Anal. Chem. 1996, 68, 2127-2134
Multicomponent NMR Titration for Simultaneous Measurement of Relative pKas Charles L. Perrin* and Miles A. Fabian
Department of Chemistry, University of California at San Diego, La Jolla, California 92093-0358
An NMR titration method has been developed to simultaneously measure the difference in acid dissociation constants (∆pKa) of two or more compounds with high precision and accuracy. The ∆pKa between the conjugate acids of the two stereoisomers of 4-tert-butylcyclohexylamine 1 was determined in a single 1H NMR titration experiment. A mixture of the two stereoisomers was titrated with DCl in a 3:1 (v/v) mixture of CD3OD/D2O. From the variations of the H1 chemical shifts the ratio of the acidity constants was determined. The trans stereoisomer 1t was found to be the more basic by 0.121 ( 0.002 pK unit. A repeat titration in DMSO-d6 also found 1t to be the more basic, by 0.217 ( 0.003 pK unit. The ∆pKa between the two stereoisomers of 4-tert-butylcyclohexanecarboxylic acid 2 was determined in both of these solvents using 1H and 13C NMR. Thermodynamic parameters ∆∆H° and ∆∆S° were evaluated from the temperature dependence of ∆pKa. To further demonstrate the utility of this method, the ∆pKas of the conjugate acids of the four stereoisomers of 2-decalylamine 3 were determined in a single 1H NMR titration experiment. The cis,cis stereoisomer (3cc) was found to be the most basic, with the cis,trans (3ct), trans,cis (3tc), and trans,trans (3tt) less basic by 0.012 ( 0.003, 0.037 ( 0.004, and 0.141 ( 0.005 pK unit, respectively. A second four-component titration was also performed with the two 4-tert-butylcyclohexylamines (1) and the two trans-2-decalylamines (3tc, 3tt). Chemists and biochemists have often been concerned with the measurement of acid dissociation constants (pKas).1 Such measurements have led to a better understanding of many diverse chemical and biochemical phenomena. However, relatively small free-energy differences often govern such phenomena in solution. Therefore it is essential to measure pKas with great exactness. Present methods are not always adequate to measure pKas with the accuracy needed to compare structurally similar compounds. These methods are critically dependent on the precision and accuracy of multiple measurements as well as on the purity and standardization of materials. Further, many methods also lack the ability or are not easily adapted to determine pKas of substances in a mixture or in nonaqueous solutions. Common methods available for determining pKa are potentiometric titrations and conductivity measurements, which possess (1) Albert, A.; Serjeant, E. P. The Determination of Ionization Constants, 3rd ed.; Chapman and Hall: London, 1984. S0003-2700(96)00117-5 CCC: $12.00
© 1996 American Chemical Society
varying degrees of selectivity, sensitivity, accuracy, precision, and rapidity.2 In potentiometric titrations, the most common method, the potential of a suitable indicator electrode is monitored during the titration. The pKa is obtained as the pH at the point of halfneutralization, as determined from the entire titration curve or from some physical or spectroscopic property that varies with pH. For these methods a pH meter and a glass electrode are almost universally used although there are other less convenient electrode systems, such as a hydrogen or quinhydrone electrode, for measuring pH more accurately.1 The accuracy of a pH measurement using a glass electrode is usually taken as (0.02 pH unit.3 However, the major source of error with these methods is associated with a variability from one titration to another and not with the individual points in each titration.4 Conductivity measurements are an alternative method capable of high accuracy but of limited applicability.5 From the dependence of conductivity on the concentration of incompletely dissociated acids it is possible to evaluate pKa with great accuracy. However, this method is limited to a narrow range of pKas. Further, since the conductivity of a solution is the summation of contributions from all the ions present, materials must be laboriously standardized and the specific conductance of all the solutions accurately measured. Nuclear magnetic resonance (NMR) is extremely selective for distinguishing different species in solution, so it can be a powerful method for monitoring the extent of ionization. In the special case that exchange between protonated and unprotonated forms is slow on the NMR time scale, the intensities of the separate signals can be integrated and the ratios evaluated as a function of pH. This is not generally feasible for protonation but may be applicable to dissociation constants of metal chelates.6 A variant is applicable to a mixture of two stereoisomers that interconvert slowly on an NMR time scale but rapidly on a laboratory time scale. By measuring the equilibrium proportions of the stereoisomers under conditions of both protonation and deprotonation, a thermodynamic cycle then provides the difference in pKa between the two isomers.7 This method has been applied to rotational isomers of 9-[2-[(dimethylamino)methyl]-6-methyl(2) Bates, R. G. Determination of pH: Theory and Practice, 2nd ed.; Wiley: New York, 1973. (3) Westcott, C. C. pH Measurements; Academic Press: New York, 1978; pp 106-109. (4) Simon, W. Helv. Chim. Acta 1958, 41, 1835-1851. Fisicafo, E.; Braibanti, A. Talanta 1988, 35, 769-774. (5) Harned, H. S.; Owen, B. B. Chem. Rev. 1939, 25, 31-65. Robinson, R. A.; Stokes, R. H. Electrolyte Solutions; Butterworths: London, 1955; pp 330333. (6) Smith, G. A.; Hesketh, R. T.; Metcalfe, J. C.; Feeney, J.; Morris, P. G. Proc. Natl. Acad. Sci. U.S.A. 1973, 80, 7178-7182. Levy, L. A.; Murphy, E.; Raju, B.; London, R. E. Magn. Reson. Chem. 1992, 30, 723-732. (7) Stolow, R. D. J. Am. Chem. Soc. 1959, 81, 5806-5811.
