THE pka OF PROTONATED CARBOXYLIC ACIDS. T. S. SORENSEN Department of Chemistry, University of Alberta, Calgary, Alberta

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Department of Chemistry, University of Alberta, Calgary, Alberta Received October 20, 1963

ABSTRACT T h e pK, of three, protonated a,O-unsaturated carboxylic acids have been determined from their ultraviolet absorption curves by using several of the well-known empirical methods. A detailed study of the absorptiorl curves has been attempted in order to learn more about the "solvent effect" inherent in this spectral method of calculating pK, values. Methyl substitution a t the p-carbon of the acid results in large differences in the calculated pK,.

The pKa of protonated o- (1) and $-substituted (2) benzoic acids and of propionic (3) and acetic (4) acid have been reported. These values range from -6.2* to -8.6 for phthalic acid and m-nitrobenzoic acids (the extremes for substituted benzoic acids which have been measured), -6.4 for acetic acid and -7.3 for propionic acid. The values for acetic and propionic acids are likely to be only approximate since the ultraviolet transition used in the measurement (n + a*) is weak and in the region of the spectrum where stray light and other effects can cause erroneous absorption. We have measured the complete accessible ultraviolet spectral curves for acrylic, crotonic, and P,P-dimethylacrylic acids in a wide range of sulphuric acid -water mixtures and have used these measurements to calculate the respective pKa values by several different techniques. In addition, the roughly Gaussian shape of the spectral curves allows us to make an investigation of the "solvent effects" which appear as a serious complication in many pKa determinations using ultraviolet spectroscopy t o determine the concentration of the unprotonated and protonated species. The structure of the protonated carboxyl group has been discussed by Stewart and Yates (2) and by Palmer and Urch (5) and is considered to have a symmetrical structure, e.g. I for protonated crotonic acid.

A pK, value is a measure of the stability of the protonated form of a base relative to the unprotonated form, but since there is not likely to be much difference in energy between the unprotonated molecules, differences in pK, can be attributed to differences in the stability of the protonated forms. I t is to be expected that the substitution a t carbon 3 of the oxonium ion I will cause some difference in the stability of this ion (tertiary > secondary > primary) but the magnitude is unknown. Except for a very weal; band (n + T*) which is hardly observable (6), the only accessible ultraviolet absorption in solutions of a,p-unsaturated acids is the intense T -+ a* *All literature pK, values are corrected by using the new HOscale i n ref. 14. Canadian Journal of Chemistry. Volume 42 (1904)


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transition. This absorption band is very satisfactory for pKa measurements except for acrylic acid where the A,, in water is a t 1940 A, only some 100 A above the cutoff point of the instrument and therefore subject to the usual inaccuracies. I t has been reported (7) that Beer's law is not valid for the absorption spectra of certain a,@-unsaturatedacids in ethanol solution. We have checked Beer's law for crotonic acid in 50% sulphuric acid and find that it holds well. The reported deviations are likely instrumental since these results were obtained with machines with effective cutoffs a t 2100 A. We have made recovery and dilution experiments to verify that the spectrum we have recorded is not due to some irreversibly formed decomposition product. Solutions of P,P-dimethylacrylic acid underwent decomposition (decreasing ultraviolet absorption with time) with certain concentrations of sulphuric acid but no difficulty was encountered with crotonic and acrylic acids. We were able to obtain rough kinetics for this decomposition and t o extrapolate the spectra to zero time. RESULTS

The complete spectra for crotonic acid are shown in Fig. 1 plotted in wave numbers.

FIG.1. Ultraviolet spectra of crotonic acid in aqueous sulphuric acid, % w/w sulphuric acid, curves from left to right, 0, 49.2, 58.9, 67.7, 73.2, 77.8, 82.2, 96.2. The tabulated data for these curves (A,,,, em,,, and Av) as well as those for the other two acids are given in the Experimental section. A number of methods can be applied in using these curves t o calculate pK, values. Plots of EB vs. HOand E B H + VS. HOall give sigmoidshaped curves although the calculated pKa in each case is not exactly the same. The procedure of Davis and Geissman (8), which has been most widely used, was applied to the absorption curves for each acid and is shown in Fig. 2 for crotonic acid. I t is difficult t o decide where the midpoint of the signloid curve is situated and in these cases Stewart and Granger (1) have shown that a plot of log (AD,,+-AD)/(AD-AD,) versus Ho gives a straight line from which the pK, can be directly located. We have also used this method to calculate the pKa values. The remarkable thing about these plots is that they appear to be exact (a straight line is obtained) but the slope of the line is considerably less than unity.

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FIG.2. pK. calculation using the procedure of Davis and Geissman. FIG.3. A plot of the half-width, Av, for the absorption curves of crotonic acid in aqueous sulphuric acid solutions, against the Ho of these solutions.

