Retention of ionizable compounds in high-performance liquid chromatography

Journal of Chromatography A, 964 (2002) 55–66 www.elsevier.com / locate / chroma Retention of ionizable compounds in high-performance liquid chromatography 14. Acid–base pK values in acetonitrile–water mobile phases ´ * Sonia Espinosa, Elisabeth Bosch, Martı´ Roses ´ ´ , Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain Departament de Quımica Analıtica Received 22 March 2002; received in revised form 2 May 2002; accepted 3 May 2002 Abstract Linear relationships between ss pKa values in acetonitrile–water mixtures and ww pKa values in pure water have been established for five families of compounds: aliphatic carboxylic acids, aromatic carboxylic acids, phenols, amines, and pyridines. The parameters (slope and intercept) of the linear correlations have been related with acetonitrile–water composition. The proposed equations allow accurate estimation of the pKa values of any member of the studied families at any acetonitrile–water composition up to 60% of acetonitrile in volume (100% for pyridines). Conversely, the same equations can be used to estimate aqueous pKa values from chromatographic pKa values obtained from any acetonitrile– water mobile phase between the composition range studied. Estimation of pKa values have been tested with chromatographic literature data.  2002 Elsevier Science B.V. All rights reserved. Keywords: Mobile phase composition; Retention behaviour; Acidity; pKa ; Dissociation constants; Carboxylic acids; Amines; Phenols; Pyridines 1. Introduction In previous works, the importance of proper pH measurement in liquid chromatography mobile phases has been highlighted [1–8]. Measurement of the pH in the mobile phase after mixing aqueous buffer and organic modifier has been recommended [3–8]. This procedure provides fits of analyte retention to mobile phase pH much better than those obtained when the pH is measured in the aqueous buffer before mixing it with the organic modifier. In *Corresponding author. Tel.: 134-93-402-1796; fax: 134-93402-1233. ´ E-mail address: marti@apolo.qui.ub.es (M. Roses). addition, the pKa value obtained from the fits to pH values measured after mixing is the thermodynamic pKa value of the analyte in the mixed solvent used as mobile phase. This is a significant advantage over pKa parameters obtained from pH measurements before mixing, which are only fitting parameters without any physical meaning [9]. With proper measurement of mobile phase pH, known thermodynamic pKa values can be used to predict ionization of the analytes in the mobile phase and thus, retention in the chromatographic system. These pKa values refer always to the solvent system used as mobile phase, not to the pKa values in water. This is an important restriction to practical applicability of the method because the number of 0021-9673 / 02 / $ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S0021-9673( 02 )00558-7 56 S. Espinosa et al. / J. Chromatogr. A 964 (2002) 55–66 known pKa values in water–organic mobile phases is very limited. However, in previous studies [10,11] we established linear relationships between pKa values in methanol–water mixtures and pKa values in water for several families of compounds. These relationships provide a good estimation of the pKa value of the compound in any methanol–water mixture from the pKa value of the compound in water, which can be used to predict the ionization of the compound in a chromatographic system that uses pH buffered methanol–water mobile phases. In this paper, we extend these relationships to acetonitrile–water mobile phases. Methanol–water and acetonitrile–water solvent mixtures are by far the most used mobile phases in liquid chromatography. The relationships between pKa values established for these two solvent systems can be extremely useful for prediction of retention and optimization of chromatographic separations of acid–base compounds. Additionally, they can be used for determination of the aqueous pKa value from the fitting pKa value obtained by measurement of retention at several mobile phase pH values. This method has been recently used to estimate the aqueous pKa values of water insoluble arilpropionic acids with antiinflammatory properties from the chromatographic pKa values in methanol–water mobile phases [12]. 