The Structure of Aqueous Rhodizonic Acid (32) S. A. Rice and M. Nagasawa, “Polyelectrolyte Solutions”, Academic Press, New York, N.Y., 1961. (33) M. Nagasawa and L. Kotin, J . Am. Chem. SOC.,83, 1026 (1961). (34) J. J. van der Klink, L. H. Zuiderweg, and J. C. Leyte, J. Chem. phys., 80, 2391 (1974). (35) J. C. Leyte and J. J. van der Klink, J. Chem. Phys., 82, 749 (1975). (36) In spite of ref 25-31, the physical picture of this problem is still being clarified. See ref 18 and 31. (37) S. Lifson and A. Katchalsky, J . Polym. Sci., 13, 43 (1954). (38) G. S. Manning and B. H. Zimm, J . Chem. Phys., 43, 4250 (1965).
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(39) A. Kowblansky, R. Sasso, V. Spagnola, and P. Ander, Macromolecules, 10, 78 (1977). (40) S. Oman and D. Dolar, Z . Phys. Chem. (Frankfurf am Main), 58, 1 (1967). (41) D. Korak, J. Kristan, and D. Dolar, Z . Phys. Chem. (Frankfurf am Main), 78, 85 (1971). (42) A. Takahashi, N. Kato, and M. Nagasawa, J. Phys. Chem.,74, 944 (1970). (43) S. Oman, Makromol. Chem., 178, 475 (1977). (44) Th. Odijk and M. Mandel, private communication.
The Structure of Aqueous Rhodizonic Acid R.
I. Gelb, L. M. Schwarfz,* and D. A. Laufer
Department of Chemistry, University of Massachusetts, Boston, Massachusetts 02 125 (Received April 14, 1978)
An investigation of the dissociation of aqueous rhodizonic acid dihydrate H2C606.2H20is made by temperature-dependent pH potentiometric titration and I3C NMR spectroscopy. The standard molar entropies for the first and second acid dissociations are found to be -4.6 f 0.8 and 11 f 1cal mol-’ K-’, respectively. These values, when compared to standard entropies of other oxocarbon acid dissociations and other carbonyl dehydration reactions, confirm the hypothesis that the two chemically bound water molecules dissociate along with the second acid dissociation. The NMR spectra indicate that the ortho-dihydrated rhodizonic acid slowly isomerizes to a more stable para-dihydrated structure and that the slow approach to equilibrium observed in the aqueous rhodizonic acid system in the pH range 3-6 is due to this isomerization.
Introduction The physical chemistry of aqueous rhodizonic acid H2C6o6.2H20(I) has been the subject of several investi-
.2H20 0
I
gations in the past. The most recent of these by Patton and West1 reviews the studies made prior to 1970 and reports spectrophotometric pK values of 4.25 f 0.05 and 4.72 f 0.07 for the primary and secondary acid dissociations, respectively. Also, Patton and West interpret the slow rate of equilibration observed between pH 3 and 6 as due to a slow hydration of the unhydrated rhodizonate dianion to form dihydrated monoanion and dihydrated acid. In our laboratory, we have made a study of the homologous five-membered ring compound H2C505 (croconic acid) and have utilized I3C NMR methods2 to detect the simultaneous existence of anhydrous H2C5O5 and a monohydrated species in strongly acidic media and to determine the partition coefficient between the two. This I3C NMR study was prompted by our previous determination3 of an anomalously positive value for the standard entropy change of the primary dissociation of croconic acid and this anomalous entropy change was then explained in terms of a high positive entropy of dehydration accompanying the dissociation. In this communication, we wish to report the extension of this methodology to the case of rhodizonic acid. We have determined the standard entropy change for both dissociations by pH potentiometric measurement of the temperature dependencies of the dissociation constants. These entropy change values, when compared with analogous quantities for other oxocarbon acids, indeed, 0022-365417812082-1985$01 .OO/O
TABLE I : Rhodizonic Acid Dissociation Constants from pH Potentiometric Titrations temp, C PKI PK, S~K,a S~K,(I O
