The Perils of Carbonic Acid and Equilibrium Constants William P. Jencks and Rachel A. Altura Graduate Department of Biochemistry. Brandeis University. Waltham. MA 02254 We all learn that water usually contains dissolued carbon dioxide. Or do we? I t is well known that pyridine and substituted pyridines undergo some sort of association behavior in aqueous solution. One manifestation of this is the downward curvature with increasing concentration of the pyridine in plots of observed rate costants for reactions of phosphate esters with phosphorylated pyridines.'s2 This behavior is especially troublesome for the larger substituted pyridines, such as 4dimethylaminopyridine, which shows marked curvature a t low buffer concentrations. The curvature can be accounted for by self-association of 4-dimethylaminopyridine to give a dimer, with a dissociation constant of Kd = 9 M-' (eq 1).
In alcohol, or mixed aqueous-organic solvents, anew peak in the ultraviolet absorbance spectrum appears as the concentration of 4-dimethylaminopyridine or related compounds is varied. The spectra of solutions with different concentrations of 4-dimethylaminopyridine show an isoshestic point that is consistent with the equilibrium formation of acomplex between twospecies in the solution (Fig. l). Very similar results were reported previously with increasing concentration of 4-dimethylaminopyridine in methanol.3 The dimerization hypothesis was further supported by use of the method of Zanker4to determine the association numher of aggregates by plotting log [ d l - &,)I against log [c,(r - r,)/c,], in which c, is concentration and c, and c, are the extinction coefficients of the nth polymer and monomer at the same wavelength. Such plots were linear over a range of more than 103with a slope of 2, which is consistent with the formation of 1:l complexes for 4-aminopyridine and for 4-dimethylaminopyridine.3 Figure 2 shows that similar results are obtained with increasing water concentration a t a constant substrate concentration in a series of ethanol-water mixtures. Aeain there is an isosbestic point, confirming earlier results;? Further investiration of this heno omen on was of s ~ e c i a l interest because ;he equilibrium can be measured a i very low concentrations, on the order of 10-5 M. This i m ~ l i e an s extremely favorable equilibrium constant for self-aswciarion.'l'he fart that thesperies formed at high concentrations of 4-dimethylaminopyiidine is also the species favored at high ethanol concentration suggested that the association reaction is favored by organic solvents. Indeed, dimethylaminopyridine at 5 X 10-5 M is almost completely converted to this form in pure ethanol.
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70% acetonilrile:30%water (w).
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Brandeis publication no. 1657. 'Kirby, A. J.; Jencks, W. P. J. Am. Chem. Soc. 1965, 87, 32173224. SkoOg, M. T.: Jencks, W. P. J. Am. Chem. Soc, 1984, 106,75977606. Kaneko, C.: Shiba. K: Jugii. H. Heterocycles 1981. 15, 11951198. Zanker, V. Z.Phys. Chem. 1952,200, 250.
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Fmgure 2. Spectra of 5 X 10.' M Cdlmethylamlnoprldlne in &nol-water rninures Tne ethanol:water ratios (v:v) are 11) 100. (2) 9 1. (3)82. (41 7:3.(5) 6:4, (6)5:s.
Several interestine hv~othesescan be considered to account for such resulk. simple association from "hydrophobic" interactions, which are often invoked to explain association in aqueous solution, should he weakened rather than strengthened by the addition of organic cosolvents. This would be expected for "classical" hydrophobic interactions involving changes in water structure and also for association that is brought about by favorable van der Waals or London dispersion forces between solutes, which are less favorable in aqueous-organic mixtures. This raises the possibility that the interaction is brought about by dipole-dipole interactions, which would be expected to he stronger in a solvent of
Thus, the "dimerization" is simply an acid-base reaction. It arises largely from dissolved carbon dioxide and carbonic acid in water (eq 2).
mo; +
Figure 3. Spectra of 1.6 mM 4dimelhyiaminopyridinein water (palh lengm = 0.05 cm). (1) 1 mM potassium hydraxlde. (2) boiled glassdistilled water. (3) gladistilled water. (4)glassdistilled water saturated with carbon dioxide.
