5048
J. Phys. Chem. 1982, 8 6 , 5048-5052
An Experimental and Theoretical Study of the Thermodynamic Properties of the Acetone-Hydrogen Chloride Complex Howard D. Mettee,' Janet E. Del Bene, and Sheila I. Hauck Department of Chemistry, Youngstown State University, Youngstown, Ohio 44555 (Received: February 16, 1982; In Final Form: July 6, 1982)
-
Molar energies of formation (AE)for the vapor-phase reaction (CH3)+20 + HCl (CH3)2CO-.HC1have been determined from the thermal pertubation of the V C region ~ of the infrared absorption spectrum. The value of AE = -4800 f 500 calemol-' compares well with the theoretically computed energy of -4900 cal-mol-' for the analogous CH3CHO-HC1 system. Computed Mulliken population shifts in the carbonyl bonds were used to calculate the ratio of extinction coefficients of the free and H-bonded C=O groups, which then yielded K , (303 K) = 0.14 f 0.5 atm-' and AGO = +1180 f 220 cal-mol-' for the reaction of acetone with HC1. The corresponding AH of -5400 f 500 cal-mol-' was used to find a A S = -21.7 f 1.8 cal-mol-'.K-', which compares with a computed ASoof -26.89 cal-mol-'.K-' based on partition function evaluation. The computed Hartree-Fock normal-mode frequencies for the complex are slightly too high and not anharmonic, which accounts for the discrepancy between the two entropy values.
Introduction Experimental studies' of the thermodynamic properties of simple hydrogen-bonded complexes in the vapor phase have not kept pace with the active theoretical2 work on the structure and energetics of these systems. Even the most recent experimental method, the spectroscopy of supercooled vapor^,^ has yielded principally structural information. Thus there is a need to develop a comparable body of empirical thermodynamic data related to hydrogen bonding in these complexes. The principal reason that experimental studies have not been fruitful in the past is mainly due to the relatively minor abundance of the weakly bound complexes in the presence of larger excesses of donor and/or acceptor species. However, as an earlier work4 has demonstrated, there are occasional circumstances under which spectroscopic evidence of complex formation manifests itself in the form of additional or overlapping absorption bands in the infrared spectrum. Such a fortunate case is the present one, where a complex between HC1 and acetone is indicated by a low-frequency shoulder appearing on the vc+ band (1740 cm-') of acetone in the presence of excess pressures of HC1. Until the present work, perhaps the most closely related, theoretically treated system is that of water-acetone, whose H-bond energy was computed to be -4.2 kcal.mo1-' at the Hartree-Fock level with a small basis set.5 In the present study a higher level ab initio theoretical treatment of the CH,CHO.-HCl complex, including electron correlation and zero-point vibrational corrections, has been carried out. Such a study is tractable and the HC1-acetaldehyde system (1) (a) A. C. Legon, P. D. Aldrich, and W. H. Flygare, J. Chem. Phys., 75,625 (1981); (b) L. A. Curtiss, D. J. Frurip, and M. Blander, ibid., 75, 5900 (1981); (c) J. A. Odutola, T. R. Dyke, B. J. Howard, and J. S. Muenter, ibid., 70, 4884 (1979), and references therein; (d) S. A. McDonald, G. L. Johnson, B. W. Keelan, and Lester Andrews, J. Am. Chem. SOC.,102,2892 (1980). (2)(a) H.Umeyama, K. Morokuma, and S.Yamabe, J. Am. Chem. SOC.,99,330 (1977); (b) P.A. Kollman in 'Applications of Electronic Structure Theory", H. F. Schaefer, Ed., Plenum Press, New York, 1977, pp 109-52. (3) (a) D.H. Levy, Adu. Chem. Phys., 47,323(1981); (b) K.C.Janada, J. M. Steed, S. E. Novick, and W. Klemperer, J. Chem. Phys., 67,5162 (1977). (4) H.D. Mettee, J . Phys. Chem., 77,1762 (1973). (5)J. E.Del Bene, J. Chem. Phys., 63,4666 (1975). 0022-365418212086-5048$01.25/0
is an appropriate model for the experimentally investigated HC1-acetone system. Figure 1shows that the carbonyl stretching band of the HC1-acetone complex overlaps that of acetone itself so that a direct estimate of the equilibrium constant is less than exact. However, to measure the energy of complex formation, AE, one finds it is only necessary to measure the temperature dependence of an absorbance intensity ratio and to assume that the proportionality constant relating this ratio to the integrated band areas is temperature independent. Since no noticeable change in band contours occurs within our limited range of temperatures, this assumption is not unrealistic. Thus for the equilibrium (CHJ2CO + HC1+ (CH3)2CO...HCl