2. Theory The approach followed is based in the linear relationship proposed by Chantooni and Kolthoff [13] to measure the ‘‘resolution of acid strength’’ of a family of compounds in a solvent (s) in reference to water (w). In this approach, the pKa values of a series of related compounds (commonly compounds that share the same charge and functional acidic group) in the solvent s ( ss pKa ) are plotted against the pKa values of the same compounds in water ( ww pKa ). A straight line (Eq. (1)) is usually obtained with a slope value (a s ) that measures the ‘‘resolution of acid strength’’ for the compounds in solvent s as regards to water (slope unity), i.e. the ability of the solvent to differentiate between the acidities of the compound’s set s s pKa 5 a s ww pKa 1 b s (1) The intercept of the correlation (b s ) is related to the differences in basicities, dielectric constants, and specific solvation interactions of the solute (e.g. hydrogen bonding) between solvent s and water. The first two differences depend only on the solvents considered (s and w), but the specific solvation differences depend also on the family of compounds studied. The slope of the correlation (a s ) is related to differences between specific solvation interactions, which depend on the solvent and family of compounds studied. The larger the specific solvation of the compound in solvent s, in reference to water, the larger the slope value. Detailed explanations about theoretical derivation of Eq. (1) have been given in previous studies [10,11,14]. We shall use here the same notation recommended by the IUPAC [15] for pK and pH definition we have used in previous works. A lower-case left-hand superscript in pH or pK term indicates the solvent (w or s) in which measurements are being made; a lower-case left-hand subscript indicates the solvent in which the ionic activity coefficient g is referred to unity at infinite dilution (w or s). Notice that the possibility of choosing two different standard state solvents for the ionic activity coefficients leads to two different scales for pH measurement in nonaqueous or mixed solvents [16]. The ss pH scale refers to pH measured in solvent s with pH standardization in the same solvent s, and the sw pH scale refers to pH measurement in solvent s with pH standardization with aqueous reference buffers. ww pH scale refers to pH measurement in water. Linear relationships for resolution of acid strength have been well established for the pK values of families of compounds in different solvents in reference to the pK values in water [10,11,14,17–23]. In two previous studies, we applied them to the available ss pKa data in methanol–water mobile phases [10,11]. The ss pKa values of 121 acid–base compounds belonging to six different chemical families in several methanol–water compositions were fitted to Eq. (1) and the a s and b s parameters of the equation were obtained for each compound family and solvent composition. The a s and b s sets of values obtained for each family were related to solvent composition through polynomials. For mobile phase compositions measured in volume fraction of methanol (vMeOH ), the equations take the forms: S. Espinosa et al. / J. Chromatogr. A 964 (2002) 55–66 2 1 1 a 1 vMeOH 1 a 2 v MeOH a s 5 ]]]]]]] 2 1 1 a 3 vMeOH 1 a 4 v MeOH (2) 2 b 1 vMeOH 1 b 2 v MeOH b s 5 ]]]]]]] 2 1 1 b 3 vMeOH 1 b 4 v MeOH (3) where a 1 , a 2 , a 3 , a 4 , b 1 , b 2 , b 3 , and b 4 were fitting parameters constant for all acids of the same family at all methanol–water mixtures. This approach shall be applied here to the available data for acetonitrile–water mixtures in order to establish equations for the different families of compounds, which should allow an accurate estimation of the compound pKa value at a given acetonitrile–water mobile phase from the pKa value of the compound in water. 