic pK a of 9.25.
The oximes ( Figure S5-3) are a group of compounds generally displaying two pK a values, an acidic and a basic one. Due to the constraints posed by the available buffers and thus the measurable range (Section S6), only one of those pK a values could be obtained for each of the eight compounds listed in Table 4. For the analytes benzaldehyde oxime, dimethylglyoxime, 2,3-butanedione-2-oxime, benzhydroxamic acid, and di-2-pyridyl ketone oxime, we were able to determine the acidic pK a values ranging from 7.79 to 10.57 via the IS method, whereas the basic pK a values were out of range. For the amidoximes 4-methylbenzamidoxime, benzamidoxime, and 3-aminobenzamidoxime, only the respective basic pK a values were available for determination, as the additional amide group has a stabilizing effect on the cation and thus facilitates protonation and increases pK a values. The IS method was applied here as well. For the chemicals 3-aminobenzamidoxime, benzamideoxime, and 4-methylbenzamideoxime, it can be seen that the +I effect of the methyl group in para position leads to an increased F I G U R E 1 Experimentally determined pK a values were plotted against the predicted pK a values of ACD and JChem. The 1:1 line and the corresponding deviations of 1 log unit are marked in the plot. pK a value, whereas the −I effect of the NH 2 group in meta position reduces the pK a . As both groups would induce a partial charge delta minus (δ−) at the aliphatic carbon, the negative mesomeric effect (−M) could explain the lower pK a value for 3-aminobenzamidoxime.
As can be seen in Figure 1, greater differences between experimentally determined pK a values and the predicted ones are observed for the pyridines with low pK a values. Here, both prediction tools do not perform well. Although JChem often overestimates the corresponding pK a value, no clear trend can be seen for ACD predictions. In the higher pK a range, the prediction errors are increased as well. In particular, the oximes with higher pK a values are underestimated by JChem.

CONCLUDING REMARKS
The determination of pK a values by CE is a fast alternative compared to the classical approaches. We applied two different methods, whereas the IS method is much faster compared to the classical approach and should be used for acids within the pK a range of 3-10.5 and bases in the range of 4.0-12 ( Figure S6). Outside these corresponding ranges, the classical method should be applied. In the case of diprotic acids and bases, the corresponding pK a values should differ at least in ∼3 log units for the determination via IS method. Nowadays, there is still a demand for experimentally determined pK a s. Although there are prediction methods available, the accuracy of the respective approaches needs to be improved. Especially for chemicals like oximes, there is a data gap in experimental values. Thus, prediction methods often fail when applied for such structures. However, the approach is still limited for poorly soluble chemicals [29], chemicals with extremely low or high pK a values, and chemicals with multiple pK a values within a narrow range. Some attempts have been made already to overcome these problems [29] especially using cosolvents [8], or extending the pH range for pK a measurements using variable ionic strengths of the buffers applied [30], but there is a demand for further strategies to determine such pK a values more accurately in the future.

C O N F L I C T O F I N T E R E S T S TAT E M E N T
The authors have declared no conflict of interest.

D ATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available in the Supporting Information of this article.