J . Am. Chem. SOC.1994,116, 9233-9240
9233
Study of the Energetics and Dynamics of Hydrogen Bond Formation in Aliphatic Carboxylic Acid Vapors by Resonant Phot oacoustic Spectroscopy A. Winkler and P. Hess' Contributionfrom the Institute of Physical Chemistry, University of Heidelberg, Im Neuenheimer Feld 253, 0-69120 Heidelberg, FRG Received May 23, 1994'
Abstract: Dissociation rates of dimeric formic (methanoic), acetic (ethanoic), and propionic acid in the gas phase were measured over the pressure range 0.01-100 mbar and for temperatures between 290 and 325 K. Consistent sets of kinetic and thermodynamic data of the dimer/monomer mixture were obtained from the parameters of the first radial acoustic resonance of a cylindrical resonator. The standing acoustic waves were excited by absorption of amplitudemodulated COz-laser radiation. The entropy and enthalpy of dissociation of the equilibrium reaction (R-COOH)z 2R-COOH with R = H, CH3, and C H ~ C H Zthe , rate constant of the dissociation of the dimer, and the mean relaxation time of the vibrational modes of the mixtures were determined by fitting a detailed model of the resonator to the measured values for the resonance frequency and the resonance broadening. The well-established value for the enthalpy of dissociation of about 60 kJ/mol was confirmed. It is nearly independent of the R group. For the first time the dissociationprocess in isolated propionic acid dimers was studied. The activation energy of the dissociation of the dimer was found to be 33 f 1 kJ/mol for formic acid, 32 f 2 kJ/mol for acetic acid, and 32 f 2.5 kJ/mol for propionic acid. For the first time an accurate determination of the pressure dependence of the rate constant was possible. It was found that the system is in the second-order regime. The dissociation rate constant, the relative collision efficiency of the monomer, and the collision efficiencies of the noble gases increase with the number of C atoms. The rate constant was found to be 4.2 X l o 3 l / s for formic acid, 9.0 X 103 l / s for acetic acid, and 5.6 X lo4 l / s for propionic acid in mixtures of 9 mbar of He and 1 mbar of acid at 300 K. The pressure dependence and the resulting activation energy, which corresponds to the dissociation energy of one H bond, suggest a stepwise dissociation process due to bimolecular activation. A possible mechanism is slow dissociation of the cyclic dimer with two H bonds into an open dimer with one H bond and subsequent fast decay of the chain dimer into two monomers.
*
Introduction A large number of publications deal with the geometric structure, the energetics, and tge spectroscopy of H bonds.'.* However, very few experiments have been carried out concerning the kinetics of this type of chemical bonding. Since the liquid state of carboxylic acids consists of dimers and the vapor is a mixture of monomers and dimers, where the dimer is coupled via two H bonds from the carbonyl oxygen of one monomer to the hydroxy hydrogen of the other, these acids represent an ideal system for investigating the basic principles of the association/ dissociation process of these bonds in isolated molecules. Most experiments have concentrated on ultrasonic studies of liquid carboxylic acid systems. Carsaro and Atkinson3 deduced from ultrasonic measurements on acetic acid solutions in acetone and water that the observed relaxation effects are based on the reaction D C, where D is the cyclic form of the dimer and the postulated species C was assumed to be a chain dimer with only one H bond. However, theintrinsic behavior of H bond relaxation cannot be extracted accurately from relaxation measurements in the liquid state. It was found that the solvent has a pronounced influence on the dissociation rate constant and the energetics of the system495 and that H bonds between the acid and the solvent complicate the situation.6.7 These problems can be overcome by investigations of H bond relaxation in the gas phase, where isolated molecules interact. The first attempt to deduce the kinetics of the association/