10 15 20 25 25 25 25b 30 35
4.502 4.492 4.449 4.377 4.372 4.391 4.372 4.332 4.257
i 0.004 i0.005 -L. 0.005 t0.005 t0.007 t 0.008
k0.004 k 0.006
i 0.004
5.094 4.925 4.804 4.661 4.662 4.655 4.631 4.544 4.454
i 0.004
t 0.005 k 0.005 ?: 0.005
i 0.004 i 0.005 ?: 0.006
t0.006 +0.005
Standard error estimate of pK parameters. Titration of H,R with NaOH. All other entries are K,R titrated with HCl. corroborate the Patton and West conjecture that both aqueous rhodizonic acid and the monoanion are doubly hydrated whereas the dianion is unhydrated. A 13C NMR study of aqueous rhodizonic acid solution seems to indicate the existence of two distinct dihydrated species, but one appears to be unstable with respect to isomerization to the other so that an equilibrium coefficient is not measurable by NMR. pH Potentiometric pK Determinations
We have measured both pKl and pK, at several temperatures between 10 and 35 “C by titration of aqueous solutions of dipotassium rhodizonate (K2R) with standardized HC1. The thermodynamic (zero ionic strength) pK1 and pK2 values were found from the pH vs. HCl volume titration data by an elaborate computational procedure necessitated by two complicating circumstances: (1)The proximity of pK1 and pK2 values precluded the usual approximation that only two of the three species R2-, HR-, and H2R concurrently exist at substantial concentrations in any given solution. (2) Both pH and volume data were recorded with equally high precision (about @ 1978 American Chemical Society
1986
The Journal of Physical Chemistry, Vol. 82, No. 18, 1978
R. I. Gelb, L. M. Schwartz, and D. A. Laufer
TABLE 11: Parameters, Variances, and Covariances in the Empirical Equations pK = a t b/T t c/T2 Fitted t o the Data in Table I DK,
DK.
- 18.535
a b
19.403 -1.0903 x lo4 1.2662 X lo4 C -1.7377 X lo6 1.9401 X l o 6 31.11 var(a)" 31.19 1.083 X 10' var(b )" 1.079 X l o 7 var(c)" 2.347 X 10" 2.335 X 10'' c o v ( ~ , c ) ~ 2.705 x l o 6 2.694 X lo6 cov(b,c)a - 1.594 x lo9 -1.587 X lo9 a Based on the variance of residuals about the fitted curves which were 1.484 X and 1.386 x l o v 4 for pK, and pK,, respectively.
0.1 %) so that neither variable could be regarded as having less statistical certainty than the other. This invalidated the contrary assumption required by usual least-squares regression procedures. An exposition of the model equations, computational strategies, and statistical analysis of titration data recorded in these experiments has been reported in detail in a separate communication4and so will not be repeated here. The results of nine titrations of KzR with HC1 and of one titration of HzR with NaOH are given in Table I. The standard error estimates calculated for the pK parameters are approximately 0.005 pK units and so we note that our 0.1% precision has been propagated into these parameter values. To find the standard thermodynamic functions AHo and ASo, we fit each set of ten pK data in Table I to power series polynomials in (1/T) K-l by successively increasing the degree of the polynomial. The fitting was done by a weighted leastsquares regression technique using weighting factors inversely proportional to the squared standard error estimates given in Table I. After each successive polynomial was calculated, the quality of the fit was examined by a statistical F test5 to see if the additional higher order term was justified by a corresponding decrease in the variance of the residuals. The appropriate polynomials in both cases were found to be quadratic, Le., of the form pK = u + b/T + c / P . This least-squares analysis also provided variance and covariance estimates for the parameters a, b, and c. All these empirical results are given in Table 11. To calculate the functions AHo and ASo at 25 "C for both dissociations, we applied the well-known thermodynamic relationships to the pK vs. 1 / T polynomial to derive AHo= 2.303R(b 2c/T) and ASo = 2.303R(-a + c / P ) . To estimate statistical uncertainties for AHo and ASo, we calculated the variances from these formulas. Propagation-of-variance procedures5 yield the estimates var(AHo) N (2.303R)z[var(b) + -+ 4 var(c) + T
