J. Phys. Chem. 1993,97, 11451-11455
11451
Heat of Formation of CH2OH and ~ ( H - C H Z O H ) B. Ruscic and J. Berkowitz' Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 Received: July 15. 1993'
The appearance potential (AP) of CH20H+ from CH3OH has been reexamined by photoionization mass spectrometry, using higher resolution, better statistics, and a more extensive analysis. The result, AP(CH2OH+/CH30H) = 11.649 f 0.003 eV, when combined with IP(CH20H) = 7,549 f 0.006 eV, yields Do(HCHIOH) = 395.6 f 0.6 kJ/mol. Other quantities which can be derived from this value include 0298, AHfo (CH2OH) at 0 and 298 K and the proton affinity of CH20. A prior thermochemically deduced value for u f 0 2 9 8 (CH20H) is corrected, utilizing a hindered rotor in calculating So298(CH20H). The revised value, AHf02g8(CH20H) = -12.2 f 1.7 kJ/mol, still differs from the present value, -16.6 f 0.9 kJ/mol, but a recent high-quality ab initio calculation is in good agreement with the present result.
I. Introduction In 1991, we'reportedmeasurementsoftheionization potentials (IPS) of the isomeric transient species CDzOH and CD30 by vacuum ultraviolet photoionization mass spectrometry. Then, utilizing an appearance potential measurement of CH20H+ from CH30H (1 1.67 f 0.03 eV) reported much earlier from this laboratory,2 we were able to deduce Do(H-CH20H) 1 95.0 f 0.7 kcal/mol(I397.5 f 2.9 kJ/mol) or equivalently we inferred MrOo(CH20H) I -2.1 f 0.7 kcal/mol (1-8.6 f 2.9 kJ/mol), AHf02g8(CH20H)I -3.7 f 0.7 kcal/mol (1-15.5 f 2.9 kJ/ mol). In this calculation, the IP of CHzOH was estimated to be 0.01 eV larger than that of CD20H, from zero-point energy considerations. Subsequently? we have measured IP(CH2OH) = 7.549 f 0.006 eV, compared to IP(CD20H) = 7.540 f 0.006 eV. Thus, the major uncertainty in thevalues of AHfo(CH20H) and Do(H-CH20H) cited above stems from the AP (CH20H+/ CH3OH). In the short span of time since that publication, there have been a number of articles either questioning these results or agreeing with them. (1) Seetula and Gutman4 investigated the chemical kinetics of two reactions: CH20H
+ HBr F? C H 3 0 H + Br
context, they are about midway between those results and ours, with the more precise third-law value essentiallyoverlapping with ours. (3) Traeger and Holmes6subsequently proposed two improvements, one which seemed to resolve the discrepancy, and another which revived it, but in the oppositedirection. First, they pointed out that S o 3 ~ ( C H 2 0 Hused ) by Seetula and Gutman came from a compilation in which the torsional mode was assumed to be a free rotor. By utilizing instead an experimental torsional frequency, they recalculated AHfo298(CH20H)from the data of Seetula and Gutman, and deduced -14.7 f 1.4 kJ/mol (reaction 1) and -15.8 f 7.8 kJ/mol (reaction 2). These recalculated values are seen to be in very good agreement with our initial results. However, they questioned the old appearance potential of CH2OH+ from CH3OH. Upon repeating that experiment, they obtained a linearly extrapolated onset of 11.578 f 0.007 eV at the experimental temperature. Proceeding further by their analysis, they concluded that AHf0298(CH20H)= -18.9 f 1.0 kJ/mol, about 3.4 kJ/mol lower than our upper limit. The purpose of this paper is to examine in greater detail both of the proposals of Traeger and Holmes, and hopefully, to arrive at more definitive values for AZffo(CH20H) and Do(H-CH2OH).