3. Results and discussion 3.1. pKa values in pure acetonitrile The resolution of acid strength for the families of compounds studied was first investigated in pure acetonitrile. The available literature ss pKa values in pure acetonitrile [24–26] were collected (Table 1) and plotted against its ww pKa values in water [27,28]. Fig. 1 depicts the plots obtained. It is evident that the compounds can be divided in five families that follow five different straight lines, with only four outliers of the 101 pairs of pKa data points plotted. These five families are aromatic carboxylic acids, aliphatic carboxylic acids, phenols, pyridines, and amines. The parameters of the straight lines obtained are given in Table 2. All families present a resolution of acid strength in acetonitrile larger than in water (a s .1). This behaviour is usual in solvents with a poor hydrogen bond donor acidity, such as acetonitrile. In a good hydrogen bond donor solvent, e.g. water, the negative charge of the anion (carboxylic acids and phenol families) or the lone electron pair of the neutral base (amines and pyridines) are stabilized in the oxygen or nitrogen atom of the acid–base group by hydrogen bonding. However, in a poor hydrogen bond donor solvent, the negative charge or lone electron pair can be easily delocalized along the structure of the 57 molecule. In this instance the effect of the substituents in the molecule is more important and produces a larger variation of the acid–base strength (pKa values) [10,11,13,14]. The families with a larger resolution of acid strength are aliphatic carboxylic acids and phenols, whereas aromatic carboxylic acids and the protonated bases, amines and pyridines present a lower resolution of acid strength. In contrast with pure methanol [14] and other alcohols [17,19], ortho effect (variation of the resolution of acid strength caused by substituents in ortho position) was not observed in acetonitrile. 3.2. Acetonitrile–water mobile phases The same compound families investigated in pure acetonitrile were studied in acetonitrile–water mixtures. The available ss pKa data in acetonitrile–water mixtures were compiled for round percentages of acetonitrile in volume and they are given in Table 3. Most data were taken from a previous compilation [29]. The equations given in that study for each compound were used to calculate the ss pKa value of each compound at each round percentage of acetonitrile. The early compilation for neutral acids was complemented with the ss pKa data of some amines [31] and substituted pyridines [32]. The ss pKa data for these substituted pyridines were determined in the molality scale at a constant ionic strength of 0.01 mol kg 21 . These ss pKa data were converted to thermodynamic ss pKa values (zero ionic strength) in the molarity scale used through all this work by ¨ using the densities and Debye–Huckel parameters for acetonitrile–water mixtures given elsewhere [4]. Finally, the linear equations proposed in a previous study [6] and the cubic equations given by Sarmini and Kendler [30] to relate the sw pKa values of some compounds to acetonitrile composition were used to calculate the sw pKa of these compounds at the round acetonitrile percentages. ss pKa values of the compounds were calculated from the sw pKa values and the d parameter of the corresponding acetonitrile–water mixture (determined in a previous work [4]) by means of the following relationship: s s pKa 5 sw pKa 2 d (4) The a s and b s parameters of the correlations S. Espinosa et al. / J. Chromatogr. A 964 (2002) 55–66 58 Table 1 Acid–base pKa values of compounds in pure water and pure acetonitrile Acid H2O pKa a MeCN pKa Ref. w w s s Aliphatic carboxylic acids Trifluoroacetic acid Trichloroacetic acid Oxalic acid (pK1 ) Dichloroacetic acid Dichloroacetic acid Cyanoacetic acid Malonic acid (pK1 ) Chloroacetic acid Fumaric acid (pK1 ) Tartaric acid (pK1 ) Glycolic acid (pK1 ) Succinic acid (pK1 ) Glutaric acid (pK1 ) Adipic acid (pK1 ) Nonanedioic acid (pK1 ) Acetic acid Butyric acid 0.23 0.63 1.27 1.33 1.33 2.46 2.85 2.87 3.02 3.04 3.83 4.16 4.34 4.43 4.53 4.76 4.82 12.7 10.6 14.5 13.2 15.8 b 18.0 15.3 18.8 18.6 14.9 19.3 17.6 19.2 20.3 20.9 22.3 22.7 [24] [24] [24] [24] [25] [24] [24] [25] [24] [24] [24] [24] [24] [24] [24] [25] [24] Aromatic carboxylic acids 2,6-Dinitrobenzoic acid 2,6-Dihydroxybenzoic acid 2,4-Dinitrobenzoic acid 2-Nitrobenzoic acid 2,4-Dichlorobenzoic acid 3,5-Dinitrobenzoic acid 3,5-Dinitrobenzoic acid 2-Chlorobenzoic acid o-Phthalic acid (pK1 ) 2-Hydroxybenzoic