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phenyl]fluorene.8 However, both this variant and the previous general method are limited by inaccuracies in NMR integration, and it would be preferable to rely on chemical shifts, which can be measured far more precisely. Since it was first observed that chemical shifts vary with the extent of ionization,9 NMR has been used in titrations with the glass electrode. From the pH dependence of the chemical shift, the pKa can be determined, using 1H, 13C, 15N, 31P, or 19F NMR spectroscopy.10 Because of the specificity of NMR, these are especially powerful methods for measuring pKas of individual groups in macromolecules.11 A further advantage of NMR is that it is capable of simultaneously monitoring the extent of protonation of each of the species in a multicomponent mixture. Thus it is possible to determine the individual pKas of those species. This method, using 13C NMR, was applied to the cis and trans isomers of several small peptides.12 This method can also be applied to determining isotope effects on acid/base equilibria. From a titration of a mixture of isotopologues,13 the equilibrium constant can be determined from a nonlinear fit of a plot of the difference between the chemical shifts of the two isotopologues against the pH or against the extent of protonation. This method has been used to measure 18O, 2H, or 15N isotope effects on the acid dissociation constants of formic acid, glycine, glycerol phosphate, and adenosine triphosphate14 and on the tautomeric equilibrium constants of dicarboxylic acid monoanions.15 However, unless the extent of neutralization can be evaluated from the chemical shifts,14d this method, whether for a single component or for multiple ones, is still limited by the inaccuracies of pH measurement. Recently an NMR titration method was developed to measure the ratio of acidity constants between two structurally similar compounds without the necessity of measuring pH.16 From the variations of the NMR chemical shifts during a titration of a single solution, the ratio of acidity constants of two or more compounds can be determined. During a titration, the spectral characteristics of the most basic or acidic compound will change earlier than (8) Nakamura, M.; Oki, M. Chem. Lett. 1985, 255-258. (9) Grunwald, E.; Loewenstein, A.; Meiboom, S. J. Chem. Phys. 1957, 27, 641642. (10) Sudmeier, J. L.; Reilley, C. N. Anal. Chem. 1964, 36, 1698-1706. Rigler, N. E.; Bag, S. P.; Leyden, D. E.; Sudmeier, J. L.; Reilley, C. N. Anal. Chem. 1965, 37, 872-875. Rabenstein, D. L. J. Am. Chem. Soc. 1973, 95, 27972803. Rabenstein, D. L.; Sayer, T. L. Anal. Chem. 1976, 48, 1141-1146. Buchner, P.; Maurer, W.; Ruterjans, H. J. Magn. Reson. 1978, 29, 45-63. Cistola, D. P.; Small, D. M.; Hamilton, J. A. J. Lipid Res. 1982, 23, 795799. Sowers, L. C.; Fazakerley, G. V.; Kim, H.; Dalton, L.; Goodman, M. F. Biochemistry 1986, 25, 3983-3988. Wang, C.; Gao, H.; Gaffney, B. L.; Jones, R. A. J. Am. Chem. Soc. 1991, 113, 5486-5488. Onasch, O. F.; Schwartz, H. M.; Aikens, D. A.; Bunce S. C. J. Chem. Educ. 1991, 68, 791-793. Newton, G. L.; Dwyer, T. J.; Kim, T. H.; Ward, J. F.; Fahey, R. C. Radiat. Res. 1992, 131, 143-151. Skvortsov, N. K.; Dogadino, A. V.; Tereshchenko, G. T.; Morkovin, N. V.; Ionin, B. I.; Petrov. A. H. Zh. Obshchei Khim. 1971, 41, 2807-2808. Taft, R. W.; Levine, P. L. Anal. Chem. 1962, 34, 436-437. (11) Fersht, A. Enzyme Structure and Mechanism; W. H. Freeman: New York, 1984; p 475. (12) Evans, C. A.; Rabenstein, D. L. J. Am. Chem. Soc. 1974, 96, 7312-7317. (13) Seeman, J. I.; Secor, H. V.; Disselkamp, R.; Bernstein, E. R. J. Chem. Soc., Chem. Commun. 1992, 713. (14) (a) Ellison, S. L. R.; Robinson, M. J. T. J. Chem. Soc., Chem. Commun. 1983, 745-746. (b) Knight, W. B.; Weiss, P. M.; Cleland, W. W. J. Am. Chem. Soc. 1986, 108, 2759-2761. (c) Jones, J. P.; Weiss, P. M.; Cleland, W. W. Biochemistry 1991, 30, 3634-3639. (d) Rabenstein, D. L.; Mariappan, S. V. S. J. Org. Chem. 1993, 58, 4487-4489. (15) Perrin, C. L.; Thoburn, J. D. J. Am. Chem. Soc. 1989, 111, 8010-8012. (16) Perrin, C. L.; Fabian, M. A.; Armstrong, K. B. J. Org. Chem. 1994, 59, 52465253. Fabian, M. A.; Perrin, C. L.; Sinnott, M. L. J. Am. Chem. Soc. 1994, 116, 8398-8399.