(1) 11. Experimental Arrangement
CH20H
+ HI e CH,OH + I
(2)
Rate constants for the forward reactions were measured and combined with kinetic information for the reverse reactions taken from the literature to give equilibrium constants, and thence PFO and AHo for the respective reactions. This, in turn, enabled them to infer several values for AZff0298(CH20H): -9.1 f 1.7 (reaction 1, third law), -8.7 f 7.6 (reaction 2, second law), -8.1 f 8.0 (reaction 2, third law), and -8.9 f 1.8 kJ/mol (recommended). These results for AHfo(CH20H) were somewhat higher than given by our upper limit, and correspondinglyincreased the C-H bond energy by -6.6 kJ/mol. (2) D6bt5 then reported corresponding results for the reaction
+
C H 2 0 H HCl e C H 3 0 H + C1 (3) From a similar kinetic analysis, he inferred AHfo298(CH20H)= -9 f 4 kJ/mol (second law) and -14 f 2 kJ/mol (third law) and recommended -12 kJ/mol. He offered these values as support for the results of Seetula and Gutman, although in the present Abstract published in Advance ACS Abstracts, October 1, 1993.
The basic apparatus consists of a 3-m vacuum ultraviolet monochromator (McPherson) mated to a quadrupole mass spectrometer. The light source for this experiment was the manylined molecular spectrum of Hz, generated in a dc discharge. These lines served as an internal wavelength calibration. A stepping motor established the increments, which were monitored by a shaft encoder. The mass-resolved photoions were pulse counted. The dispersed light intensity was detected as a photocurrent, converted to a voltage and then to a frequency by a voltage-to-frequencyconverter,and counted. The photocathode had been calibrated previously for its wavelength dependence. We note here that the much earlier measurement from our laboratory2 utilized a 1-m monochromator and a magnetic mass spectrometer. III. Experimental Results The photoion yield curve of CH20H+ from CH3OH in the near threshold region obtained currently is shown in Figure 1. It was acquired with a photon resolution of 0.84 %I (fwhm) and measured at intervals of 0.2 A. The much earlier work from this laboratory was performed with a wavelength resolution of 1.66
0022-3654/93/2097-1145 1 %04.00/0 0 1993 American Chemical Society
11452 The Journal of Physical Chemistry, Vol. 97,No. 44, 1993 10
~
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
i!
9-1 h
Ruscic and Berkowitz
81
0
11.2
11.4
11.6
11.8
12.0
12.2
PHOTON ENERGY (eV)
Figure 1. Photoion yield curveof CHzOH+fromCH3OH near threshold. Photon resolution = 0.84 A (fwhm); interval between points = 0.2 A, or about 0.002 eV.
A (FWHM) and measured at 2-A intervals.
A 2-A interval in this wavelength region is equivalent to -0.022 eV 3 2.1 kJ/mol, which is comparable to the levels of discrepancy being discussed. Nevertheless, it is noteworthy that both the old curve and the present one display some curvature (concave downward) as the curves approach threshold. Traeger and Holmes6 used an apparatus with a resolution of 1.25 A, with points measured at 1-A intervals. They purported to observe linear behavior near threshold and furthermore stated that “the theoretical threshold law for this fragmentation process is a linear function of excess energy.” We know of no such theoretical law. Rather than proceeding with a standard analysis based on assumed linear behavior and adjustment for the effect of the internal energy of the target species, we have opted in this case for a more extensive analysis. The internal energy (vibrational and rotational) of CH3OH at 298 K is 0.0544 eV 4 5.245 kJ/moL7 Ofthissum,O.O385eVI 3.718 kJ/molisdue tothethreerotational degrees of freedom. Methanol is a hindered rotor, with a barrier to rotation of only 0.0466 eV7 4.49 kJ/mol. The heat content at 298 K for this hindered rotor is 0.013 eV = 1.25 kJ/moL8 This is essentially the value for a free rotor. The sum of the external and internal rotor modes accounts for -0.051 eV, almost the entire internal energy of CH30H at 298 K. Consequently, it is possible to model the distribution functionof the internal thermal energy of CHJOHby employing four rotors. Following H a a r h ~ f f , ~ it can be shown that this distribution function has the form f
P(E,T) = aEe-EfkT where the normalization constant a = (l/kT)*, and E is the combined rotational energy. Our procedure is to convolutethis thermal distribution function withvarious kernel functions, which includes (1) a linear increase of ion yield with excess energy, (2) a square root function (because of the concavedownward character of the curve in two data sets), and (3) an exponential function (of the form 1 - e-bx). A fitting program is used to provide the best fit between each of the trial functions and the current experimental data. The value of the threshold (0 K) is obtained for each trial function, as is the quality of the fit, judged by the least-squares sum. The explicit forms of the kernel functions, after convolution with the thermal distribution function, are given in Appendix 1. These functionshave been fitted to the experimental data between 11.24 and 11.88 eV, which is approximately the region for which data have been reported by Traeger and Holmes. Our experimental data have been corrected for a weak sloping background, observable well below threshold. The sloping background correction has been determined by a separate least-squares fit of the region 11.12-11.40 eV (well beyond the point where any
0
3
2
0
1 3
I
c,
i 11.3
11.4
11.5
11.6
11.7
11.8
11.9
PHOTON ENERGY (eV)
Figure 2. Least-squaresfit of various kernel functions, after convolution with a four-rotor internal energy distribution function at 298 K, with the experimentaldata. Also shown are the kernel functions(0 K): (a) linear kernel function; (b) square root; (c) exponential of the form 1 - eaE.