acid 4-Nitrobenzoic acid 2,4,6-Trimethylbenzoic acid 3-Nitrobenzoic acid 3,4-Dichlorobenzoic acid m-Phthalic acid (pK1 ) 3-Bromobenzoic acid 3-Bromobenzoic acid 4-Bromobenzoic acid Benzoic acid Benzoic acid 3,4-Dimethylbenzoic acid 4-Hydroxybenzoic acid 1.14 1.22 1.42 2.22 2.72 2.82 2.82 2.94 2.95 2.98 3.43 3.44 3.49 3.60 3.62 3.82 3.82 3.97 4.21 4.21 4.41 4.58 15.8 12.6 b 16.1 18.2 18.4 17.2 16.9 19.0 14.3 b 16.9 b 18.7 20.5 19.2 19.0 19.3 19.5 20.3 20.3 20.1 20.7 21.2 20.8 [24] [24] [24] [24] [24] [24] [25] [24] [24] [24] [25] [24] [24] [25] [24] [24] [25] [24] [24] [25] [25] [24] Phenols 2,4,6-Trinitrophenol 4-Chloro-2,6-dinitrophenol 2,6-Dinitrophenol 2,4-Dinitrophenol 3,4-Dinitrophenol 4-Nitrophenol 0.65 2.97 3.71 4.02 5.42 7.16 11.0 15.0 16.0 16.0 17.9 20.7 [25] [24] [24] [24] [24] [24] Acid Amines 2-Nitroaniline 3-Nitroaniline Aniline p-Toluidine Benzylamine Trimethylamine 1,5-Pentanediamine (pK1 ) 1,3-Propanediamine (pK1 ) Isobutylamine Butylamine Methylamine Propylamine Ethylamine Dimethylamine Triethylamine Triethylamine 1,4-Butanediamine (pK1 ) Tributylamine Diethylamine Dibutylamine Pyridines 2-Chloropyridine 2-Bromopyridine 2-Hydroxypyridine 3-Cyanopyridine 4-Cyanopyridine 2-Acetylopyridine 3-Bromopyridine 3-Chloropyridine 3-Acetylopyridine 3-Hydroxypyridine Pyridine Pyridine 3-Methylpyridine 4-Ethylpyridine 2-Methylpyridine 4-Methylpyridine 3-Aminopyridine 3,5-Dimethylpyridine 3,4-Dimethylpyridine 2,3-Dimethylpyridine 2-Aminopyridine 2,6-Dimethylpyridine 2,4-Dimethylpyridine 4-Aminopyridine H2O pKa a MeCN pKa Ref. w w s s 2.17 3.49 4.61 5.08 9.33 9.81 10.25 10.30 10.43 10.61 10.62 10.69 10.70 10.73 10.78 10.78 10.80 10.90 10.98 11.30 4.9 7.6 10.6 11.3 16.8 17.6 19.1 19.7 17.9 18.3 18.4 18.2 18.4 18.7 18.7 18.5 20.1 18.1 18.8 18.3 [24] [24] [25] [24] [24] [24] [24] [24] [24] [25] [24] [24] [25] [24] [24] [25] [24] [25] [25] [25] 0.49 0.71 1.25 1.38 1.90 2.76 2.84 2.84 3.55 4.75 5.17 5.17 5.58 5.87 5.91 5.93 6.03 6.15 6.47 6.57 6.66 6.68 6.70 9.06 6.8 7.0 8.3 8.0 8.5 9.6 9.5 10.0 10.8 12.6 12.6 12.3 13.7 13.6 13.9 14.5 14.4 13.9 14.7 14.8 14.7 14.4 15.0 18.4 [26] [26] [26] [26] [26] [26] [26] [26] [26] [26] [26] [25] [26] [25] [26] [26] [26] [26] [26] [26] [26] [26] [26] [26] S. Espinosa et al. / J. Chromatogr. A 964 (2002) 55–66 59 Table 1. Continued Acid 2-Nitrophenol 4-Cyanophenol 3-Nitrophenol 2-Bromophenol 3,4-Dichlorophenol 3-Chlorophenol 4-Bromophenol 4-Chlorophenol Phenol 3-Methylphenol 4-Methylphenol 2-Methylphenol a b H2O w a w pK a MeCN pKa Ref. s s 7.24 7.95 8.39 8.42 8.63 9.08 9.37 9.42 9.98 10.00 10.25 10.28 22.0 22.7 23.8 23.9 24.0 25.0 25.5 25.4 26.6 26.5 27.5 27.5 [24] [24] [24] [24] [24] [24] [24] [24] [24] [24] [24] [24] Acid H2O pKa a w w MeCN pKa Ref. s s From Refs. [27,28]. Excluded from the correlations. between ss pKa values in acetonitrile–water and ww pKa values in water (Eq. (1)) are given in Table 2 for the families and solvent compositions studied. The variation of these parameters for the families studied with the composition of acetonitrile–water mixtures, compared with the variation of the same parameters in methanol–water mixtures, is depicted in Figs. 2 and 3. As compared with methanol–water, acetonitrile–water mixtures exhibit larger a s values (except for aromatic carboxylic acids), that demonstrate a larger resolution of acid strength. This is already Fig. 1. Plot of the ss pKa values in pure acetonitrile vs. the ww pKa values in pure water. Symbols: (앳) aliphatic carboxylic acids, (n) aromatic carboxylic acids, (s) phenols, (h) amines, (3) pyridines. expected because the resolution of acid strength in pure acetonitrile is much larger than in pure methanol. The a s and b s values have been fitted to solvent composition in terms of the volume fraction of acetonitrile according to Eqs. (2) and (3). The parameters obtained for the fits are given in Tables 4 and 5. The parameters of Tables 4 and 5 allow calculation of the slope and intercept of the correlation between ss pKa values in acetonitrile–water mixtures and ww pKa values in water for the families of compounds studied. The ss pKa value of any member of these families, including compounds not studied in the original set, in any acetonitrile–water composition can be precisely estimated from the pKa value of the compound in water. Conversely, the pKa value of the compound in water can be calculated from the s s pKa value of the compound at any acetonitrile– water composition. The studied ss pKa data cover the range 0–60% of acetonitrile in volume (plus pure acetonitrile), except for the pyridines studied by Pawlak [32] which comprise all the acetonitrile– water composition range. Thus, accurate estimation of pKa values is restricted to these acetonitrile–water composition ranges. 