+
-
var(ASo) N (2.303R)2 var(a)
-
var(c) 2 +- - cov(u,c) P P
1
The standard error estimates of the uncertainties are the square roots of these variances. These results are shown in Table I11 together with comparable values for H2C505 and H2C404.The squaric acid results were taken from our previous investigation^.^!^ The most interesting new H2C606results are the ASzo = +I1 eu mol-l, an extremely positive value in comparison to the ASz' values of the other oxocarbon acids, while ASl' is not greatly different than ASl' of squaric acid. The high positive ASl' value of croconic acid is some 16 eu mol-' more positive than that of squaric acid. In ref 2, we interpret this phenomenon by showing that croconic acid's primary dissociation is accompanied by loss of one water molecule and that this dehydration entropy change is probably about +17 eu mol-I by analogy with other measured carbonyl dehydration reactions. If we apply this line of reasoning to rhodizonic acid, we must conclude that the primary dissociation here involves no dehydration and to this extent is similar to squaric acid for which both H2C404 and HC40; are unhydrated.2t8 On the other hand, the secondary dissociation entropy change of rhodizonic acid is 31 eu mol-' more positive than croconic acid and 37 eu mol-l more positive than squaric acid, and these values imply that a loss of two water molecules accompanies the dissociation of the rhodizonate monoanion. These results, therefore, confirm the Patton and West1 conjecture that aqueous rhodizonic acid and rhodizonate monoanion are dihydrated but rhodizonate dianion is unhydrated.
13C NMR Measurements As with our study of croconic acid, we then attempted to measure partition coefficients between hydrated and unhydrated species using 13CNMR. Our strategy consisted of determining the pH dependence of the I3C NMR spectrum of rhodizonic acid. The displacements of the I3C resonances and the number and location of these resonances would presumably lead to information regarding the hydration reactions of rhodizonate anions. Consequently, we obtained the 13CNMR spectra of rhodizonate solutions which had been prepared by addition of portions of LiOH solution to weighed samples of solid rhodizonic acid dihydrate. In each case, data acquisition was begun immediately after solution preparation. The results of these measurements appear in Table IV. A single resonance observed at 177.9 ppm in the most basic solution (mole ratio LiOH/R = 2.00) confirms a similar observation by Stadeli et a1.8 This clearly implies that all carbons in R2- are equivalent and presumably this ion is unhydrated having &h symmetry upon delocalization of charges. In the less basic solutions, with mole ratios 1.29 and 1.51, significant proportions of HR- must exist in solution together with R2- yet the resonance at 177.9 ppm remains unchanged. Using the following reasoning we conclude from this fact that unhydrated HRcannot exceed 1% of total HR-.Since proton exchange among all unhydrated rhodizonate species would be rapid with respect to the 13C NMR time scale, an observed
TABLE 111: Thermodynamic Parameters for the Acid Dissociation Reactions at 25 "C for Oxocarbon Acids HZC606a
HZC,05C
0.80 c 0.08 4.378 c O.OOgb t 4 . 6 i 0.3 t 3.9 c 0.2 A H , " , kcal mol-' A S , " , cal mol-' K-l -4.6 * 0.8 t 9 . 5 * 0.7 2.24 i 0.01 PK, 4.652 * 0.014b -2.95 * 0.11 + 9 . 6 i 0.3 A Hz,", kcal mol-' -20.1 i: 0.4 A S , , cal mol'' K-' t11 f 1 a This work. Mean and standard deviation of four entries at 25 "C in Table I. Reference 3.