dissociation process in gaseous acetic acid from temperature jump experiments gave an activation energy somewhat lower than the dissociationenergy but no informationon details of thedissociation process.* More information was obtained from temperature jump experiments on formic acid?JO The activation energy was found to be approximately one-half the dissociation energy. However, this method yielded values for the dissociation rate constant with large uncertainties, so that no pressure dependence could be established.9 The basic questions which remain are the following: (1) Is the system (R-COOH)z 2R-COOH in the second-order regime at low pressureas expected? (2) What is the pressuredependence of thedissociation rateconstant? (3) What valuewill be obtained for the activation energy if the available data are evaluated with the correct pressure dependence? (4) Is the dissociation process a stepwise reaction as proposed for the liquid? (5) What is the nature of the activation process? Is the dimer chemicallyactivated or is the energy content only increased by vibrationaland rotational energy transfer? (6)How do the rate constant and the activation energy depend on the R group? In the present work, the kinetic parameters were obtained from precise measurements of the resonance frequency and the width
Abstract published in Advance ACS Absrructs, September 1, 1994. (1) Schuster, P.; Zundel, G.; Sandorfy, C. The Hydrogen Bond; NorthHolland: Amsterdam, 1976; Vols. 1-111. (2) Schuster, P., Ed. Hydrogen Bonds; Topics in Current Chemistry, Vol. 120; Springer-Verlag: Berlin, Heidelberg, New York, Tokyo, 1984. (3) Carsaro, R. D.; Atkinson, G. J. Chem. Phys. 1971,54,4090. Carsaro, R. D.; Atkinson, G. J. Chem. Phys. 1971, 55, 1971.
(6) Rassing, J. J. Chem. Phys. 1972, 56, 5225. (7) Sims, R. W.; Willcott, M.R.; Inners, R. J. Chem. Phys. 1979,70,4562. ( 8 ) Voronin, A. U.; Gerasimov, I. V.; Denisov, G.S.;Rutkovski, K. S.; Tokhadze, K. G. Chem. Phys. Lett. 1983, 101, 197. (9) Borchardt, D.; Caballero, J. F.; Bauer, S.H. J . Am. Chem. Soc. 1987, 109, 6651. (10) Rutkovskii, K. S.;Bykov, M. G. Khim. Fir. 1991, 10, 1457.
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OO02-7863/94/ 1516-9233$04.50/0 0 1994 American Chemical Society
9234 J. Am. Chem. SOC.,Vol. 116, No. 20, 1994
Winkler and Hess
of acoustic resonance profiles for temperatures between 290 and 325 K and for pressures between 0.01 and 100 mbar. Standing acousticwaves in a cylindrical cavity were excited by absorption of amplitude-modulated laser radiation. Karbach et a1.11J2 demonstrated that the resonant photoacoustic method can be used to measure the effect of vibrational relaxation on the speed of sound and the sound absorption very precisely by evaluating the resonance frequency and the broadening of the resonance profile. The same method was employed later to investigate the kinetics of the reaction N2O4 + 2N02.13.14 The resonance frequency at the maximum signal contains information about the speed of sound, and the broadening of the profile represents the sound absorption processes.
the dissociation rate constant of the dimers. The real part of US corresponds to the speed of sound, and the imaginary part represents the damping of the sound waves. For slow relaxation ( w / k h >> l), the chemical relaxation has no influence on the speed of sound and no damping is observed. The speed of sound becomes slower for fast relaxation (w/kdk > kc-o because otherwise it should be a t least as large as the dissociation energy. This holds true also for the more detailed mechanism. Therefore kdiss
kD+CcX
In this case, the experimental data give information only on the first reaction step and its temperature and pressure dependence. This is in agreement with the observed activation energy.
Winkler and Hem
9240 J. Am. Chem. SOC.,Vol. 116, No. 20, 1994
I I 1
‘
7
C
TLR
Reaction coordinate
0
Figure 10. Enthalpy diagram for the dissociationof the carboxylic acid dimer in the gas phase.
Figure 9. Proposed structure of D*and C. The different rotations are indicated.