Kc = C,/(CACHCI) K,
(C'HCJ-'U,/IA)
(EA,'
ec) (PA/&)
(1)
(2)
where the concentrations of complex (c) and acetone (A) are given by measured intensities (I, and IA),the respective peak extinction coefficients (e), and the proportionality constants (p) between the extinction coefficients and their respective band areas. It has been shown4 for a cell of constant volume in which the temperature is varied In K , = -AE/RT + constant (3) AGO may be estimated from spectral data if the observed band profile is graphically resolved into separate contributions from "free" and "bonded" carbonyl groups by standard difference techniques. However, the resultant band areas can only be related t o population numbers of the free and bonded forms if the ratio of extinction coefficients is known. Here theory provides data from which the bond dipole strengths of the two carbonyl groups can be estimated. These are related to the normal coordinate derivative of the bond dipole moments. Finally, A S may be determined in two independent ways. One is from the conventional AG = A H - TAS relationship, which is essentially experimental. The other is to use theory to compute the most stable structures, the moments of inertia, and the vibrational frequencies of the hydrogen-bonded modes of the complex. This information in turn is used to calculate a A S o from the appropriate partition functions. A comparison of the two A S values
0 1982 American Chemical Society
The Journal of Physical Chemistry, Vol. 86, No. 26, 1982 5049
Thermodynamic Properties of Acetone-HCI
61
_ _ _ _ _H_ _ _ _ _ - _ _ _ 0
ti i
I H-
/
C
Flgure 2. Computed minimum-energy structure of the CH,CHO-.HCI complex.
in the presence of complex. This correction changed the measured area ratio, A,/AA,from 0.12 f 0.05 to 0.16 f 0.05. 4
'
I
"
1800
I
'
I
'
"
I
I
I
1750
'
'
1700
FREQUENCY Icm-lj Figure 1. Infrared absorption spectrum of acetone and acetone-HCI vapors in the fundamental carbonyl stretching region. Path length 10 cm. Dashed ordinates indicate frequencies at which absorbances of acetone ( I Aand ) acetone-HCI complex (I,) were measured.
permits an evaluation of the ability of ab initio theory to predict thermodynamic properties, and also lends some credibility to the experiment.
Experimental Section The techniques used in this study parallel those described earlier4 so that only a brief summary is provided here. The infrared gas cell (Wilks, 10 cm path) was heated by a nichrome wire embedded in an asbestos jacket and the wall temperature was sensed by a calibrated pyrometer (3M). A negligible error was introduced by the assumption that the average vapor temperature was that measured a t the wall, since 80% of the internal surface area was heated wall. The windows themselves were heated by contact with the vapor, and temperature gradients due to convection have been shown to be ~ n i m p o r t a n t . The ~ acetone was standard reagent grade material passed thru several freeze-pump-thaw cycles, and Matheson HC1 was used without purification. The cell was first filled with 10 torr of acetone and closed off. Then an atmosphere of HC1 was admitted to the cell. An immeasurable amount of acetone back-diffused out of the cell with this filling procedure. Spectra were measured with a Beckman IR-12. Figure 1 shows a sample trace in the fundamental carbonyl stretching region of acetone, and the absorption was verified to obey Beer's law within the reproducibility of the instrument. A pressure-dependent, low-frequency shoulder developed when higher pressures of HC1 were added, which was assigned to the (CH3)2CO-.HC1complex. Peak intensites at 1765 and 1731 cm-' (uncorrected) were taken to be proportional to the integrated areas of the acetone and the acetone-plus-complexbands, respectively. To calculate the intensity of just the complex absorption, I,, we substracted the amount due to acetone as calculated from the high-frequency absorption, IA, in pure acetone vapor. This method assumes that the complex makes no appreciable contribution to I*. So that an equilibrium constant could be estimated from these spectra it was necessary to subtract the acetone spectrum from that of the acetone-plus-complex and plot the residual numerically. When this was done with the measured spectra, the areas of both the complex and pure acetone were corrected for the loss of acetone absorption
