Electronic Annex
Semi-empirical proton binding constants for natural organic matter Anthony Matynia1,2, Thomas Lenoir1,3, Benjamin Causse4,5, Lorenzo Spadini4, Thierry Jacquet2, and Alain Manceau1
1
Mineralogy & Environments Group, LGCA, Université Joseph Fourier and CNRS, 38041 Grenoble Cedex 9 France 2 Phytorestore – Site et Concept, 7 impasse Milord, 75018 Paris, France 3 Laboratoire Central des Ponts et Chaussées (LCPC), Route de Bouaye, BP 4129, 44341 Bouguenais cedex, France 4 Environmental Geochemistry Group, LGIT, Université Joseph Fourier and CNRS, 38041 Grenoble cedex 9 France 5 LSE-ENTPE, Université de Lyon, 69518 Vaulx-en-Velin cedex, France
1. Calculation of Δlog KH,i This calculation quantifies mesomeric and inductive effects of a substituent on the log KH,i of a six-carbon aromatic ring. Our approach, derived conceptually from linear free energy relations of Hammett (Hepler, 1963; Ren, 1998), was applied to describe how acidity constants vary with the type and position of the substituent on the ring. Adjusted values were calculated for carboxyl, hydroxyl, methoxy, methyl, amine, and thiol functional groups attached in ortho, meta, and para positions on the ring, and then combined to calculate the unknown proton dissociation constants of the reactive structural units (RSUs). The additivity of pK values results from the relationship between the Gibbs free energy and the equilibrium constant : A+B = C+D ΔG1 = GC + GD - GA - GB = -RT(ln K1) E+F = G+H ΔG2 = GH + GG - GE - GF = -RT(ln K2) ΔG1+2 = ΔG1 + ΔG2 = -RT(ln K1 + ln K2) 1.1. Carboxyl group The Δlog KH,COOH value for substituent A (A = hydroxyl, methoxy, and methyl) was obtained by subtracting the constant of benzoic acid (log KH, COOH= 4.01) from that of the A-substituted species (Table EA-1). (i) Hydroxyl substituent. The log KH, COOH of 2-, 3-, and 4-hydroxybenzoic acids are shifted by -1.21, -0.02, and 0.36 log units relative to benzoic acid, respectively. Consideration of chemically complex ligands, with known acidity constants, show that Δlog KH,COOH values can be approximated as additive. For example, log K for 2, 3, 4-trihydroxylbenzoic is 3.02, and the predicted value obtained by adding
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Δlog KH, COOH for 2-, 3- and 4-hydroxybenzoic acid to log KH,COOH of benzoic acid is 4.01 - 1.21 - 0.02 + 0.36 = 3.14. (ii) Methoxy (ph-O-CH3) substituent. The log KH, COOH of 2-, 3-, and 4-methoxybenzoic acids are shifted by -0.14, -0.19 and 0.25 log units relative to benzoic acid, respectively. The additivity rule also applies for this substituent. For example, the acidity constant of 2,3-dimethoxybenzoic acid is 3.50, and the predicted value obtained by adding Δlog KH, COOH for 2- and 3- methoxybenzoic acid to log KH,COOH of benzoic acid is 4.01 - 0.14 - 0.19 = 3.68. (iii) Methyl substituent. The log KH, COOH for 2- or 3- or 4-methylbenzoic acids are shifted by -0.10, 0.27, and 0.37 log units relative to benzoic acid, respectively. Predicted and experimental constants for benzoic acids with several -CH3 substituents differ by more than 0.2 log units. From the crosscomparison with more complex ligands, the values retained for this substituent are -0.40, 0.15, and 0.25. With these values, 2,3,4,6- tetramethylbenzoic acid has an experimental constant of 3.47 and a predicted constant of 4.01 - 0.40 + 0.15 + 0.25 - 0.40 = 3.61. Deviation from the additivity rule for this substituent has little impact on the predicted acidity constants of HA and FA because most methylsubstituted benzoic acid reactive structural units are referenced in the NIST