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Chart 1
those of the other compounds. A linear plot created from the chemical shifts of the neutral and ionic forms of each compound and the observed chemical shifts after each addition of titrant gives the desired ratio and thus ∆pKa, the difference between the pKas of the compounds. This method differs from the closest previous method14d in that it relies explicitly only on chemical shifts and on a linear plot. To demonstrate the utility of this new NMR titration method, the ∆pKa between the conjugate acids of the two stereoisomers of 4-tert-butylcyclohexylamine 1 (see Chart 1) was measured in a single 1H NMR titration experiment in aqueous methanol. A sample containing a mixture of the stereoisomers in an NMR tube was titrated with small aliquots of acid. A repeat titration was also performed in DMSO-d6. Further, the ∆pKa between the two stereoisomers of 4-tert-butylcyclohexanecarboxylic acid 2 was measured in titrations with NaOD using both 1H and 13C NMR. The thermodynamic parameters ∆∆H° and ∆∆S° were also evaluated using this methodology from the temperature dependence. To further demonstrate the flexibility and convenience of this methodology, the ∆pKas of the conjugate acids of the four stereoisomers of 2-decalylamine (2-decahydronaphthalenamine, 3) were determined in a single 1H NMR titration experiment. For comparison, the ∆pKas were also determined for the separate mixtures of the cis-2-decalylamines 3cc and 3ct) and the trans-2decalylamines 3tc and 3tt. (The first cis, trans designation applies to the ring junction and the second to the relation between H2 and the nearer ring junction hydrogen.) A second four-component titration was performed with the two 4-tert-butylcyclohexylamines 1 and the two trans-2-decalylamines 3tc and 3tt. Lastly, the two trans-2-decalylamines (3tc, 3tt) and isopropylamine (4) were titrated to establish the absolute pKas of all the amines.
This new methodology allows for the “direct” comparison of pKa between multiple compounds without the necessity of measuring pH. Identical conditions are assured since the compounds are titrated in a single solution. Although only relative pKas are obtained, rather than absolute ones, they are very accurate. Often relative pKas are all that are needed, as for structure/activity correlations.17 Besides, the absolute pKa of a compound can be easily established by a comparison to one compound of known pKa. The accuracy and precision of this method are limited only by the exactness by which chemical shifts are measured. Further, the necessity to purify compounds and standardize reference solutions is eliminated. This new methodology represents a powerful probe of ionization, with high accuracy and precision. EXPERIMENTAL SECTION Materials. Isopropylamine, cis- and trans-4-tert-butylcyclohexanecarboxylic acids (44:56 mixture), cis- and trans-4-tert-butylcyclohexylamines (19:81 mixture), 2-decalols (mixture of stereoisomers), D2O, DCl/D2O, NaOD/D2O, CD3OD, and other reagents were obtained from commercial suppliers and used as received. 2-Decalylamines. cis,cis-2-Decalol and trans,cis-2-decalol were each separated from a mixture of stereoisomers of 2-decalol (decahydro-2-naphthol) by recrystallization from pentane18 and confirmed from their known melting points19 and 13C NMR spectra.20 Each alcohol was converted to the corresponding ketone by chromic acid oxidation.21 A mixture (72:28) of the cis stereoisomers (3cc, 3ct) and a separate mixture (70:30) of the trans stereoisomers (3tc, 3tt) of 2-decalylamine (decahydro-2-naphthaleneamine) were prepared by reductive amination of the corresponding cis or trans ketone with ammonium acetate and sodium cyanoborohydride.22 Spectral Assignments. Assignments of the 1H signals were based on chemical shifts and coupling constants.23 The characteristic H1 signals of 1 or of 2 and the H2 signals of 3 are downfield, well separated from all other signals. The equatorial H1 signals of 1c and 2c and the H2 signal of 3tt are further downfield, with only small gauche couplings to the hydrogens on the adjoining carbons. Also, the H2 signal of 3ct is shifted downfield by steric compression.24 These assignments for 1 and 3 are consistent with the preference for axial attack of hydride in reductive aminations.25 (17) Exner, O. Correlation Analysis of Chemical Data; Plenum: New York, 1988. Chapman, N. B., Shorter, J., Eds. Correlation Analysis in Chemistry: Recent Advances; Plenum: New York, 1978. Zalewski, R. I., Krygowski, T. M., Shorter, J., Eds. Similarity Models in Organic Chemistry, Biochemistry, and Related Fields; Elsevier: Amsterdam, 1991. (18) Cohen, T.; Daniewski, A. R.; Solash, J. J. Org. Chem. 1980, 45, 2847-2853. (19) Hu ¨ ckel, W. Liebigs Ann. Chem. 1938, 533, 1-45. Dauben, W. G.; Hoerger, E. J. Am. Chem. Soc. 1951, 73, 1504-1508. Cohen, T.; Malaiyandi, M.; Pinkus, J. L. J. Org. Chem. 1964, 29, 3393-3395. (20) Metzger, P.; Casadevall, E.; Pouet, M. J. Org. Magn. Reson. 1982, 19, 229234. (21) Dauben, W. G.; Tweit, R. C.; Mannerskantz, C. J. Am. Chem. Soc. 1954, 76, 4420-4426. (22) Borch, R. F.; Bernstein, M. D.; Durst, H. D. J. Am. Chem. Soc. 1971, 93, 2897-2904. (23) Silverstein, R. M.; Bassler, G. C.; Morrill, T. C. Spectrometric Identification of Organic Compounds, 5th ed.; Wiley: New York, 1991. (24) Jackman, L. M.; Sternhell, S. Applications of Nuclear Magnetic Resonance Spectrospcopy in Organic Chemistry, 2nd ed.; Pergamon: Oxford, UK, 1969; pp 71-72. (25) Hutchins, R. O.; Su, W.-Y.; Sivakumar, R.; Cistone, F.; Stercho, Y. P. J. Org. Chem. 1983, 48, 3412-3422.