Additional collisions are required because it is unlikely that the chain dimer has enough initial energy to dissociateby unimolecular decay. But we only have experimental information about the first reaction step. It is evident from the experimental results that a dissociation of a chain dimer into two monomers should be much faster than a regeneration of D kc-^ > kc+. For C D*we estimate the following for formic acid: (1) entropy gain: one vibrational degree of freedom of about 260 cm-1, AS = 6 J/(mol.K); (2) entropy loss: (a) torsional frequency of one monomer” of 610 cm-I, AS = -2 J/(mol.K), (b) change of the product of the three moments of inertia, AS = -3 J/(mol.K), (c) one free internal rotation of a monomer with an estimated reduced moment of inerta of €lrdc 10-39 g-cm2, AS = -27 J/(mol.K), (d) rotation of a R-C=O group with €lrdc 4 X 10-39g-cm2, AS = -36 J/(mol.K), (e) rotationof a R-C-0-H group with €lrdc 4 X g-cm2, AS = -36 J/(mol.K), (f) change of the frequency in the stretched H bond, AS = -6 J/(mol.K). Thus, AStot= -104 J/(mol-K). This is similar to the estimate of Borchardt et ala9for the entropy difference between C and D (-92 J/(mol.K)). If we assume AStot= 20 J/(mol.K) due to the lower frequency in the stretched bond for C Cs then
--
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The observed influenceof noble gases also allows an explanation of why Borchardt et aL9observed the acceleration of the process by collisions with organic compounds. These substances have many degrees of freedom and should have a high collision efficiency. The increase of the dissociation rate constant with the increase of the specific heat of the dimer can also be explained in view of the proposed mechanism. The energy transfer by collisions depends strongly on the number and the frequenciesof the normal modes. A large number of vibrational modes or low-frequency normal modes of the dimer lead to a fast energy transfer and hence to a fast relaxation.
Conclusions
H bond.
This work is one of the few experiments dealing with the dynamics of the association/dissociation process of the H bond in isolated molecules. Resonant photoacoustic spectroscopyoffers the possibility of investigating fast relaxation processes in the microsecond range. The highest time resolution was achieved in experiments with added buffer gases. The fastest dissociation process was observed for propionic acid. We estimate that even 40 times faster processes could be detected. For the first time, the pressure dependence of the dissociation rate constant of hydrogen bonds in carboxylic acids was determined because the method provides information over a broad pressure range. The data give the first experimental evidence that the kinetics of the carboxylic acid dimer to monomer transformation are in the second-order regime at pressures below 100 mbar. Since we evaluate the data with the correct pressure dependence, the activation energy of the process is determined very precisely. This pressure dependence and the resulting activation energy, which corresponds to the dissociation energy of one H bond, suggest a stepwise dissociation process due to bimolecular activation. A possible mechanism, consistent with the entire experimental data, is slow dissociation of the cyclic dimer with two H bonds into an open dimer with one H bond and subsequent fast decay of the chain dimer into two monomers. In addition to the kinetic parameters, the thermodynamic parameters were obtained from our data. The equilibrium constants agree very well with values reported in the literature. This is an important aspect since for many reaction systems the thermodynamic parameters are not very well-known.
A proposed energy diagram is given in Figure 10. There is no information available about the depth of the minimum for the noncyclic dimer and the behavior of the potential curve between the noncyclic dimer and the two monomers.
Acknowledgment. Financial support of this research by the Deutsche Forschungsgemeinschaft, the Fonds der Chemischen Industrie, and the European Union is gratefully acknowledged.
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kc--,, = 60 kc+,
(19)
at 300 K. That means that indeed k c - 2 ~ >> kc-o. More illustrative is a geometrical argument. In the species C, the two monomers have many different possible configurations. However, only a few of these configurations can re-establish the cyclic dimer. Thus, collisions may more easily lead to bond breaking than the formation of a cyclic compound with a second