PK,
HZC40,d 0.54 c 0.06 -1.5 ? 0.1 -7.5 0.7 3.48 c 0.02 -3.0 0.5 -26.1 1.6 References 6 and 7. +_
The Journal of Physical Chemistry, Vol. 82, No. 18, 1978
The Structure of Aqueous Rhodizonic Acid
TABLE IV: C NMR Spectraa of Rhodizonic Acid and Its Anions in 5%D,O/H,O at 25 "C mole ratio C NMR resonances, ppm relative LiOH/RC to TMS
0.1 0.1 0.4 0.6 2.6 177.88 1.6 2.1 177.87 177.88 2.5 a These spectra were obtained at 67.89 MHz and employed a Bruker HX-270 NMR spectrometer. Broad line. R represents total rhodizonate species in solution. 0 0.15 0.57 0.75 1.05 1.29 1.51 2.00
191.2 191.1 191.3 191.3 191.3 191.3 191.2
142.8 143.3 -144b -145b
acquistion time, h
95.0 94.9 95.1 95.1 95.1 95.0 95.0
resonance aobsd wodld represent the weighted-averageshift of the unhydrated species involved. This is expressed as &[HzR] + 61[HR-] + 82[R2-] (1) aobsd = [HzR] + [HR-] + [R2-] where tio, al, and a2 are the intrinsic shifts of the species whose concentrations they multiply in the numerator. At LiOH/R ratios as high as 1.29 and 1.51, the undissociated species H2R must be very small and so its contribution to this equation can be neglected. We do not know a1 but it is reasonable to assume that the a2 - a1 difference is similar to the difference between analogous quantities in the H2C606system. This difference was found to be2 189.32 - 184.22 or about 5 ppm and so we estimate a1 for HR- to be about 173 ppm. This reasoning implies that in the 1.29 LiOH/R mole ratio solution, the HR- to R2proportion is about 7:3 and if HR- is totally unhydrated, the observed shift as predicted by eq 1 would be about 174.5 ppm. Yet we see no difference compared to the 2.00 mole ratio solution. Finally, if we hypothesize that some fraction of HR- is unhydrated and assume that we could detect a resonance difference of 0.1 ppm above the statistical scatter of the measurements, eq 1predicts that the fraction cannot exceed 1%. The resonances observed in the rhodizonic acid solution to which no LiOH was added are in excellent agreement with Stadeli et ala8and are consistent with an ortho-dihydrate (o-H2R.2H20)structure (11)for the undissociated
0
I987
TABLE V: C NMR Spectraa of Rhodizonic Acid and Its Anions in 5%D,O/H,O at 30 "C with Prior Equilibration
mole C NMR resonances, ppm relative to ratio LiOH/RC TMS
equilibration time,b h
0 191.1 142.8 95.0 0 0 191.3 172.7 142.9 95.1 92.7 50 0.07 191.2 172.8 142.9 95.0 92.6 50 0.07 172.4 92.6 75 0.19 172.7 92.7 50 0.27 173.0 92.8 50 0.50 173.9 93.1 50 a These spectra were obtained at 20 MHz and employed a Varian CFT-20 NMR spectrometer. The stated equilibration times correspond to the time interval between solution preparation and the start of data acquistion, which generally required about 20 h. Solutions were at ambient temperature (- 21 "C) during the equilibration period. R represents total rhodizonate species in solution which was 0.5 F in all solutions.
-
the o-HR-.2H20 concentration becomes negligible early in the data acquisition period. In other words, a slow chemical reaction is depleting the o-HR--2H20and this depletion must occur faster in the more basic solutions. This slow equilibration behavior was observed in the pH potentiometric experiments described above. Upon adding base to aqueous rhodizonic acid at the very start of the titration, we noted a very slowly decreasing pH and had to allow more than 0.5 h for equilibration. Under such conditions the amount of unhydrated R2-formed must be negligibly small and so the sluggish behavior cannot be ascribed to a slow dehydration reaction alone. In order to gain further information about this reaction, we obtained 13C NMR spectra of rhodizonate solutions which had been allowed to equilibrate for some time before data acquisition was begun. These experiments are summarized in Table V and we interpret the observed behavior in terms of a slow rearrangement of the orthodihydrate 11, presumably present in our samples of crystalline H2R-2H20,to a different structure which is more stable in aqueous solution. This structure has only two 13CNMR resonance lines near 172 and 92.7 ppm and so is consistent with a para-dihydrate p-H2R.2H20 structure (III). We assign the 92.7-ppm line to the geminal
Ho HO
OH
I1
111
acid. We agree to the assignments of resonances 191.2 ppm to the carbonyl, 142.8 ppm to enol, and 95.0 ppm to the geminal diol carbons. Upon addition of LiOH, the carbonyl and geminal diol resonances are unchanged, but the enol resonance displaces significantly and then broadens and eventually disappears. The displacement observed upon addition of a small amount of LiOH and corresponding to a short (about 10 min) data acquisition time is consistent with the formation of an ortho-dihydrated monoanion, o-HR-.2H20 or I P , in rapid exchange equilibrium with o-H2R.2H20. The dissociation of H+ from an enol hydroxyl would perturb the enol resonance line but not the other carbon resonances. The broadening of this line upon addition of more LiOH apparently means that the o-HR-.2H20 concentration changes during data acquisition, and the disappearance of the line means that