Assignments of the 13C signals of 2 were based on chemical shift correlations,26 a 1H-coupled spectrum, and the isomer ratio observed in the 1H spectrum. The two signals furthest downfield were assigned to the two CO signals. Of the remaining signals, the C4 signals are shifted strongly downfield by steric compression, and the C1 signals are shifted downfield by the adjacent carboxyl. That the latter are less downfield was confirmed from their larger variation upon ionization. The C2 signals are distinguished from C3 because the former are shifted slightly downfield by the nearby carboxyl. Aqueous Methanol (75% v/v) Stock Solutions. A stock solution of DCl was prepared from 0.66 g of CD3OD, 0.08 g of D2O, and 0.27 g of 35% DCl/D2O solution. A similar stock solution of NaOD was prepared from 0.66 g of CD3OD, 0.09 g of D2O, and 0.25 g of a 40% NaOD/D2O. DMSO Stock Solutions. A stock solution of trifluoroacetic acid (TFA) was prepared from 1.00 g of DMSO-d6 and 0.20 g of TFA. A similar stock solution of t-BuOK was prepared from 1.00 g of DMSO-d6 and 0.19 g of t-BuOK. Titrations. The NMR samples prepared for each titration contained 1.00 mL of solvent, 5 µL of tetramethylsilane (TMS) or 1,4-dioxane as internal standard, and a 0.05, 0.10, or 0.20 mmol mixture of stereoisomers. An initial 1H or 13C NMR spectrum was taken of the sample, which is listed as the “0” titration point. Aliquots of 5 µL of the appropriate stock solution were then continually added until the chemical shifts no longer changed. The 1H or 13C NMR chemical shifts were recorded after each addition of the stock solution. The amines titrated in CD3OD/D2O required two separate titrations since a small percent of the amine becomes protonated in the solution. Therefore, two samples were prepared by splitting a solution containing 1.33 g of CD3OD, 0.50 g of D2O, 10 µL of TMS, and a 0.20 mmol mixture of amines. A 5-µL aliquot of the NaOD stock solution was added to the first sample. A 1H NMR spectrum was taken of the sample, which is recorded as the “-1” titration point. Further addition of base gave no further change in the chemical shifts. A 1H NMR spectrum was taken of the second sample, which is recorded as the “0” titration point. Aliquots of 5 µL of the DCl stock solution were then continually added until the chemical shifts no longer changed, indicating that the end point of the titration had been passed. The 1H NMR chemical shifts were recorded after each addition of the stock solution. Titrations performed at multiple temperatures were done using a single sample. During each point along the titration, the sample was heated to each of the five temperatures and allowed to equilibrate within the probe for 15 min at each temperature. Temperatures were calibrated using a separate CD3OD/D2O sample with an internal ethylene glycol reference. NMR Spectroscopy. Spectra were recorded on a Varian Unity-500 spectrometer (499.8 MHz 1H, 125.7 MHz 13C) using an indirect probe. Chemical shifts are referenced to TMS (δ 0.00) for 1H spectra and 1,4-dioxane (δ 66.5) for 13C spectra. Data Analysis. Certain NMR chemical shifts of a compound undergo sufficient change upon protonation or deprotonation to permit the NMR determination of the extent of ionization. For a mixture of two compounds, A and B, the chemical shifts of the more basic compound will change earlier during a titration with (26) Levy, G. C.; Nelson, G. L. Carbon-13 Nuclear Magnetic Resonance for Organic Chemists; Wiley: New York, 1972.
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acid than those of the other compound. Likewise, the chemical shifts of the more acidic compound will change earlier during a titration with base. The ratio of acidity constants of the different compounds, K in eq 1, can be readily measured from the variations in chemical shifts.
KaAH
Table 1. 1H NMR Chemical Shifts of H1 in Titrations of Mixtures of Stereoisomeric 4-tert-Butylcyclohexylamines 1 with DCl in 3:1 CD3OD/ D2O at 25 °C 0.20 M
K)
KaBH
+
) [AH+][B]
(1)
Proton exchange is rapid on the NMR time scale, with secondorder rate constants for thermoneutral exchange of at least 3 × 108 M-1 s-1 in water and reduced only to ∼5 × 106 M-1 s-1 for hindered amines in CDCl3.27 These values mean that residual peak broadening from insufficiently rapid exchange is negligible even at 0.01 M concentrations (lower than those used here) and at 600 MHz (higher than used here), although this is not the case for some metal chelates6 and for some enzymes in solutions lacking sufficient buffer to mediate proton transfer.28 Thus the observed chemical shifts are weighted averages of the chemical shifts of the resonances for the protonated and deprotonated species. The observed chemical shift of base A is given by eq 2, where δA° and δAH+ are the limiting chemical shifts of the neutral and protonated forms, respectively. A similar equation holds for the competing base B.