departure from linearity can be discerned) and then kept fixed while fitting the threshold region. In Figure 2, the quality of the fits can be visually discerned for (a) the linear function, (b) the square-root function, and (c) the exponential function. The linear function misses completely the curvature inherent in the data, while the square-root function introduces too much curvature. The exponentialfunction, which is less curved than the square-root function, clearly provides the best fit, with almost nodiscernibledeviationfrom theexperimental points. Incidentally, the fitted parameter b of the exponential function is 2.25. Thus the function 1 - e-bxroughly corresponds to which is obviously more curved than xl, but less curved than x0.5.The visual conclusions about the quality of the fits are completely borne out by the least-squares analysis. The leastsquares sum is about 3.5 times smaller for the exponential function than for the linear one, which is in turn about a factor 2 smaller than for the square root function. This is about the same relative quality of fitting which we obtain from the earlier data of Refaey and Chupka: although the actual points in that experiment were much sparser. The values of Et (threshold at 0 K) obtained from our data are 11.628 eV (linear), 11.684 eV (square root), and 1 1.646 eV (exponential). The uncertainty of the fit is about 1 meV. The corresponding numbers from the Refaey-Chupka data are 11.632 eV (linear), 11.687 eV (square root), and 11.649 eV (exponential). Thus, even though the experimental data in the latter case involved intervals of -22 meV, the extracted values of E,, differ only by -3-4 meV from the current data. Figure 2 also displays graphically the inferred kernel functions. If these functions are displaced to lower energy by 2kT (which is the average internal energy implied by the thermal distribution function given in Appendix l), the curves match the experimental points very well both for the linear and exponential functions
Heat of Formation of CH20H and Do(H-CH20H) (except for the low-energy exponential tail). Previously, it has been shown in rather general formlo that the effect of internal energy (vibrational, as well as rotational) upon a linear kernel function is to displace the linear function to lower energy by precisely the average internal energy. It now appears as if this is at least approximately the case for an exponential kernel function. We now utilize this observationto improve the fitted threshold. The average internal energy of CH3OH at 298 K is 5.245 kJ/mol = 0.0544eV. Our model function has accounted for 2kT = 4.958 kJ/mol = 0.0514 eV. The internal energy lacking in our model amounts to 0.287 kJ/mol 0.0030 eV. Thus, we correct our best fit, Et = 11.646 eV, to 11.649 eV. It has been shown previously1° that the broadening effect of the monochromator slit function does not shift the threshold, in the case of a linear kernel function. We shall assume that this conclusion applies to the exponential function as well. Thus, our final result is Et = 11.649 f 0.003 eV, where the error bar incorporatesuncertainty in the wavelength calibration. From this threshold, and AHfOo(CH3OH) = -190.0 f 0.6 kJ/ mol? AHfoo(H) = 216.034 kJ/m01,~we infer AHfoo(CH20H+) = 7 17.9 f 0.7 kJ/mol. Utilizing this value, together with A H f O O (CH20)7= -104.9 f 0.5 kJ/mol and AHf00(H+)7= 1528.083 kJ/mol, we obtain a proton affinity PA(CH20) = 705.3 f 0.8 kJ/mol at 0 K, or PA298(CH&) = 71 1.4 f 0.9 kJ/mol. For the latter calculation, the vibrational frequencies of CH20H+ calculated by DeFrees and McLean" (which do not differ greatly from those of Botschwina12)have been used. The value of Do(H-CH2OH) can be directly determined from two experimental quantities, AP(CH20H+/CHsOH) = 11.649 f 0.003 eV given above, and IP(CH20H) = 7.549 f 0.006 eV reported by us previously. Their difference, 4.100 f 0.007 eV = 395.6 f 0.6 kJ/mol, is an upper limit to Do(H-CH20H). It is an upper limit because, in principle, an appearance potential is always an upper limit. However, in this instance the upper limit is lower than the corresponding value deduced from the independent kinetiothermochemical measurements of Seetula and Gutman (vide infra). Therefore, there is good reason to believe that this upper limit is the true thermochemical bond energy. This bond energy, together with AHfOo(CH30H) and AHfoo(H) (see above), yields AHf'o(CH20H) = -10.47 f 0.90 kJ/mol, or AHf0298(CH20H) = -16.6 f 0.9 kJ/mol. These various deliberations are summarized in Table I.