3.3. Estimation of pKa values and degrees of protonation of pyridines in acetonitrile–water mixtures Estimation of pKa values and degrees of ionization S. Espinosa et al. / J. Chromatogr. A 964 (2002) 55–66 60 Table 2 Parameters of linear Eq. (1) for each family of compounds studied and acetonitrile–water composition Acetonitrile (v / v) 0% 10% 20% 30% 40% 50% 60% 100% Aliphatic carboxylic acids as 1.000 bs 0.000 SD – r – 1.076 20.089 0.18 0.987 1.095 0.091 0.21 0.984 1.118 0.289 0.24 0.979 1.146 0.507 0.29 0.972 1.183 0.744 0.33 0.965 1.235 0.997 0.39 0.956 2.135 10.784 1.62 0.893 Aromatic carboxylic acids as 1.000 bs 0.000 SD – r – 0.953 0.374 0.13 0.981 0.933 0.717 0.19 0.960 0.930 1.008 0.24 0.939 0.998 1.130 0.28 0.931 1.046 1.313 0.30 0.926 1.193 1.273 0.33 0.929 1.511 14.095 0.60 0.933 Phenols as bs SD r 1.000 0.000 – – – – 1.163 20.804 0.15 0.998 1.186 20.672 0.13 0.998 1.215 20.508 0.17 0.998 1.213 20.120 0.16 0.998 1.216 0.378 0.21 0.996 1.706 9.455 0.42 0.996 1.000 0.000 1.011 20.144 0.14 0.999 1.029 20.418 0.12 0.999 1.044 20.661 0.16 0.999 1.050 20.760 0.19 0.998 1.073 21.011 0.23 0.997 1.080 21.007 0.28 0.996 1.479 2.842 0.81 0.983 42.20% 1.008 20.570 0.15 0.997 66.07% 1.000 20.848 0.14 0.997 81.41% 0.999 20.779 0.10 0.998 92.11% 0.970 20.166 0.16 0.996 94.30% 1.042 20.071 0.14 0.997 – – Amines as bs SD r – – Pyridines as bs SD r 0% 1.000 0.000 – – in acetonitrile–water mixtures with the method proposed is illustrated with the set of 16 pyridines studied by McCalley [33,34] by liquid chromatography. The pyridines were studied in isoelutropic mixtures of methanol (55%), acetonitrile (40%) and tetrahydrofuran (25%) in combination with a phosphate buffer at aqueous pH 7.0. Table 6 presents the aqueous pKa values of the pyridines as reported by McCalley [33,34]. We have also calculated the degree of ionization of these pyridines (aHB ) at the aqueous pH 7.0 of the phosphate buffer through the equation: HB 1 1 a 5 ]]] 1 5 ]]]] B 1 HB 1 1 10 pH2pK a (5) According to the aqueous pKa and pH of the buffer, pyridines should be partially protonated, especially the most basic dimethylpyridines. However, McCalley found that pyridines behaved chro- 100% 1.314 6.136 0.29 0.996 matographically as completely unprotonated in 55% methanol, 40% acetonitrile and 25% tetrahydrofuran mobile phases [34]. Based on potentiometric and spectrophotometric measurements he deduced that the pKa value of pyridines decreased and the pH value of the buffer increased with the addition of the organic modifier to the aqueous buffer, resulting in a much lower degree of protonation of the pyridines. From Eqs. (1)–(3) and the parameters of Tables 4 and 5 and the similar parameters given in the literature [11] for methanol–water one can calculate the ss pKa values of the pyridines in 40% acetonitrile and 55% methanol mobile phases. The equations give a s 50.959 and b s 5 21.013 for 55% methanol and a s 50.996 and b s 5 20.583 for 40% acetonitrile, which led to the ss pKa values given in Table 6. pKa values in 40% acetonitrile and 55% methanol are about 0.6 and 1.3 pK units lower than in water, respectively. The variation of the pH of the aqueous buffer by addition of methanol or acetonitrile can be S. Espinosa et al. / J. Chromatogr. A 964 (2002) 55–66 61 Table 3 s s pK a values of the compounds studied in acetonitrile–water mixtures Acetonitrile (v / v) 0% 10% 20% 30% 40% 50% 60% Ref. Aliphatic carboxylic acids 2,3-Dibromopropionic acid Chloroacetic acid 2,3-Dichloropropionic acid 2-Chloropropionic acid Tartaric acid (pK1 ) Citric acid (pK1 ) 3-Bromopropionic acid Cinnamic acid Acetic acid Valeric acid Isobutyric acid Propionic acid 2.17 2.87 2.89 2.90 3.03 3.13 4.02 4.44 4.76 4.80 4.85 4.88 2.46 3.01 