database. (iv) Carboxyl substituent. Since di- and tri-carboxylates are polyacids, their mean acidities were used in the calculations. The shift for 1,2- and 1,3-di-carboxylic acids is 3.84 - 4.01 = -0.17 relative to benzoic acid, and for 1,4-di-carboxylic acid is 3.76 - 4.01 = - 0.25 log units. The validity of the additivity rule for a second carboxyl substituent can be verified only with 4-methylbenzene-1,2dicarboxylic acid, because the NIST database contains only one acid with four dicarboxylates. Its average acidity constant is 4.15 and the predicted constant is 4.01 - 0.17 + 0.25 = 4.09. The known constants of the three tricarboxylic acid isomers (1,2,3; 1,2,4; 1,3,5) are 3.99, 3.71, and 3.74, and their Δlog KH,COOH values -0.02, -0.30, and -0.27 log units (Table EA-1). 1.2. Other functional groups (-OH, -NH2 or –SH) The Δlog KH,OH, Δlog KH,NH2, and Δlog KH,SH values were calculated by taking phenol (log KH,OH = 9.79), aniline (log KH,NH2 = 4.64) and benzenethiol (log KH,SH= 6.46) as references. Table EA-1. Δlog KH,i values used for the calculation of proton binding constants by the chemical substituent approach. Missing substituent 2-hydroxybenzoic acid 3-hydroxybenzoic acid 4-hydroxybenzoic acid 2-methoxybenzoic acid 3-methoxybenzoic acid 4-methoxybenzoic acid 2-methylbenzoic acid 3-methylbenzoic acid 4-methylbenzoic acid Benzene-1,2-dicarboxylic acid Benzene-1,3-dicarboxylic acid Benzene-1,4-dicarboxylic acid Benzene-1,2,3-tricarboxylic acid
log KH,COOH -1.21 -0.02 0.36 -0.14 -0.19 0.25 -0.40 0.15 0.25 -0.17 -0.17 -0.25 -0.02
Missing substituent 2-methylphenol 3-methylphenol 4-methylphenol 2-hydroxyphenola 3-hydroxyphenolb 4-hydroxyphenolb 2-carboxylicphenolc 3-carboxylicphenol 4-carboxylicphenol 2-methoxyphenol 3-methoxyphenol 4-methoxyphenol 2-mercaptobenzoic
log KH,OH 0.30 0.30 0.25 -0.53 0.39 0.83 3.61 -0.17 -0.81 0.19 0.07 0.17 -0.55
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Benzene-1,2,4-tricarboxylic acid Benzene-1,3,5-tricarboxylic acid
-0.30 -0.27
log KH,SH 0.43 -0.08 0.32 1.63
Missing substituent 2-methoxybenzenethiol 3-methoxybenzenethiol 4-methoxybenzenethiol 3-carboxylicbenzenethiol a
2-aminophenol 3-aminophenol 1,2,4-trihydroxyphenold 2-acetylphenol 4-acetylphenol Missing substituent 2-hydroxyaniline 3-methylaniline 2-methoxyaniline 3-methoxyaniline
0.08 0.03 0.41 0.15 -1.94 log KH,NH2 0.10 0.26 0.08 -0.26
Only one binding constant has been considered, because the second is questionable (13.3).b Average of the two binding constants.c This value is questionable (occurs in parenthesis in the NIST database), thus the effect of adjacent COOH on the acidity of OH was dismissed.d Two constants considered, because the third is questionable.
2. Calculations of
,
values
2.1. HA-S model
2.1.1. log KH,COOH RSU1
log K H,COOH 4.30 0.15 4.45 RSU2
log K H,COOH 4.37 0.19 0.15 4.33 RSU4
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Same structure as glycine (2.33). RSU8
log K H,COOH Average
log K H,COOH
2.83 0.25 4.37 0.19 0.02 0.17 3.45 2 4.45 4.33 2.33 3.45 3.64 4
2.1.2. log KH,Ph-OH RSU1
log K H,Ph-OH
10.09 0.53 0.81 10.10 0.53 0.17 9.07 2
RSU2
log K H,Ph-OH 8.98 0.30 0.19 9.47 RSU3
log K H,Ph-OH 9.98 0.17 0.03 10.18
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RSU5
log K H,Ph-OH 10.10 0.19 0.03 10.32 RSU6
log K H,Ph-OH 10.10 0.19 1.94 8.35 RSU7
log K H,Ph-OH 10.09 0.07 0.30 0.15 10.61 RSU8
log K H,Ph-OH 14.80 0.17 0.07 14.70 This value is too high (i.e., above the cutoff set at 10.80) and was dismissed in the calculation of the average. Average
log K H,Ph-OH
9.07 9.47 10.18 13.32 8.35 10.61 9.67 6
2.2. HA-SS model