δa )
δA°[A] + δAH+[AH+] [A] + [AH+]
0.05 M
δc
δt
δc
δt
δc
δt
-1 0 1 2 3 4 5 6 7 8 9 10 11
3.058 3.063 3.089 3.125 3.165 3.205 3.249 3.303 3.352 3.403 3.461 3.520 3.542
2.516 2.523 2.561 2.610 2.660 2.710 2.761 2.819 2.873 2.922 2.975 3.026 3.045
3.058 3.066 3.101 3.136 3.174 3.223 3.277 3.381 3.427 3.489 3.534
2.517 2.528 2.577 2.625 2.673 2.730 2.793 2.901 2.944 2.999 3.038
3.058 3.073 3.105 3.148 3.190 3.230 3.282 3.386 3.440 3.491 3.533
2.517 2.539 2.582 2.639 2.692 2.739 2.800 2.905 2.956 3.000 3.037
+
[A][BH+]
0.10 M
titr
(2)
Algebraic manipulations of these equations lead to eq 3, which is nonlinear whenever K * 1. The desired ratio, K, can be
δa ) δA° +
(δAH+ - δA°)(δb - δB°) (1 - K)(δb - δB°) + K(δBH+ - δB°)
(δb - δB°)(δAH+ - δa) ) K(δa - δA°)(δBH+ - δb)
(3) (4)
obtained from a nonlinear least-squares fit of eq 3. However, further manipulations lead to the linearized form in eq 4, relating observed chemical shifts to the desired K. From a titration of a mixture of compounds, the ratio of acidity constants can be calculated from a plot of (δb - δB°)(δAH+ - δa) vs (δa - δA°)(δBH+ - δb), which ought to be a straight line, with slope K and zero intercept.16 Therefore, the beginning chemical shifts of the neutral compounds and the ending chemical shifts of the ions must be known to accurately determine the ratio of acidity constants using this methodology. In principle, any nucleus reports on the state of protonation of the molecule. However, the greatest precision is obtained from monitoring the NMR chemical shifts that undergo the largest change upon ionization. Therefore, those nuclei closest to the site of protonation/deprotonation are best suited for this method. These also prove to be ideal, since they are shifted downfield from other signals and are readily discerned in the NMR spectrum. (27) Grunwald, E.; Cocivera, M. Discuss. Faraday Soc. 1965, 39, 105-111. Perrin, C. L.; Wang, W.-h. J. Am. Chem. Soc. 1982, 109, 2325-2326. (28) Sudmeier, J. L.; Evelhoch, J. L.; Jonsson, N. B.-H. J. Magn. Reson. 1980, 40, 377-390. Bachovchin, W. W.; Roberts, J. D. J. Am. Chem. Soc. 1978, 100, 8041-8047.
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Figure 1. Plot of H1 chemical shifts during titration of cis and trans stereoisomers of 1 with DCl in 3:1 CD3OD/D2O at 25 °C. The curve shows the nonlinear least-squares fit. The dotted straight line demonstrates the curvature of the plot.
Figure 2. Linearized plot of H1 chemical shifts, (δt - δT°)(δCH+ δc) vs (δc - δC°)(δTH+ - δt), of cis and trans stereoisomers of 1 during the titration of a mixture with DCl in 3:1 CD3OD/D2O at 25 °C.
Using variable-temperature 1H NMR, the thermodynamic parameters ∆∆H° and ∆∆S° (eqs 5 and 6) for the two stereoiso-
∆∆H° ) (HBH+° - HB°) - (HAH+° - HA°)
(5)
∆∆S° ) (SBH+° - SB°) - (SAH+° - SA°)
(6)
Table 2. ∆pKas from Linearized Plots of 1H NMR Chemical Shifts of the H1 Signals from Titrations of Mixtures of Stereoisomeric 4-tert-Butylcyclohexylamines 1 at 25 °C solvent
conc (M)
3:1 CD3OD/D2O 3:1 CD3OD/D2O 3:1 CD3OD/D2O DMSO-d6 DMSO-d6 DMSO-d6
0.20 0.10 0.05 0.20 0.10 0.05
titrant DCl DCl DCl TFA TFA TFA
slope
y-intercept
corr coeff
∆pKa
1.324 ( 0.007 1.322 ( 0.006 1.324 ( 0.008 1.647 ( 0.012 1.650 ( 0.013 1.649 ( 0.015
0.0000 ( 0.0003 -0.0001 ( 0.0002 -0.0002 ( 0.0003 -0.0001 ( 0.0003 -0.0002 ( 0.0003 -0.0003 ( 0.0003
0.99987 0.99990 0.99986 0.99976 0.99977 0.99974
0.122 ( 0.002 0.121 ( 0.002 0.122 ( 0.003 0.217 ( 0.003 0.217 ( 0.003 0.217 ( 0.004
Table 3. ∆pKas from Linearized Plots of NMR Chemical Shifts of Cis and Trans Stereoisomers of 4-tert-Butylcyclohexanecarboxylic Acid 2 in 3:1 CD3OD/D2O at 25 °C signal 1H1 13CO 13C1 13C2 13C4
Figure 3. Plot of H1 chemical shifts during the titration of cis and trans stereoisomers of 2 with NaOD in 3:1 CD3OD/D2O at 25 °C.
mers can be evaluated from the temperature dependence of ∆pKa. A van’t Hoff plot of -ln K vs 1/T gives a slope of ∆∆H°/R and an intercept of -∆∆S°/R. RESULTS AND DISCUSSION A mixture of cis- and trans-4-tert-butylcyclohexylamines (1) was titrated with DCl in a 3:1 (v/v) mixture of CD3OD/D2O. The H1 chemical shifts were followed during the titration and are listed in Table 1. Both H1 peaks move downfield during the titration upon successive additions of acid. Close inspection shows that the two peaks are slightly closer to each other in the middle of the titration. The limiting shifts δT°, δTH+, δC°, and δCH+ at the beginning and end point of the titration are 2.517, 3.039, 3.058, and 3.533 ppm, respectively. It is clear that the chemical shifts change substantially (∼0.5 ppm) on protonation of the amine, so that the observed chemical shift is a good monitor of the extent of protonation. A plot of δc vs δt (Figure 1) shows a slight but systematic upward curvature, indicating that the trans stereoisomer 1 is more readily protonated. A nonlinear least-squares fit to eq 3 gives a value of 1.322 for K. A linearized plot (eq 4) of (δt - δT°)(δCH+ - δc) vs (δc - δC°)(δTH+ - δt) (Figure 2) gives a straight line with a slope K also 1.322 ( 0.006 and an intercept of -0.0001 ( 0.0002, which is properly zero. The excellent linearity is confirmed by a correlation coefficient of 0.99990. This slope corresponds to a ∆pKa ) pKatrans - pKacis of 0.121 ( 0.002, with the trans stereoisomer 1t the more basic of the two stereoisomers. Equilibria can be affected by medium effects, so that thermodynamic pKas must be extrapolated to infinite dilution. However, diverse salts and impurities in the titration solution are very unlikely to affect the ∆pKa that is determined by this methodology. The relation between the observed ∆pKa, the thermodynamic ∆pKa° at infinite dilution, and activity coefficients is given in eq 7.