2.52 3.14 3.21 3.31 4.26 4.74 4.95 5.13 5.23 5.11 2.76 3.22 2.77 3.40 3.38 3.49 4.52 4.94 5.17 5.46 5.62 5.35 3.10 3.44 3.06 3.69 3.59 3.68 4.82 5.19 5.42 5.82 6.03 5.63 3.48 3.67 3.40 4.03 3.83 3.90 5.16 5.52 5.73 6.20 6.48 5.96 3.90 3.89 3.79 4.43 4.11 4.16 5.57 5.97 6.10 6.63 6.96 6.36 4.39 4.13 4.25 4.90 4.46 4.45 6.04 6.59 6.57 7.09 7.48 6.85 [29] [29] [29] [29] [29] [29] [29] [29] [29] [29] [29] [29] Aromatic carboxylic acids 2-Nitrobenzoic acid o-Phthalic acid (pK1 ) 4-Nitrobenzoic acid 3-Nitrobenzoic acid 1-Naphthoic acid 3-Chlorobenzoic acid 3-Hydroxybenzoic acid 3-Methylbenzoic acid Benzoic acid 2.19 2.89 3.45 3.49 3.69 3.79 4.00 4.21 4.21 2.58 3.08 3.50 3.54 4.07 3.88 4.23 4.41 4.49 2.95 3.26 3.82 3.75 4.44 4.06 4.50 4.68 4.77 3.29 3.45 4.10 4.01 4.79 4.29 4.79 4.98 5.05 3.60 3.68 4.45 4.39 5.24 4.64 5.19 5.39 5.44 3.89 3.93 4.85 4.77 5.67 4.99 5.57 5.78 5.75 4.16 4.23 5.39 5.31 6.26 5.49 6.10 6.34 6.25 [29] [29] [29] [29] [6] [30] [30] [30] [6] Phenols Resorcinol Phenol 2,4-Dichlorophenol 2,4-Dinitrophenol b-Naphthol 2-Nitrophenol 3-Bromophenol 4-Chlorophenol 3-Methylphenol 3-Aminophenol (phenol) 9.81 9.98 7.85 4.07 9.57 7.24 8.87 9.42 10.00 9.99 – – – – – – – – – – 10.51 10.80 8.18 4.07 10.27 7.40 9.63 10.11 11.06 10.87 10.81 11.13 8.56 4.25 10.72 7.71 10.02 10.47 11.35 11.20 11.13 11.69 9.02 4.51 11.32 8.06 10.46 10.90 11.73 11.57 11.48 11.89 9.50 4.81 11.59 8.57 10.80 11.21 12.11 12.14 11.92 12.38 10.14 5.25 12.08 9.20 11.25 11.66 12.65 12.81 [6] [6] [6] [6] [6] [6] [6] [6] [6] [6] Amines 2,6-Dimethylaniline 4-Chloroaniline Aniline p-Toluidine N-Ethylaniline N,N-Dimethylbenzylamine Ammonia Ethanolamine Triethylamine 3.95 4.00 4.61 5.08 5.12 8.91 9.29 9.48 10.66 3.79 3.68 4.56 5.07 5.28 8.73 9.27 9.47 10.63 3.60 3.58 4.38 4.86 4.98 8.54 9.21 9.45 10.54 3.43 3.40 4.20 4.73 4.77 8.35 9.17 9.41 10.41 3.36 3.25 4.10 4.72 4.71 8.29 9.19 9.38 10.30 3.21 3.27 3.99 4.53 4.41 8.11 9.21 9.44 10.33 3.24 3.39 4.03 4.54 4.33 8.14 9.34 9.60 10.33 [6] [6] [6] [6] [6] [6] [31] [31] [31] 42.20% 8.61 5.91 5.47 5.38 5.07 4.78 4.39 2.87 66.07% 8.30 5.56 5.13 5.03 4.72 4.39 4.10 2.62 81.41% 8.31 5.74 5.17 5.10 4.81 4.44 4.13 2.68 92.11% 8.63 6.21 5.59 5.55 5.20 4.86 4.77 3.10 94.30% 9.39 6.78 6.10 6.08 5.72 5.32 5.17 3.49 [32] [32] [32] [32] [32] [32] [32] [32] Pyridines 4-Aminopyridine 2-Aminopyridine 4-Methylpyridine 2-Methylpyridine 3-Methylpyridine Pyridine 3-Hydroxypyridine 3-Acetylopyridine 0% 9.06 6.66 5.93 5.91 5.58 5.17 4.75 3.55 62 S. Espinosa et al. / J. Chromatogr. A 964 (2002) 55–66 Fig. 2. Variation of the slope of the linear correlations between ss pKa values in acetonitrile–water or methanol–water and the ww pKa in pure water with solvent composition for the studied series of acids. Acetonitrile–water, symbols as in Fig. 1. Methanol–water: (♦) aliphatic carboxylic acids, (m) aromatic carboxylic acids without ortho substituents, (.) ortho-substituted aromatic carboxylic acids, (d) phenols, (j) amines, (1) pyridines. also calculated from pK variation. The pH of a dihydrogen phosphate / hydrogen phosphate buffer can be calculated in a good approximation by the Henderson equation, which follows: pH 5 pKa 1 log ([HPO 422 ] / [H 2 PO 42 ]) (6) 2 Since the [HPO 22 4 ] / [H 2 PO 4 ] ratio remains constant with the addition of organic modifier, the pH variation is equal to the pKa variation of dihydrogen phosphate acid. The variation of the pKa value of dihydrogen phosphate in methanol–water and acetonitrile–water has been studied in previous studies [2,29]. From the equations developed in these works, we can calculate that the addition of methanol up to 55% in volume or acetonitrile up to 40% increases the pKa value of dihydrogen phosphate in 1.22 pKa units or 0.85 pKa units, respectively. Thus, the ss pH values of the phosphate aqueous buffer of pH 7.0 should be 8.22 and 7.85 in 55% methanol and 40% acetonitrile, respectively. The methanol calculation agrees very well with the potentiometric measurements of McCalley [33] who determined an ss pKa value of 8.25 for the same buffer in 55% methanol. The acetonitrile buffer was not measured. From the estimated ss pKa values of pyridines and s s pH values of the buffer, the degree of ionization of the pyridines in the 55% methanol and 40% acetonitrile mobile phase has been calculated. The results are given in Table 6 and they demonstrate that the pyridines are practically unprotonated (less than 2% protonated) in those mobile phases. 