diol carbons and the 172-ppm line to the four carbons drawn as ene-ols and carbonyls in (111) but which are equivalent because of rapid exchange of H+ among these. The data in Table V show that isomerization is as yet incomplete after 50 h in the solution containing only rhodizonic acid but seems essentially complete in that same period of time when LiOH had been added in mole ratios of 0.19 and higher. Consequently, this confirms the notion that the rate of isomerization is faster in those more basic solutions which contain greater concentrations of rhodizonate anions and Li+ ions. To examine the possibility that the observed rate behavior is due to some specific interaction between Li+ ions and the rhodizonic acid system, we added LiCl in a 2:l mole ratio with rhodizonic acid and after 24 h observed only three resonance lines with chemical shifts identical to those obtained with pure
1988
The Journal of Physical Chemistty, Vol. 82,No. 18, 1978
o-HzR.2Hz0. This result obviates the role of Li+ as a catalytic agent and leads to a preliminary hypothesis for the isomerization which involves rhodizonate anions alone. Experiments are underway in this laboratory to investigate the mechanism of the isomerization and results will be reported in a future communication. We must now explain the absence of p-H2R.2Hz0 and p-HR-.2Hz0 resonance lines in the short-time spectra listed in Table IV. Since we hypothesize that the broadening and disappearance of the resonance near 144 ppm is due to depletion of the ortho-hydrate as it converts to the para-hydrate, one would expect to see para-hydrate lines from those same solutions. The explanation rests on the relative magnitudes of the intrinsic chemical shifts a0 and for the two nonequivalent carbons of the parahydrate system. To estimate these we utilize the four spectra involving only two lines each as listed in Table V. These solutions contain varying proportions of p-HzR2Hz0 and p-HR--2H20but essentially no R2- and so we can apply eq 1 with R2- terms omitted. For each carbon resonance four observations overdetermine the two parameters 6o and fil. A multiple regression technique5 based on the method of least-squares calculates those a0 and a1 values which yield the best fit of the equation 6ob,d[total R] = 60[p-HzR.2H20] + 61[p-HR-*2Hz0] to the Table V data. Only approximate values are needed for this explanation and so only approximate species concentrations are needed here. These concentrations are calculated directly from the solution LiOH/R mole ratios assuming complete reaction of the added OH- to form p-HR-.2Hz0. The resulting chemical shifts are 6o = 172.1 ppm and a1 = 175.6 ppm for carbonyl, enol carbons and 6o = 92.5 ppm and J1 = 93.7 ppm for the geminal diol carbons. What is significant here is that and a1 differ by as much as 3.5 ppm in one case and by 1.2 ppm in the other case. Consider the shifting equilibria within, say, the 0.57 mole ratio solution in Table IV. Before LiOH is added the solution is essentially all o-HR-.2Hz0 and oH2R-2H20which has a certain initial pH. We observe in the pH potentiometric experiments that this pH is higher than the equilibrium pH. (o-HzR.2Hz0is thus a weaker acid than p-HzR.2Hz0). As the isomerization proceeds, the solution pH gradually decreases and this results in a gradual decrease of the o-HR-.2HzO/o-H2R.2H20ratio in the unreacted ortho system in order to satisfy the primary dissociation constant of this system. This changing proportion of ortho species causes 6obsd for the ortho resonance at 144 ppm to decrease in intensity and to shift gradually during the 13CNMR data acquisition time and the broad line is recorded. While this is happeaing, the ortho system is gradually converting to the para system and by the same reasoning the ratio p-HR-.2HzO/pH2R.2H20 gradually decreases also as the solution pH decreases. Consequently, with 6o and 61 in this system differing by 1.2 or 3.5 ppm, the two resonance lines are continually shifting as they develop. In addition, the time-averaged concentration of p-HzR.2Hz0species, which increases from zero to a fraction of the total rhodizonic acid concentrations during the acquisition time of 0.4 h, is smaller than the average o-H2R.2Hz0concentration during that period. As a result, the p-H2R.2Hz0resonances would be expected to appear as small broadened peaks, at best, or to be lost in instrument noise as appears to have happened.