IV. Discussion of Results A. Standard Entropy of CHzOH. In attempting to rationalize thevalueof AHfO(CH2OH) obtained by thekinetic measurements of Seetula and Gutman4 with the corresponding value based on photon impact threshold measurements, Traeger and Holmes6 have drawn attention to the entropy of CH2OH. Seetula and Gutman obtained So3m(CH20H) = 255.55 J/(K mol) from a compilation of Tsang,13 in which this molecule was assumed to have unhindered internal rotation. Instead, Traeger and Holmes6 utilized an experimentally measured torsional frequency of 420 cm-1, "which is supported by two different theoretical calculations". One of the calculations cited14is a normal mode analysis involving other measured frequencies. The other is an ab initio calculation,15 which clearly states that this torsional motion corresponds to a hindered rotor, with a barrier to rotation of 2.75 kcallmol (HF/6-31G**) and 3.98 kcal/mol (MP3/6-31G**). Some experimental support for this conclusion is also cited in the paperofSaebpretal.15 Ifwe focusour attentionon thecontribution of this single mode to S0298(CH20H), we obtain the following results: torsional vibration, u = 420 cm-':
3.73 J/(K mol)
hindered rotor, Vo= 3.98 kcal/mol: 9.9 f 0.9 J/(K mol)
The Journal of Physical Chemistry, Vol. 97, NO. 44, I993
11453
TABLE I: Summary of Experimental Results A. Appearance Potential of CH20H+from CH3OH at 0 K (in eV) 11.67 f 0.03 ref 2 11.632 f 0.007 ref 6a 11.649 f 0.003 present results B. C-H Bond Energy of CH3OH (in kl/mol) Do(H-CH20H) Dzga(H4HzOH) 393.2 i 1.2 400.0 i 1.2 ref 66 400.0 i 2.0 395.6 f 0.6
406.8 i 2.0 402.3 i 0.6
ref 4c
present results
C. Heat of Formation of CHzOH (in kl/mol) mfoo
*
-6.1 1.7 -12.8 f 1.0 -19.8 i 6 -10.5 f 0.9 718 712.9 i 1.0 711.4 i 0.9
mro298
-12.2 -18.9 -25.9 -16.6
f 1.7 f 1.0
ref 4c ref 6
f6 i 0.9
ref 19
present results D. Proton Affinity of CH2O (in kJ/mol) ref 27 ref 6
present results Extrapolated threshold given in ref 6 (298 K) shifted by our internal energy correction. b BasedonAHrOm(CH20H)giveninref 6. c Corrected from ref 4, using the currently calculated S0298(CH~0H). free rotor: 17.2 f 1.0 J/(K mol) Thus, the entropy contribution for the hindered rotor lies roughly midway between a free rotor and the low frequency vibrator, and implies that Traeger and Holmes have over-correctedS029g(CH2OH).l6 However,there are other factors entering intoS0pg(CH2OH) which need to be reexamined. We have included our detailed calculations, using the best currently available geometry and vibrational frequencies, in Appendix 2. Our final result is S029g(CH20H) = 245.6 f 0.9 J/(K mol), compared to 240.2 J/(Kmol) (Traeger and Holmes6)andS03m= 255.55J/(Kmol) (Tsang,13Seetula and Gutman4). D6bk5 refers to an article by Burcat17 as his source of So298(CH20H). The latter author presents SO(CH20H) in terms of a polynomial function, which is based on the assumption of a hindered rotor, a product of inertia ZxxZyyZzz= 4.06 X g2cm6and vibrational frequencies not very different from the present ones, except that the lowest is 1060 cm-l, instead of 735.5 cm-1. From Burcat's polynomial expression,17we calculate S029g(CH20H) = 242.2 J/(K mol). With more accurate vibrational frequencies, Burcat's expression should yield an entropy close to the currently calculated one. The consequences of these entropies can be summarized in the results stemming from the data of Seetula and Gutman4 (reaction 1): So2,,(CH20H), J/(K mol) 255.55 (300 K) 245.6