3.4. Estimation of aqueous pKa values from liquid chromatography retention data The proposed equations that relate pKa values in acetonitrile–water mixtures with pKa values in water S. Espinosa et al. / J. Chromatogr. A 964 (2002) 55–66 63 Fig. 3. Variation of the intercept of the linear correlations between ss pKa values in acetonitrile–water or methanol–water and the ww pKa in pure water with solvent composition for the studied series of acids. Symbols as in Fig. 2. Table 4 Parameters for prediction of the slope (a s ) of the linear correlations between ss pKa values in acetonitrile–water and the ww pKa values in pure water (Eqs. (2) and (3)) Aliphatic carboxylic acids Aromatic carboxylic acids Phenols Amines Pyridines a1 a2 a3 a4 SD F 9.97 22.42 10.05 20.73 21.67 28.59 3.14 210.04 20.27 0.67 8.83 21.98 7.97 20.87 21.66 28.72 2.12 28.37 20.12 0.67 0.01 0.02 0.02 0.00 0.03 5464 362 386 3476 38 Table 5 Parameters for prediction of the intercept (b s ) of the linear correlations between ss pKa values in acetonitrile–water and the ww pKa values in pure water (Eqs. (2) and (3)) Aliphatic carboxylic acids Aromatic carboxylic acids Phenols Amines Pyridines b1 b2 b3 b4 SD F 20.68 9.97 25.33 21.82 21.78 9.94 29.12 9.95 2.25 1.89 8.45 5.96 0.19 21.75 20.58 28.59 26.90 20.70 0.90 20.40 0.08 0.14 0.11 0.05 0.10 5152 2607 2406 1559 1293 S. Espinosa et al. / J. Chromatogr. A 964 (2002) 55–66 64 Table 6 pKa values of protonated pyridines in water and in isoelutropic methanol–water (55:45 v / v) and acetonitrile–water (40:60 v / v) mixtures and degree of ionization (aHB ) of pyridines in the three solvents prepared from an aqueous phosphate buffer of ww pH57.00 Compound H2O pH57.00 w w w w Pyridine 2-Methylpyridine 3-Methylpyridine 4-Methylpyridine 2-Ethylpyridine 3-Ethylpyridine 4-Ethylpyridine 2,3-Dimethylpyridine 2,4-Dimethylpyridine 2,6-Dimethylpyridine 3,4-Dimethylpyridine 3,5-Dimethylpyridine 2-Propylpyridine 4-Isopropylpyridine 4-tert.-Butylpyridine MeOH–H 2 O (55:45 v / v) pH58.22 s s MeCN–H 2 O (40:60 v / v) pH57.85 s s pKa aHB s s pKa aHB s s pKa aHB 5.17 5.96 5.68 6.00 5.89 5.80 5.87 6.57 6.74 6.71 6.47 6.09 6.30 6.02 5.99 0.01 0.08 0.05 0.09 0.07 0.06 0.07 0.27 0.35 0.34 0.23 0.11 0.17 0.09 0.09 3.94 4.70 4.43 4.74 4.63 4.55 4.61 5.28 5.45 5.42 5.19 4.82 5.03 4.76 4.73 5.3E205 3.0E204 1.6E204 3.3E204 2.6E204 2.1E204 2.5E204 1.2E203 1.7E203 1.6E203 9.3E204 4.0E204 6.4E204 3.4E204 3.2E204 4.57 5.35 5.07 5.39 5.28 5.19 5.26 5.96 6.13 6.10 5.86 5.48 5.69 5.41 5.38 5.2E204 3.2E203 1.7E203 3.5E203 2.7E203 2.2E203 2.6E203 1.3E202 1.9E202 1.7E202 1.0E202 4.3E203 6.9E203 3.6E203 3.4E203 for families of compounds can be used to estimate the aqueous pKa values of members of the studied families from the chromatographically determined pKa values in particular acetonitrile–water mobile phases. Tables 4 and 5 show that the standard deviations of the fits of the experimental a s and b s parameters for the different families to mobile phase composition are 0.03 or less for a s and between 0.05 and 0.14 for b s . According to Eq. (1), these standard deviations should produce errors about 0.2 pK units or less in pKa estimation, which is the precision expected for pKa measurement in non-aqueous and mixed solvents. The accuracy of the method for pKa estimation in water from pKa values determined in chromatographic mobile phases has been tested with the chromatographic pKa data obtained in a previous work for several compounds at different acetonitrile–water mobile phases [4]. The compounds belong to four different chemical families (aromatic carboxylic acids, pyridines, phenols, and amines). The results obtained are presented in Table 7. It can be observed Table 7 Estimation of aqueous ww pKa values from chromatographic ss pKa values in different mobile phases by Eqs. (1)–(3) Compound Solvent as bs s s Benzoic acid 20% MeCN 40% MeCN 60% MeCN 20% MeCN 40% MeCN 60% MeCN 40% MeCN 40% MeCN 50% MeOH 50% MeOH 50% MeOH 50% MeOH 50% MeOH 0.932 0.979 1.183 0.998 0.996 0.993 1.199 1.055 1.279 1.087 1.087 1.087 0.970 