slope
y-intercept
corr coeff
∆pKa
0.99935 0.99999 0.99995 0.99983 0.99797
0.453 ( 0.004 0.451 ( 0.001 0.449 ( 0.002 0.446 ( 0.004 0.453 ( 0.014
2.835 ( 0.023 -0.0002 ( 0.0001 2.821 ( 0.007 -0.011 ( 0.017 2.810 ( 0.014 -0.003 ( 0.012 2.792 ( 0.026 0.002 ( 0.003 2.838 ( 0.091 0.000 ( 0.001
Table 4. ∆pKas from Linearized Plots of 1H NMR Chemical Shifts of Cis and Trans Stereoisomers of 4-tert-Butylcyclohexanecarboxylic Acid 2 in 3:1 CD3OD/D2O T (°C)
slope
y-intercept
corr coeff
∆pKa
15 22 33 41 56
2.97 ( 0.03 2.87 ( 0.04 2.70 ( 0.04 2.62 ( 0.03 2.48 ( 0.03
0.0001 ( 0.0001 0.0000 ( 0.0001 0.0002 ( 0.0002 0.0001 ( 0.0001 0.0000 ( 0.0001
0.99969 0.99962 0.99933 0.99970 0.99970
0.473 ( 0.005 0.457 ( 0.005 0.431 ( 0.007 0.418 ( 0.005 0.394 ( 0.005
For structurally similar compounds, the term involving the activity coefficients should vanish. As an experimental test of the contribution of these activity coefficients, titrations were also performed at concentrations of 0.20 and 0.05 M, and the chemical shifts are included in Table 1. The ∆pKas were found to be 0.122 ( 0.002 and 0.122 ( 0.003 for 0.20 and 0.05 M, respectively (Table 2). At three different concentrations the ∆pKas were found to be identical, within 0.001 of one another. It is therefore reasonable to conclude that these results do represent ∆pKa at infinite dilution. It is also worth noting the great reproducibility with which the ∆pKa was determined in the three separate titrations.
∆pKaobs ) ∆pKa° + log
γAγBH+ γAH+γB
(7)
The two stereoisomers of cis- and trans-4-tert-butylcyclohexylamine (1) were also titrated with TFA in DMSO-d6 to demonstrate the flexibility of this methodology and its applicability to a nonaqueous solvent (see supporting information). Even in this solvent proton exchange appears to be fast, since the signals remain sharp throughout the titration and do not broaden as they move. From the titration the ∆pKa was found to be 0.217 ( 0.003, with the trans stereoisomer 1t again more basic. Titrations were also performed at concentrations of 0.20 and 0.05 M since ionic activity coefficients are more likely to vary in a less polar solvent. The ∆pKas were found to be 0.217 ( 0.003 and 0.218 ( 0.004 for 0.20 and 0.05 M, respectively (Table 2). These results are once Analytical Chemistry, Vol. 68, No. 13, July 1, 1996
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Figure 4. 1H NMR of the H2 region of a mixture of the four stereoisomeric 2-decalylamines 3 at the beginning and end of a titration with DCl in 3:1 CD3OD/D2O at 25 °C.
again identical, within the small experimental error, and it is therefore reasonable to assume that these results are accurate to infinite dilution. The values for these two stereoisomers agree with previous ones. The relative basicities had been measured using a glass electrode in methyl cellosolve,29 water, methanol, and DMSO.30 The ∆pKas were found to be 0.26, 0.10, 0.11, and 0.15, respectively, also with the trans stereoisomer 1t the more basic. The ∆pKa obtained in this study in aqueous methanol is in excellent agreement with those previously reported in methanol and water. The result previously obtained in DMSO-d6 differs somewhat from ours, which we consider more reliable. A mixture of cis- and trans-4-tert-butylcyclohexanecarboxylic acids 2 in 3:1 CD3OD/D2O was titrated with a NaOD solution, and the H1 chemical shifts are listed in supporting information (Table S2). During the titration, the signals move upfield rather than downfield as for the amines. A plot of δc vs δt is shown in Figure 3. The greater curvature, compared with Figure 1, is indicative of a larger ∆pKa. From a linearized plot of the chemical shifts, the ∆pKa ) pKacis - pKatrans was found to be 0.453 ( 0.004 (Table 3), with the trans stereoisomer 2t the more acidic. The 1H NMR chemical shifts of H1 of the cis and trans 2 proved to be more problematic than those of the amines. The H1 signal of the trans stereoisomer 2t starts partially covered by the more intense signal of the equatorial H2,6 of the cis stereoisomer 2c and moves through the signal of the equatorial H2,6 of the trans stereoisomer 2t toward the end of the titration. Although a 500-MHz spectrometer allows for adequate assignment of the 1H signals, even though some of them overlap, 13C signals are (29) Sicher, J.; Jona´sˇ, J.; Tichyˇ, M. Tetrahedron Lett. 1963, 13, 825-830. (30) Edward, J. T.; Farrell, P. G.; Kirchnerova, J.; Halle, J.-C.; Schaal, R. Can. J. Chem. 1976, 54, 1899-1905.