Mf0298(CH20H),kJ/mol -9.1 f 1.74 -12.2 f 1.7 240.2 -14.7 f 1.46 B. Heat of Formation of CH20H. Our currently deduced A H H ~ " ~ Q ~ ( C His~-16.6 O H ) f 0.9 kJ/mol. The value arrived at by Traeger and Holmes6is -18.9 f 1.0 kJ/mol. The difference lies primarily in the appearance potential of CH20H+ from CH3OH, which is discussed at length in section 111. With S0298(CH2' OH) calculated in section IVA and Appendix 2, our correction of the data of Seetula and Gutman amounts to 3.1 kJ/mol for AHfo298(CH20H).Thus, one of their values [AHfo29g(CH20H) = -9.1 f 1.7 kJ/mol] becomes -12.2 f 1.7 kJ/mol. This is still about 4.4 kJ/mol above our value, while the combined errors amount to 2.7 kJ/mol. Since our value is essentially an upper limit, the Seetula-Gutman value is difficult to rationalize with the present result. We believe that it isunlikely that theremaining discrepancy lies in the entropy, for which the largest residual uncertainty is the magnitude of the barrier to internal rotation. It should be noted that only one of the three determinations they4 cite has an error as low as f1.7 kJ/mol; the others are f7.6 and
Ruscic and Berkowitz
11454 The Journal of Physical Chemistry, Vol. 97, No. 44, 1993
f8.0kJ/mol. That one is a third-law measurement of reaction 1, based on their determination of the forward rate constant, and a reverse rate constant extracted from the data of Buckley and Whittle. Hence, the discrepancywith our data probably hinges on the accuracy of one (or both) of those absolute rate constants. All threeof thevalues cited above differ significantly from AHf0298 (CH20H) = -25.9 f 6 kJ/mol cited by Lias et al.I9 taken from an earlier compilation by McMillen and Golden.2o C. Comparison of ab Mtio Calculations of Do(H-CH20H) with Experimental Results. We are aware of three ab initio calculations on Do(H-CH20H) either contemporary with, or subsequent to our prior work. Curtiss et al.21using G2 theory, obtained 96.2 kcal/mol(402.5 kJ/mol), which they estimate to be accurate to f 2 kcal/mol, based on previous comparisons of calculated bond energies with accurate experimental values. Bauschlicher et al.22 using a modified coupled-pair functional (MCPF) method and a large basis set, obtained 94.2 kcal/mol (394.1 kJ/mol), which they corrected to 96.2 f 2 kcal/mol(402.5 f 8 kJ/mol), based on previous comparisons of their calculations with other C-H bond energies. Espinosa-Garcia and Olivares del Vallez3used the GAUSSIAN 90 system of programs with Merller-Plesset perturbation theory in fourth order, with a frozen core approximation and single, double, triple, and quadruple excitations (MP4SDTQ(FC)). Three different extended basis sets were utilized. The post-MP4 total energies were estimated using the empirical PMP-SAC4 method24and the theoretical fourth-order invariant quantity of F e e ~ ~ b e r gThey . ~ ~ expressed their final result as AHf0298(CH20H) = -15.6 f 1.5 kJ/mol, which corresponds to Do(H-CH20H) = 396.6 f 1.6 kJ/mol. We note that all of the ab initio calculations agree with our result, 395.6 f 0.6 kJ/mol, within their respective error bars. They do not agree with the value of Traeger and Holmes. The bond energy calculated by Bauschlicher et al.22prior to their correction is in better agreement with our result than that after correction. The extensive calculation of Espinosa-Garcia and Olivares del Valle,23with its tighter error bar, is in excellent agreement with the present result but does not overlap with the other experimental values (within their respective error bars). D. Proton Afkity of ( 3 4 2 0 . Smith and Radom26have recently calculated PA(CH2O) = 71 1.8 kJ/mol at the G2 level. Although this type of calculation has an estimated error of f8 kJ/mol, it is perhaps fortuitously in excellent agreement with the present result (7 11.4 f 0.9 kJ/mol). Traeger and Holmes report 7 12.9 f 1.0 kJ/mol, while the compilation of Lias et a1.27lists 718 kJ/mol.