Method of Calculation Optimized Hartree-Fock structures of HC1 and acetaldehyde with the 3-21G basis set6 have been determined previously.' In the present study, gradient optimization technique^^*^ have been employed to fully optimize with respect to both intra- and intermolecular coordinates the structure of an HC1-acetaldehyde complex with C, symmetry, with the methyl group of acetaldehyde cis to HC1 with respect to the C=O bond, as shown in Figure 2. Since the split-valence 3-21G basis set severely overestimates the strengths of hydrogen bonds formed with lone pairs of electrons, further calculations have been peformed with the more extended 6-31G* basis setlo which includes polarization functions on non-hydrogen atoms. Inclusion of polarization functions on hydrogens in first- and second-row hydrogen-bonded dimers does not appear to lead to significant energy changes." Second-order MerllerPlesset calculation^'^^'^ (MP2) with the 6-31G* basis set have also been carried out to evaluate the correlation energy contribution to the stabilization energy of the HC1acetaldehyde complex. For the correlation calculations on the monomers and the complex, all electrons except 1s on the non-hydrogen atoms have been included. This level of theoretical treatment is designated MP2/6-31G*// HF/3-21G, where " I / "is read "at the geometry of ". Although it would be desirable to carry out such a study a t optimized 6-31G* geometries, the size of this system precludes such an investigation a t this time. Analytical second derivatives of the Hartree-Fock energy with respect to the nuclear coordinates have been determined for the complex and the isolated monomers at the optimized 3-21G geometries with the 3-21G basis set. The force constants obtained were used to determine the harmonic vibrational frequencies and associated zero-point vibrational energies, using the principal isotopes. The computational details of the second-derivative calculations and estimates of the accuracy of Hartree-Fock frequencies have been presented.14J5 These calculations (6) J. S. Binkley, J. A. Pople, and W. J. Hehre, J. Am. Chem. SOC.,102, 939 (1980). ( 7 ) R. A. Whiteside, M. J. Frisch, D. J. DeFrees, K. Raghavachari, J. S. Binkley, H. B. Schlegel, and J. A. Pople, The Carnegie-Mellon Univesity Quantum Chemistry Archive, Pittsburgh, P A 15213. (8)P. Pulay, Mol. Phys., 17,197 (1969). (9)H. B. Schlegel, Ph. D. Thesis, Queen's University, 1975. (10)P. C. Hariharan and J. A. Pople, Theor. Chim. Acta, 28, 213 (1973). (11)J. E.Del Bene, M. J. Frisch, and J. A Pople, to be published. (12)J. A.Pople, J. S. Binkley, and R. Seeger, Int. J. Quantum Chem. Symp., 10,l(1976). (13)R. Krishnan and J. A. Pople, Int. J . Quantum Chem., 14, 91 (1976).
5050
The Journal of Physical Chemistry, Vol. 86, No. 26, 7982 0.5
1
Mettee et al.
TABLE I : Net Charges o n C=O in CH,CHO and CH,CHO...HCl at HF/6-31G*//HF/3-21G CH,CHO CH,CHO...HCl O O/
1-
0
C
0
0.335+ 0.363t
0.481-
0.517-
values of AE are considered to be in good agreement. It is not usually possible to estimate equilibrium constants from the type of IR data measured here, unless a reasonable assumption about the relative extinction coefficients of the absorption bands in question can be made. In the present case, an estimate of the change in polarization is possible by using the change iil the Mulliken electron population data" in going from the free molecules to be H-bonded complex. If the change in the carbonyl bond moment, pC+, is assumed to reflect the change in (dp/dq), then the square of the ratio of bond moments, I(pc/pA)C=012, gives the ratio of extinction coefficients. From Table I it is readily determined that the dipole moment ratio is (0.880/0.816) = 1.08. Thus the estimated extinction coefficient ratio ( E A / E ~is) (1.17)-' in eq 2. Measurement of the integrated band areas A, and A A , by standard numerical procedures, was done at the instrumental cell compartment temperature (30 "C). At this low temperature the weakly absorbing complex was most abundant. The above data were then combined as indicated in eq 4 and 5. P H C l refers to the initial pressure
I 2.9
3.0
3.1
3.2
3.3
Figure 3. Van't Hoff plot of infrared intenslty ratio ( I c / I A ) used to calculate A€ for acetone-HCI complex formatlon from the Isolated molecules as -4800 f 500 cabmoi-'.