lower dielectric constant. Another hypothesis is that i t represents preferential hydrogen bonding to the monomer in aqueous solution. These curious results were investigated further because of their relevance to the problem of the nature of interactions between solutes in aoueous solution. These interactions are important because they provide the driving force for the binding of substrates to enzvmes. . . the maintenance of the native structure of biological macromolecules, and many other imoortant ohenomena. The earlier work was reproduced and extended to other solvent mixtures. However, we found it difficult to obtain constant values of the equilibrium constant for dimerization at different roncentrationsof thepyridine. It did not help to posiulate different aggregation numhers. Furthermore, the data were not strictly reproducible in different experiments. Further work showed that the rcsultsdepend on the history and purity of the solvent used in the experiments. Glassdistilled water cave a variable amount of thesnecies absurbing at high wavelength, while organic solvents gave predominantlv the low-wavelength soecies. However. the oroduct was predominantly the l&wkelength species, especially a t higher substrate concentrations, if the water was boiled hefore the experiment. Addition of M potassium hydroxide gave complete conversion to the low-wavelength species. Bubbling carbon dioxide into the water gave complete conversion to the high-wavelength (Fig. 3). Further. species . more, it was noted that the spectrum of the-"dimer" measured at high concentrations corresponds to the spectrum of the free base of 4-dimethvlaminonvridine.while the soectrum of the "monomer" o6served &dilute squeous solukon corresponds to that of protonated 4-dimethylaminopyridine. A series of experiments with increasing concentrations of 4-dimethylaminopyridine up to 10-2 M in alkaline solutions of EtOH, and EtOH-H20 mixtures, using a shortpath-length cell for spectroscopy, showed no indication of spectral changes due to aggregation. Experiments with reagent-grade acetonitrile also gave two peaks with 4-dimethylaminopyridine. However, HPLCgrade acetonitrile gave only a single peak, and the results with the reagent-grade solvent were traced to an acetic acid impurity.
M ~ , N ~ N H(2)+
I t is "well known" that water in the laboratory always contains dissolved carbon dioxide, unless special precautions are taken to remove it. Dissolved carbon dioxide can be removed by boiling the water. Carbon dioxide is not the only problem. There is also a contribution from "hydrolysis" of the pyridine base. When moderately strong bases are dissolved in water, they will remove a proton from water to give hydroxide ion and a significant concentration of the protonated base, even in the absence of dissolved carbon dioxide. The hydrolysis is described by the dissociation constants for the protonated base, K., and for water, K,, according to eq 3 and 4.
(4) The pK, of protonated 4-dimethylaminopyridine is 9.7, which gives KB = 5 X 10-5M. Thus, for 10-'M 4-dimethylaminopyridine dissolved in pure water, there will be equal amounts of the orotonated and free base snecies because of hydrolysis. For the experiment shown in Figure 3, with 1.6 mM 4-dimethylaminopyridine, eq 4 predicu that 16%of the added base will beconverted toBH7asaresult ofhydrulysis. This is the same as the observed difference in BH' concentration in samples 1and 2, measured at the absorption maximum of BH7 on the riaht side of the fiaure. Since the extinctioncoefficients of t6e base and protonated species of 4-dimethylaminopyridine are >lo4, spectrophotometric experiments are often carried out in the concentration range in which hydrolysis produces a larger amount of the protonated species. Hydrolysis is less important for bases with a smaller extinction coefficient, because they are studied at higher concentrations. It is also important to remember why dissolved carbon dioxide is an acid. The apparent pK, of carbonic acid in buffers, prepared by adding a strong acid to bicarbonate, is 6.4. However, the true pK, of carbonic acid is 3.8. Approximately 99.8% of carbonic acid in water dehydrates to give dissolved carbon dioxide. Thus, the apparent pK, of 6.4 represents the dissociation of a relatively strong acid of pK. = 3.8 at a concentration that is only -0.2% of the concentration of carbon dioxide in solution.5 Conclusion I t is important to remember (1)that the small amounts of carhon dioxide that are usually present in water can have large effects on acid-base equilibria of dilute solutions and (2) that dilute solutions of most weak acids and bases undergo'significant dissociation or protonation ("hydrolysis"), respectively, when they are dissolved in water. Edsall. J. T.: Wyman, J. Biophysical Chemisby; Academic: New York. 1958: p 558.
Volume 65 Number 9
September 1988
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