2132 Analytical Chemistry, Vol. 68, No. 13, July 1, 1996
more easily followed during a titration because of the larger dispersion of the chemical shifts. Chemical shifts for CO, C1, C2, and C4 carbons during a titration of cis and trans isomers 2 are given in supporting information (Table S3). Table 3 lists ∆pKa from each of these reporter nuclei. From the 13CO chemical shifts, ∆pKa was found to be 0.451 ( 0.001. Within the small experimental error, this result is identical to that of the 1H NMR titration and identical to the values obtained from the other carbons around the ring. However, the error increases to (0.014 for ∆pKa as obtained from C4. There is a decrease in precision as the nuclei being observed become more distant from the site of deprotonation and the difference in the limiting 13C chemical shifts becomes smaller. Nevertheless, high precision can be obtained with as few as six points in the titration using 13C spectroscopy. The ∆pKa between the two stereoisomers of 2 was previously measured in methyl cellosolve,31 2:1 dimethylformamide/water,7 methanol, and water.30 The values are 0.48, 0.44, 0.38, and 0.45, respectively, with the trans stereoisomer 2t the more acidic. The last value is in excellent agreement with that obtained from the NMR titration in aqueous methanol. The high degree of accuracy and precision by which the ∆pKas can be determined allows for the evaluation of the thermodynamic parameters ∆∆H° and ∆∆S°. Using variable-temperature 1H NMR, these parameters were obtained for cis and trans 2 in 3:1 CD3OD/D2O. Five titrations using 1H NMR spectroscopy were performed at temperatures of 15, 22, 33, 41, and 56 °C (Table 4 and Table S4 in supporting information). A van’t Hoff plot of -ln K vs 1/T gave a slope of -422 ( 17 K and an intercept of 0.38 ( 0.06, which correspond to a ∆∆H° ) (HC-° - HCH°) (HT-° - HTH°) of -0.84 ( 0.03 kcal/mol and ∆∆S° of 0.76 ( 0.11 cal/mol‚K. To further demonstrate the flexibility and convenience of this methodology the ∆pKas of the conjugate acids of all four stereoisomers of 2-decalylamine 3 were determined in a single 1H NMR titration experiment. Figure 4 shows the H2 region in the 1H NMR spectra of a mixture of the four 2-decalylamine 3 stereoisomers at the beginning and end of a titration. All four peaks are observed to move downfield without ever crossing. The ∆pKas between all pairs of stereoisomers were calculated from six linearized plots of the chemical shifts (Table S5, supporting information). Figure 5 shows all of the linearized plots of the chemical shifts of the cis,cis stereoisomer 3cc vs the chemical shifts of the other three stereoisomers. 3cc was found to be the most basic. The three other stereoisomers, cis,trans 3ct, trans,cis 3tc, and trans,trans 3tt were found to be less basic by 0.012 ( 0.003, 0.037 ( 0.004, and 0.141 ( 0.005 pK unit, respectively (Table 5). It is remarkable that the basicities of four so similar compounds can be distinguished so precisely in a single experiment. For comparison to the four-component titration, separate mixtures of the two trans stereoisomers of 2-decalylamine 3tc and 3tt and of the two cis stereoisomers 3cc and 3ct were each titrated with DCl in 3:1 CD3OD/D2O. The results are included in Table 5 and Table 5S (supporting information). From the titration of the trans stereoisomers, the ∆pKa was determined to be 0.104 ( 0.002, with the trans,cis stereoisomer the more basic. This is somewhat lower than the value of 0.23 previously determined in (31) Tichy´, M.; Jona´sˇ, J.; Sicher, J. Collect. Czech. Chem. Commun. 1959, 24, 3434-3440.
Table 5. ∆pKas from Linearized Plots of 1H NMR Chemical Shifts from Titration of the Four Stereoisomers of 2-Decalylamines 3 in 3:1 CD3OD/D2O at 25 °C
a
stereoisomers compared
slope
y-intercept
corr coeff
∆pKa
cis, trans vs cis, cis cis, trans vs cis, cisa trans, cis vs cis, cis trans, trans vs cis, cis trans, cis vs cis, trans trans, trans vs cis, trans trans, trans vs trans, cis trans, trans vs trans, cisa
1.028 ( 0.007 1.034 ( 0.003 1.090 ( 0.011 1.382 ( 0.015 1.061 ( 0.009 1.346 ( 0.011 1.268 ( 0.009 1.271 ( 0.012
0.0002 ( 0.0003 0.0001 ( 0.0001 -0.0003 ( 0.0005 0.0004 ( 0.0005 -0.0005 ( 0.0004 0.0002 ( 0.0004 0.0008 ( 0.0004 0.0002 ( 0.0002
0.99975 0.99997 0.99937 0.99927 0.99954 0.99957 0.99967 0.99986
0.012 ( 0.003 0.015 ( 0.001 0.037 ( 0.004 0.141 ( 0.005 0.026 ( 0.004 0.129 ( 0.004 0.103 ( 0.003 0.104 ( 0.002
Separate titration of only two stereoisomers.