Slopes of less than-unity have been found for a number of other carbonyl compounds (9), so-called "non-Hammett bases". Finally the half-widths, Av, of each curve, over the whole Ho range, have been plotted against Ho and, as shown in the following discussion, a rough pKa canlbe calculated from this. The shape of this plot for crotonic acid is shown in Fig. 3. The calculated pKa values, by each method, are collected in Table I along with the observed slopes determined by using the treatment of Stewart and Granger. DISCUSSION

I t is somewhat disturbing that qualitatively there is no real indication of two peaks in any of the complete absorption curves for P,P-dimethylacrylic and crotonic acids as shown in Fig. 1. Similar difficulties have been reported (10) in attempting to measure the pK, of protonated anisole. T h e spectral curves of acrylic acid show somewhat better behavior (in that an approximate isobestic point is observed) but unfortunately we cannot measure the complete curves. Vandenbelt and Henrich (11) have calculated the combined curves resulting from the mixing of two Gaussian curves, varying the separation of the curves and the ratio of the two in the combined curve. If the separation is small definite shoulders or inflection points are not obvious in the combined curve, e.g. if two identically shaped curves have a Av of 3 units and if the separation is 2 units, the combined curve also looks roughly Gaussian in shape. The AV of the combination curve is increased to 4 units, however, if the two


TABLE I pK, of protonated or,@-unsaturatedacids

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Method of pK, determination




Davis and Geissman Stewart and Granger AV versus Ho Slo~e

-6.15 -6.18 -5.8 0.73

-7.55 -7.55 -7.2* 0.90

-5.4 -5.35 -4.9 0.67

*Peak width at three-quarters peak height.

separate curves are of equal height. The presence of what appears to be a single peak need not cause any concern therefore except inasmuch as the component curves must be separated by amounts similar to those discussed above. The curves for these a,p-unsaturated acids in aqueous sulphuric acid, where the Ho of the solution is equal to the pKa, must by definition be composed of equal parts of the curve due to the free base and that due to the protonated base. If a curve fitting is made, assuming constant E,, and shape for the component curves, it can be shown that the A,, for the absorption curve due to unprotonated acid shifts strongly to the red and that due to the protonated acid (with reference to the peak position a t the pKa point) also shifts, although less than the unprotonated species, to the red. The general theory (12) of solvent effects on K --+ T* transitions of this type predicts that a red shift of the absorption curve of unknown magnitude should be observed for the unprotonated molecule but the protonated molecule, being a charged species, is expected to be rather insensitive to solvent polarity. The red shift of the "free" carbonyl absorption peak has been noted by many workers in this field, beginning with Hammett (13). I t has also been noted that the peak for the protonated carbonyl species shifts to the red with increasing acid concentration and also increases in intensity (1). In our spectral curves, the increase in intensity is paralleled by a decrease in Av, so that the integrated intensity remains nearly constant. If two identical Gaussian curves overlap strongly the combined curve will have a maximum Av when the two contributing curves are present in equal amounts. We have therefore plotted Av for the curves of Fig. 1 against HOand have calculated a pKa by: (1) neglecting slight errors due to the different Av of the two contributing curves; (2) assuming that the shape of curves for the protonated and unprotonated base do not change with the Ho of the solution; and (3) that within the 0.1-0.3 Ho units involved, a plot of log BH+/B versus Ho is linear with unit slope so that in the case where EB is somewhat different from EBH+, a pK, can still be calculated. Since the individual curves must by definition be rising and falling very rapidly in the region of the pK,, the assumptions which have been made do not have much effect on the value of the pKa which is calculated. The pK, values calculated in this manner agree fairly well (0.3-0.4 pK, units lower) with those obtained by the Davis and Geissman method. This method of calculating pKa values should be applicable to systems where the optical density of the absorption curves are decreasing rapidly with time, providing the time required to make the spectral measurements is fast relative to this decomposition and also that the decomposition products do not absorb themselves. The calculated pKa values are in the range reported for other carboxylic acids and a large difference, 1 pK, unit, is observed between the successive members of this series. This would imply that the double bond is considerahly delocalized by resonance with the

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protonated carboxyl group. This difference can be compared with the difference in pK, between protonated benzoic acid (-7.65) and the P-methyl ( - 7 . 2 5 ) substituted acid. The decomposition of p,p-dimethylacrylic acid was found to be catalyzed by ultraviolet light. In the absence of light the reaction, as measured by the decrease in,,,,E was found t o be approximately first order and in all cases where there was appreciable reaction, a steady state was reached where no further decoinposition occurred. At low HOvalues the rate of decomposition was slow but the position of the equilibrium was allnost completely on the side of a non-absorbing species. As the concentration of sulphuric acid increases the rate of deco~npositionincreases but the position of the equilibrium shifts in favor of the a,p-unsaturated acid. This decomposition can be satisfactorily explained as a simple hydration (equation I) since the hydrated species would have virtually no ultraviolet absorption.