have been performed either on the AMDAHL 470/V5 computer at Youngstown State University or on the VAX 11/780 computer a t Carnegie-Mellon University.
Results and Discussion The reciprocal temperature dependence of the absorbance ratio of complex to free acetone, Ic/IA,is shown in Figure 3. The linear character of this ratio, taken with ita pressure-dependent increase with HCl pressure a t constant temperature, is consistent with the assignment of the low-frequency shoulder on the fundamental carbonyl stretch of pure acetone to a complex, which is assumed to be 1:l. For this constant volume system, AE is calculated from the slope to be -4.8 f 0.5 kcal-mol-', as determined by least-squares analysis. While the scattering of points leads to a sizeable precision error, the values themselves tend to fall into the range of those previously reported for similar systems. The corresponding AH value is -5.4 f 0.5 kcal-mol-' from AH = AE AnRT, where T = 303 K, the temperature a t which AG is measured, and An = -1 mol. The experimental data may be compared with the theoretical results. The HF/6-31G*//HF/3-21G stabilization energy (AEa t 0 K) of the complex is -4.0 kcalsmol-l. The MP2 electron correlation energy further stabilizes the complex by -2.7 kcalemol-'. However, the zero-point vibrational energy correction is 1.8 kcal-mol-', giving a resultant computed stabilization energy of -4.9 kcal-mol-'. The presence of a second methyl group might lead to additional stabilization, but probably by no more than 0.5 k~al.mol-~.~J*Thus the experimental and theoretical
+
(14) J. A. Pople, R. Krishan, H. B. Schlegel, and J. S. Binkley, Int. J. Quantum Chem. Symp., 13, 325 (1979). (15) J. A. Pople, H. B. Schlegel, R. Krishnan, D. J. De Frees, J. S. Binkley, M. J. Frisch, R. A. Whiteside, R. J. Hout, and W. J. Hehre, Int. J. Quantum Chem. Symp., 15, 269 (1981). (16) Relatively minor additional terms corresponding to the loss of three translational degrees of freedom (-(3/2)RT) and two rotational degrees of freedom (-(2/2)RT) are compensated for by the thermal population of the five new low-frequency vibrational, or hindered rotational, degrees of freedom (-+1.5 kcabmol-') introduced when the complex forms.
P J P A= ( A c / A ~ ) ( c ~ / 4 (PHCl)-'(Pc/pA)
Kp
(4) (5)
of HC1, which is in such great excess that the small amount lost due to complex formation is negligible in comparison. In this manner Kp is calculated to be 0.14 f 0.05 atm-', which leads to a AGO of 1180 f 220 cal-mol-' by the well-known equation AGO = -RT In K . When AH and AGO are combined in AGO = AH - T A J , the experimentally based entropy change, AS, is found to be -21.7 f 1.8 cal-mol-'.K-'. A second, independent way to relate the experimental quantities of AH and AGO is by calculating the standard entropy change upon complex formation from partition functions. This quantity, ASo, is composed of the usual translational, rotational, and vibrational contributions, which in turn are obtainable from either spectroscopic or theoretical data as indicated below. The form of the Sakur-Tetrode equation used to calculate Sotrfor each component of the system islaa SO,, = R[(3/2) In M (5/2) In T - In Po -1.16491 (6)
+
and the other terms have their usual where PO is 1 significance. The rotational entropy change occurring on complex formation, ASorot, is conveniently reduced to
where the factor of 2 in the second term is the symmetry number of acetone. The inertial data necessary to evaluate ASo,, is based upon the structural data computed for the CH3CHO-HC1 system since experimental data are unavailable. The structure of this model complex (Figure 2) has the methyl group cis to HCI with respect to the C=O (17) R. S. Mulliken, J . Chem. Phys., 23, 1833 (1955). (18) (a) I. N. Levine, "Physical Chemistry",McGraw-Hill,New York, 1978, p 718. (b) I. M. Klotz, "Chemical Thermodynamics", W. A. Benjamin, New York, 1964, p 156.