0.717 1.130 1.273 20.323 20.583 20.765 20.560 20.822 20.130 20.014 20.014 20.014 20.327 4.70 5.48 6.43 4.95 4.75 4.49 9.55 9.86 5.24 4.38 3.97 9.09 4.20 Pyridine 3-Nitrophenol Triethylamine Benzoic acid 2,4-Dinitrophenol 2,6-Dinitrophenol 3-Nitrophenol Aniline pKa w w pKa (lit) 4.21 4.21 4.21 5.17 5.17 5.17 8.43 10.66 4.21 4.02 3.71 8.39 4.61 w w pKa (calc.) 4.27 4.44 4.36 5.28 5.35 5.29 8.43 10.12 4.20 4.04 3.66 8.37 4.67 D ww pKa 20.06 20.23 20.15 20.11 20.18 20.12 0.00 0.54 0.01 20.02 0.05 0.02 20.06 S. Espinosa et al. / J. Chromatogr. A 964 (2002) 55–66 that the predictions of aqueous pKa values for benzoic acid, pyridine and 3-nitrophenol agree with the literature aqueous pKa values in 0.2 pK units or less. However, the pKa values for triethylamine differ in 0.5 pK units. This discrepancy is attributed to the value of the original chromatographic pKa data in 40% acetonitrile (9.86) which differ considerably from the potentiometric pKa data for the same solvent composition (10.30, see Table 3). Estimation of aqueous pKa values from acetonitrile–water mobile phases can be compared with estimation from methanol–water mobile phases. Table 7 reports also estimations of pKa values from 50% methanol mobile phase [3] for five compounds (one aromatic carboxylic acid, three phenols, and one amine). The agreement between aqueous literature and estimated pKa values is better than for acetonitrile–water (less than 0.1 pK units of difference for 50% methanol). This is not surprising because the pK data analyzed in methanol–water mixtures was much more extensive and the values of the fitting parameters are expected to be more robust. 65 accurate estimation of the compound ionization can be very useful in optimization of conditions of separation of complex mixtures of acid–base compounds (mobile phase pH and composition). The simplicity of the equations proposed allows an easy implementation in optimization algorithms and computer programs. On the other hand, the equations proposed can be used for estimation of aqueous pKa values from chromatographically determined pKa values in a particular acetonitrile–water mobile phase. However, it must be emphasized that the relationships have been established between the aqueous w s w pH scale and the solvent dependent s pH scale. This means that the application of the estimation methods to practical liquid chromatography problems requires a proper measurement of the pH of the mobile phase. This pH must be measured in the particular acetonitrile–water mixture used as mobile phase. The pHelectrode system can be calibrated with ss pH standards prepared in the same acetonitrile–water mixture used as mobile phase or with the usual aqueous standards and converted to ss pH through d values [4]. 4. Conclusions It has been demonstrated that linear relationships between ss pKa values in acetonitrile–water mixtures and ww pKa values in water (Eq. (1)) hold for at least five different families of compounds: aliphatic carboxylic acids, aromatic carboxylic acids, phenols, amines and pyridines. The slopes and intercepts of these correlations can be related to acetonitrile–water composition by means of Eqs. (2) and (3). Combination of Eqs. (1)–(3) leads to simple relationships between the aqueous ww pKa value of any member of the studied families (even of those members not included in the original compound sets) and the ss pKa value of this member at any acetonitrile–water composition up to 60% of acetonitrile in volume. The established relationships have two main chromatographic applications. On one hand, they can be used to estimate the ss pKa value of a compound in a particular acetonitrile–water mobile phase from its aqueous pKa value. From the estimated ss pKa value and the pH of the mobile phase, the degree of ionization of the acid–base compound in this particular mobile phase can be easily estimated. An Acknowledgements We are grateful for financial support from the ´ General de Investigacion ´ of the Spanish Direccion Government (project BQU2001-2882) and from the Catalan Government (grant 2001SGR 00055). References ´ Anal. Chem. 68 [1] E. Bosch, P. Bou, H. Allemann, M. Roses, (1996) 3651. ´ I. Canals, H. 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