R. I. Gelb, L. M. Schwartz, and D. A. Laufer
Experimental Section Commercial samples of potassium rhodizonate were purified by dissolution of the crude salts in sufficient HC1 to adjust the pH to about 1-2, filtration, and finally neutralization to pH -6-7 with KOH. The rather insoluble potassium salt was collected by filtration and the purification process was repeated once or twice more. Commercial samples of rhodizonic acid dihydrate always gave analyses in excess of 96% and were used without further purification. pH measurements employed an Orion Model 801 meter equipped with conventional glass and reference electrodes. The meter was standardized immediately before each titration with 0.05 m potassium hydrogen phthalate buffer at the appropriate temperature. The standardization was checked after each titration and in no case was the meter drift larger than 0.002 pH units. In a typical titration, a weighted portion of KzC606(-50 mg) was added to 40 mL of water under a continuous stream of nitrogen which had been saturated with water vapor at ambient temperature. The solution was allowed to equilibrate for about 0.5 h before titration with standardized 0.1 F HC1 was begun. Particular care was taken to ensure that equilibrium was obtained with each addition of reagent so that standing times of up to 1 h were employed and pH values were recorded only after these remained constant to the nearest 0.001 pH unit for 3-5 min. Short-time 13CNMR data were obtained with a Bruker HX-270 NMR spectrometer equipped with a 10-mm sample tube. Pulsed Fourier transform proton decoupled experiments were made with the following instrument settings: 30" tip angle; 16K data points; 7-kHz spectral width; 2-9 delay time; 0.6-s acquisition time. These experiments employed 5% D20/H20solvent at 25 " C and required 100-3000 instrument transients. Data were recorded as ppm downfield from external Me4Si. Additional pulsed Fourier transform, proton decoupled, 13CNMR experiments employed a Varian CFT-20 NMR spectrometer. A 10-mm sample tube contained the analyte solution in 5% D20/Hz0 solvent at 30 "C. Typical instrument settings were 30" tip angle; 8K data points; 5-kHz spectral width; 2-s delay time; 0.8-s acquisition time. Solutions were allowed to stand for some time in the sealed sample tubes before data acquisition was begun and about 25 000 instrument cycles were obtained.
Acknowledgment. The Bruker HX-270 experiments were performed at the NMR facilities at the Francis Bitter National Magnet Laboratory, MIT. The NMR facility is supported by Grant RR00995 from the Division of Research of the NIH and by the NSF under contract C-67D. We thank Professor Elkan R. Blout for providing access to the Varian CFT-20 spectrometer at the Department of Biological Chemistry, Harvard Medical School. References and Notes E. Patton and R. West, J. fhys. Chem., 74, 2512 (1970). R. I. Gelb, L. M. Schwartz, D. A. Laufer, and J. 0. Yardley, J. fhys. Chem., 81, 1268 (1977). L. M. Schwartz, R. I. Gelb, and J. 0. Yardley, J. fhys. Chem., 79, 2246 (1975). L. M. Schwartz and R. I. Gelb, Anal. Chem., in press. 0.L. Davies and P. L. Gokismith, Ed., "Statistical Methods in Research and Production", 4th revised edition, Oliver and Boyd, Edinburgh, 1972. L. M. Schwartz and L. 0. Howard, J. fhys. Chem., 75, 1796 (1971). L. M. Schwartz and L. 0. Howard. J. fhvs. Chem., 74. 4347 (1970). W. Sgideli, R. Hollenstein, and W. von Pkillpsborn, Helv. Chim: Acta, 80, 948 (1977).