The Journal of Physical Chemistty, Vol. 86, No. 26, 1982 5051
Thermodynamic Properties of Acetone-HCi
TABLE 11: Moments of Inertia Used €or
?
ASorot (X1O4O g c m ' ) moment
CH,COCH,
(CH,),CO...HCl
1,
67.8 86.3 149
289 298 587
Ib IC
bond, the configuration which more closely mimics the presumed geometry of the experimental complex. The computer equilibrium structure has been established through vibrational analysis to be a minimum energy structure on the intermolecular surface. I t has a nearly linear hydrogen bond as the angle between the C1-H bond and the intermolecular C1-0 line is only 4.2O. The angle between the C1-0 line and the C=O bond is 122.8O and the intermolecular C1-0 distance is 3.060 A. The 3-21G calculations show that hydrogen bonding leads to a rather large 0.030 A lengthening of the H-Cl bond (from 1.293 A) and a smaller increase of 0.008 A in the length of the C=O bond. Table I1 lists the momenta of inertia for acetone and the HC1-acetone complex based upon the geometry of the minimum energy model complex. An additional simplifying assumption is that each methyl group is a point mass of 15 amu a t the respective carbon atom positions. It may be noted that the small value of ASo, resulting from these data somewhat de-emphasizes their significance. When an HC1-acetone complex forms, three translational and two rotational degrees of freedom are lost, becoming instead five normal vibrational or hindered rotational modes. Pimentells has given a general characterization of these new vibrations. In the present complex these are described as follows: vB, two low-frequency deformations due primarily to motion of the methyl group with a small C1 atom movement; the out-of-plane mode at 101 cm-l may be interpreted as a hindered rotation; Y,, the ClH-.O stretch; ut, the ClH-0 out-of-plane bend, or torsion, of the H atom; Vb, the ClH-O in-plane bend of the H atom. The modes Vb and ut are not usually considered new vibrations since they normally occur a bending modes in H-bond donors. Here, however, these modes correlate with rotation of the isolated HCl molecule. Likewise, the three low-frequency modes would correlate with the three degrees of translational freedom of the isolated HC1 molecule, but in the complex substantial methyl motion also occurs. Figure 4 summarizes the vibrational motions present in each of the five new modes introduced by complex formation. Table I11 also includes the values of all the 3-21G computed harmonic vibrational frequencies for the model CH,CHO-.HCl complex as well as for the isolated monomers. It is noteworthy that, apart from the introduction of the new modes, H bonding does not dramatically effect the normal modes of CH3CH0, which is often assumed in comparable systems but less frequently verified.lb The frequency VHG1 is dramatically decreased in the complex. Clearly these trends are consistent with H-bond formation causing both a weakening and a lengthening of the C=O and H-C1 bonds. (A search for a new H-C1 absorption in the complex did not result in an unambiguous assignment). When the computed frequencies are used it is straightforward to calculate the separate entropy contributions made by each of the new modes to the stability of the complex.20 Changes in the other frequencies result (19) G.C. Pimentel and A. L. McClellan, "The Hydrogen Bond", W. H. Freeman, San Francisco, 1960, p 68. (20) K. S. Pitzer, "Quantum Chemistry", Prentice-Hall, Englewood Cliffs, NJ,1953, p 457.
Figure 4. Vlbrational motions of the five modes introduced by CH,E HO-HCi complex formatlon as computed by normal coordinate analysis. Motlons in vB (63cm-I), u,,, and vb are in-plane (A') and are drawn to scale, whereas those of up (101 cm-') and v, are outofglane (A") and are drawn in perspective. vb (101 cm-I) may be interpreted as an internal rotation.
TABLE 111: Computed Normal Modes ( c m - l ) (C, Species) ~
no, CH,CHO...HCl
CH,CHO
~
HCl
assignme nta (cm-'Ib
63 (A') "0 (