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2.2.1. log KH,COOH RSU1
log K H,COOH
4.20 0.02 4.31 0.36 4.20 0.02 0.02 4.32 3
RSU2
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log K H,COOH 4.41 0.40 0.02 3.99 RSU3 Same structure as acetic acid (4.56) RSU4
log K H,COOH
3.31 0.36 4.41 0.40 1.21 0.17 3.07 2
RSU5
log K H,COOH
3.73 0.15 3.99 0.25 3.31 0.30 3.51 3
RSU6
RSU7
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log K H,COOH 4.20 1.21 0.02 2.97 RSU8
log K H,COOH 3.99 0.36 4.35 RSU9
log K H,COOH
4.31 4.20 0.17 4.08 2
RSU10
log K H,COOH
3.99 3.99 0.17 3.82 2
RSU11
RSU12
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log K H,COOH
4.27 0.14 3.91 0.19 0.17 3.76 2
RSU13
log K H,COOH
3.31 3.99 0.25 0.17 3.61 2
RSU14
RSU15
log K H,COOH 2.88 0.14 0.25 2.99 RSU16
log K H,COOH
5.24 3.99 4.62 2
RSU17
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log K H,COOH Average log K H,COOH
2.80 0.19 0.19 3.99 0.14 0.14 0.25 2.82 2
4.32 3.99 4.56 3 4.62 3.07 3.51 3.31 2.97 4.35 4.08 3.82 3.47 3.76 3.61 4.00 2.99 2.82 3.81 19
2.2.2. log KH,Ph-OH RSU1
log K H,Ph-OH 10.62 2 0.17 0.81 9.47 RSU2
log K H,Ph-OH 10.89 0.17 10.72 RSU4
log K H,Ph-OH 10.67 0.81 3.61 13.47 This value was dismissed. RSU7 The effect of adjacent COOH on the acidity of OH was not considered.
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log K H,Ph-OH 10.62 0.17 0.83 11.28 This value was dismissed. RSU8
log K H,Ph-OH 10.60 0.81 9.79 RSU15
log K H,Ph-OH 9.37 0.25 3.61 13.23 This value was dismissed. RSU17
log K H,Ph-OH 9.98 0.17 0.17 3.61 13.59 Average
log K H,Ph-OH
9.47 10.72 9.79 9.99 3
2.3. FA-B model
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2.3.1. log KH,COOH RSU1
log K H,COOH
3.73 0.36 4.41 0.02 4.41 1.21 0.02 3.87 3
RSU2
log K H,COOH 3.40 0.36 3.76 RSU3 Same structure as acetic acid (4.56). RSU4 Same structure as lactic acid (3.67). Average
log K H,COOH
3.87 3.76 4.56 3.67 3.97 4
2.3.2. log KH,Ph-OH RSU1
log K H,Ph-OH 10.54 3.61 0.17 0.81 13.17 This value was dismissed.
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RSU2
log K H,Ph-OH 10.89 0.81 10.08 Average log K H,Ph-OH 10.08 2.4. FA-A model
2.4.1. log KH,COOH RSU1 Structure similar to pyruvic acid (2.26). RSU3 Same structure as acrylic acid (4.09) RSU4 Same structure as lactic acid (3.67). RSU5
log K H,COOH 2.96 2 0.02 0.55 2.37 RSU6 Same structure as 3-hydroxypropanoic acid (4.40)
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RSU7 Same structure as methoxyacetic acid (3.32) 2.4.2. log KH, Ph-OH RSU2
log K H,Ph-OH 10.54 0.08 0.07 0.17 10.86 RSU5 The acidity of SH could not be calculated because some of the binding constants are unknown. The OH group next to COOH deprotonates at pH ≥ 13.
log K H,Ph-OH
10.09 0.17 10.09 0.17 0.41 10.33 2
2.4.3. log KH, NH2 RSU2
log K H,NH 2 5.09 0.10 0.26 0.08 0.26 5.27 This value was included in the calculation of the average value of log KH,COOH. 2.4.4. log KH, SH
RSU5
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log K H,SH 6.66 1.63 0.43 0.08 0.32 8.96 The OH groups were replaced by OMe, because the constants of the methylated species are known. The average value was included in the total calculation of log KH,Ph-OH. Average
log K H,COOH
2.26 4.40 4.09 3.67 3.32 2.37 5.27 3.63 7
log K H,Ph-OH
10.33 8.96 9.65 2
3. References Hepler L.G. (1963) Effects of substituents on acidities of organic acids in water: thermodynamic theory of Hammett equation. J. Am. Chem. Soc., 85, 3089. Ren T. (1998) Substituent effects in dinuclear paddlewheel compounds: electrochemical and spectroscopic investigations. Coord. Chem. Rev., 175, 43-58.
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