Table 6. ∆pKas from Linearized Plots of 1H NMR Chemical Shifts of trans,trans- and trans,cis-2-Decalylamine 3 and of cis- and trans-4-tert-Butylcyclohexylamine 1 in 3:1 CD3OD/D2O at 25 °C amines compared 1c vs 1t 1c vs 3tc 1c vs 3tt 1t vs 3tc 3tt vs 1t 3tt vs 3tc
slope
y-intercept
1.318 ( 0.004 0.0001 ( 0.0002 1.359 ( 0.006 0.0001 ( 0.0002 1.070 ( 0.004 0.0002 ( 0.0001 1.031 ( 0.004 0.0000 ( 0.0002 1.233 ( 0.004 -0.0001 ( 0.0001 1.270 ( 0.004 -0.0002 ( 0.0001
corr coeff
∆pKa
0.99994 0.99989 0.99992 0.99991 0.99994 0.99994
0.120 ( 0.001 0.133 ( 0.002 0.029 ( 0.002 0.013 ( 0.002 0.091 ( 0.001 0.104 ( 0.001
Table 7. Relative pKas of the Ammonium Salts Figure 5. Linearized plot of the H2 chemical shifts, (δc,c - δC,C°)(δisomerH+ - δisomer) vs (δisomer - δisomer°) (δC,CH+ - δc,c), of the four stereoisomers of 2-decalylamine 3 during the titration of a mixture with DCl in 3:1 CD3OD/D2O at 25 °C. The cis,cis-2-decalylamine is compared to cis,trans-2-decalylamine (4), trans,cis-2-decalylamine (+), and trans,trans-2-decalylamine (O).
methyl cellosolve.29 From the titration of the cis stereoisomers, the ∆pKa was determined to be 0.015 ( 0.001. Within the small experimental errors, these values are identical to those from the four-component titration. A second four-component titration containing the two trans stereoisomers 3tc and 3tt and the two stereoisomers of 1 was performed in 3:1 CD3OD/D2O (Table S6, supporting information). The trans,cis-2-decalylamine (3tc) was found to be the most basic and amines 1t, 3tt, and 1c less basic by 0.013 ( 0.002, 0.104 ( 0.001, and 0.133 ( 0.002 pK unit, respectively (Table 6). Since the observed signals in this titration are more disperse, the errors calculated are notably smaller than in the previous four-component titration. A three-component titration containing the two trans stereoisomers 3tc and 3tt and isopropylamine 4 was also performed in 3:1 CD3OD/D2O (Table S6, supporting information) to establish relative pKas of all the amines in this study. 4 was determined to be more basic than 3tt or 3tc by 0.201 ( 0.003 or 0.099 ( 0.002 pK unit, respectively. From the common comparison with the trans stereoisomers of 2-decalylamine 3tc and 3tt, the relative pKas of all the amines are tabulated in Table 7. The absolute pKas of all the amines are also tabulated, as referenced to the known absolute pKa of isopropylamine,32 but these are less precise. Thus ∆pKa between 3tc and 3tt was determined in a total of four separate titrations on four different mixtures. In the four titrations 3tc was determined to be more basic than 3tt by 0.104
amine
relative pKa
pKa
isopropylamine (4) cis,cis-2-decalylamine (3cc) cis,trans-2-decalylamine (3ct) trans,cis-2-decalylamine (3tc) trans-4-tert-butylcyclohexylamine (1t) trans,trans-2-decalylamine (3tt) cis-4-tert-butylcyclohexylamine (1c)
≡0.000 ( 0.004 -0.060 ( 0.005 -0.072 ( 0.004 -0.098 ( 0.002 -0.110 ( 0.001 -0.201 ( 0.003 -0.230 ( 0.002
10.63a 10.57 10.56 10.53 10.52 10.43 10.40
a
Reference 32.
( 0.002, 0.103( 0.003, 0.104 ( 0.001, and 0.103 ( 0.002 pKa unit. All of the results of the four titrations are identical within a very small error. It is remarkable that this difference in acid dissociation constants can be determined with such great reproducibility. This is a consequence of the high precision with which chemical shifts can be measured on a 500-MHz NMR spectrometer. However, lower field spectrometers are more than adequate for accurate measurement of ∆pKa. SUMMARY AND CONCLUSIONS A new methodology has been demonstrated where the difference in pKa between two or more compounds is determined from a single NMR titration experiment. Using either 1H or 13C NMR, the ∆pKas between components of a stereoisomeric mixture were obtained with high precision and accuracy. The excellent precision was confirmed in four titrations of the trans-2-decalylamines in which four different mixtures all gave results within 0.002 pK unit of one another. Likewise, multiple titrations of mixtures containing the two stereoisomers of 4-tert-butylcyclohexylamine all gave results within 0.001 pK unit. The ∆pKas determined were (32) Hall, H. K. J. Am. Chem. Soc. 1957, 79, 5441-5444.
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also in excellent agreement with those previously listed in the literature in similar solvent systems. From these results it is therefore reasonable to conclude that this methodology provides a greater level of precision and accuracy than that achieved by methods relying on a glass electrode. The measurement of ∆pKas by NMR titration also proved to be more convenient and less cumbersome than most other methods presently available. This convenience is further enhanced by the ability to acquire multiple ∆pKas in a single experiment, as demonstrated in the two four-component and one three-component titrations. Variability normally induced by titration, solution inhomogeneity, and pH calibration were eliminated by use of this methodology. The flexibility to determine ∆pKa in aprotic solvents by this method was also demonstrated. Lastly, thermodynamic parameters ∆∆H° and ∆∆S° were determined using variable-temperature NMR.
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ACKNOWLEDGMENT This research was supported by National Science Foundation Grants CHE90-25113 and CHE94-20739. Purchase of the 500-MHz NMR spectrometer was made possible by NIH Grant RR04733 and NSF Grant CHE88-14866. SUPPORTING INFORMATION AVAILABLE Tables S1-6 of chemical shifts during titrations (4 pages). Ordering information is given on any current masthead page. Received for review February 5, 1996. Accepted April 1, 1996.X AC960117Z X
Abstract published in Advance ACS Abstracts, May 15, 1996.