H ' Equation I

EXPERIMENTAL Ultraviolet measurements were obtained from a BeckmanDK-1 spectrophotometer which had been checked for accuracy of intensity and wavelength (down t o 2200 A). T h e stray light performance of this machine w a s investigated and this effect can cause errors in the region of the absorption curve near the cutoff point of the machine (1850-1950 A). No correction has beep applied b u t the curves for acrylic acid are the only ones appreciably affected. The scan speed was 100 A/minute except where decomposition was occurring when a speed of 500 A/minute was used. All peak maxima were rerun and a n expanded scale was used in order to obtain maximum accuracy. T h e samples were not thermostated but the temperature did not vary much (22f.2" C). The solutions were measured in 0.1 cm "suprasilica" cells, with a solvent blank in the reference cell of the same composition as t h a t in the sample cell. A base-line correction was made where necessary by measuring spectra with only solvent in both ~.ells.The curves for P,P-dimethylacrylic acid have been corrected back to zero time. T h e optical density of the absorption curve was determined a t time intervals measured from the time of preparation of the solution. A rough check was made on curves where substantial decrease in optical density had occurred to make certain t h a t no extraneous absorption was appearing. I t was observed t h a t decomposition was more rapid when the sample stayed in the cell compartment with ultraviolet light shining on i t than when the sample was kept in the dark. Measurements were continued until a steady state was reached where no further decomposition occurred. The kinetics (as measured by the decrease in optical density in the dark) were approximately first order and the E,,, of the curves for this acid have been corrected. On fast scan, the time necessary to record most of the absorption (1 minute) is short compared to the decomposition rate. Some rough values for the kinetics of the decomposition are:

70Sulphuric acid 63.76 70.35 73.16 77.79

Half-life of decomposition, T1Iz(min) ca. 90 ca. 28 ca. 14 ca. 7

Equilibrium position, % a,P-unsaturated acid Small 38 55 83

All curves were measured in duplicate and if the average error for the calculated,,,E was more than 295, repeat measurements were made. Tabulated data from the absorption curves are collected in Table 11. Solutions were prepared by weighing out 0.3-0.5 mg of the carboxylic acid on a small glass boat, with a microbalance. This boat was added t o the solvent previously made up to mark in a volumetric flask. Aqueous sulphuric acid solutions were titrated against standard base. The Hammett acidity function Ho for a given percentage of sulphuric acid was taken from the recent data of Jorgenson and Hartter (14).

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The absorption spectra of these carboxylic acids in 100% sulphuric acid are not unusual except in the case is a t considerably shorter wavelengths than in 98% sulphuric of p,p-dimethylacrylic acid where the A,, acid. Evidently some other change has occurred in this solvent but we have not investigated this. Unchanged carboxylic acid can be recovered from its concentrated sulphuric acid solutions. A more quantitative measurement of any decomposition was obtained by dilution experiments. Solutions of the carboxylic acids were prepared and the spectrum measured with 0.1 cm cells. This same solution was diluted 10-fold with ice and water and the spectrum (taken in 1 crn cells) was compared with that of the carboxylic acid in this medium (approximately 10% sulphuric acid). A quantitative recovery was calculated for crotonic acid; for p,p-dimethylacrylic and acrylic acids the recovery was better than 90%. p,P-Dimethylacrylic and crotonic acids were recrystallized from water, m.p. 69-70' C and 72-73' C respectively. Acrylic acid was redistilled a t reduced pressure and kept below 0" C. REFERENCES 1. R. STEWART and M. R. GRANGER.Can. J. Chem. 39, 2508 (1961). and K. YATES. J. Am. Chem. Soc. 82,4059 (1960). 2. R. STEWART 3. J. T. EDWARD and I. C. WANG. Can. J. Chem. 40,966 (1962). 4. A. K.GOLDFARB, A. MELE,and N. GUTSTEIN.J. Am. Chem. Soc. 77,6194 (1955). 5. M, H. PALMER and D. S. URCH. J. Chem. Soc. 174 (1963). 6. W. D. CLOSSEN,S. F. BRADY, E. M. KOSOWER, and P. C. HUANG. J. Org. Chem. 28, 1161 (1963). and I. ORTEGA.J. Am. Chem. Soc. 73,1564 (1951). 7. H. E. UNGNADE 8. C. T. DAVISand T. A. GEISSMAN.J. Am. Chem. Soc. 76,3507 (1954). 9. J. T. EDWARD and I. C. WANG. Can. J. Chem. 40,966 (1962). A. R. KATRITZKY, A. J. WARING,and K. YATES. Tetrahedron, 19,465 (1963). and C. Y. Wu. J. Am. Chem. Soc. 82,5660 (1960). 10. E. M. ARNETT 11. J , M. VANDENBELT and C. HENRICH.Appl. Spectroscopy, 7, 173 (1953). 12. N. S. BAYLISSand E. G. MCRAE. J. Phys. Chem. 58, 1002 (1954). 13. L. A. FLEXSER, L. P. HAMMETT, and A. DINGWALL.J. Am. Chern. Soc. 57, 2103 (1935). and D. R. HARTTER.J. Am. Chem. Soc. 85,878 (1963). 14. M. J. JORGENSON