Appendix 1. Convolution of K e d F u n c t i ~with ~ the Internal Ewrgy Distribution Function Following Haarhoff: it can be shown that the 4-dimensional rotor has the thermal distribution function
where EOis a particular value of the photon energy hvo. If we choose a kernel (Le., 0 K) photoion yield curve of the form +(E - Et), then the convolution takes the following form:
(1) Prethreshold:
(2) Postthreshold:
Here, Et is the threshold energy at 0 K, and Z(E0) is the function to be fitted to the experimental data taken at temperature T.
A. LinearFunction:
d ( E - E,) = c(E - E,) where c is an arbitrary constant.
(1) Prethreshold
(2) Postthreshold
I(&)
+
~ [ 2 k T (Eo - E t ) ]
Note that both functions become c(2kT) at threshold (EO= Et). The extrapolated linear function has an offset of 2kT, the average internal energy.
B. Square-Root Function:
d(E - E,) = c(E - Et)'/2
V. Conclusions An experiment incorporating greater precision than earlier ones, together with a more extensive analysis of the data, leads to AP(CH20H+/CH3OH) = 11.649 f 0.003 eV. Together with IP(CH20H) = 7.549 f 0.006 eV, this yields Do(H-CH2OH) = 395.6 f 0.6 kJ/mol, from which one deduces AHf0o(CH20H) = -10.5 f 0.9 kJ/mol and AHf0298(CHzOH) = -16.6 f 0.9 kJ/mol. The kinetio-thermochemical result of Seetula and Gutman? when corrected for So(CH20H), becomes AHf02B(CHr OH) = -12.2 f 1.7 kJ/mol. The revised SO(CH20H) is based on a hindered rotor, in contrast to earlier calculations assuming a free rotor or a torsional vibration. Apart from the magnitude of the discrepancy in AHf0298(CH20H), the direction of the deviation is incompatiblewith the present value, which is an upper limit. Of several recent ab initio calculations, the most extensive one23 yields AHf0298(CHzOH)= -1 5.6 f 1.5 kJ/mol in excellent agreement with the present result. From AP(CH20H), one can also deduce PA(CH2O) = 711.4 f 0.9 kJ/mol, in very good agreement with another ab initio calculation26but differing from a standard compilation.
+ (E, - Eo)]
I(,!?,,) =
(1) Prethreshold:
(2) Postthreshold:
['
Z(E0) = c $Eo
-
+
At EO = E,, both functions become 3/4 6 T .
C. Exponential Function:
4 = c[l - e-b(E-Et)1
Heat of Formation of CHzOH and Do(H-CH20H)
The Journal of Physical Chemistry, Vol. 97, No. 44, 1993 11455 References and Notes
(1) Prethreshold:
(2) Posthreshold:
[
Z(E0) = c 1 -
e-b(E~&)
(bkT + 1)2
1
At Eo = Et, both functions become c[l - l/(bkT
+ 1)2].
Appendix 2. Entropy of CHzOH Curtiss et a1.21 have recently calculated the structure of CHzOH at the MP2 (FULL)/6-3 lG* level. From this structure, we find the principal moments of inertia to be ZA = 4.443, ZB = 28.205, and ZC = 32.251, all in 10-40 g cm2. The product of inertia is 4.041 X g2 cm6. Thus, S0298(CH~OH),trans + rot. = 228.302 J/(K mol). Since the electronic ground state is ZA, the electronic entropy is Rtn2 = 5.763 J/(K mol). There are nine vibrational degrees of freedom. According to Saebra et al.15, one of these is a hindered rotor about the C-0 bond (ZR = 0.982 X 10-40 g cm2).28 Saebra et al. calculate a barrier height of 3.98 kcal/mol at the MP3/6-31GS* level. They cite experimental estimates of 2.3 kcal/mol (Hudson, A.J. Chem. SOC.A 1969,2513) and -4 kcal/mol (Krusic, P. J.; Meakin, P.; Jesson, J. P. J. Phys. Chem. 1971,75,3438). If we take a barrier height of 4 kcal/mol, then Vo/RT = 6.75 at 298 K. Using Pitzer'ss table, we obtain S0298(hinderedrotor) = 9.8 J/(K mol). The vibrational contribution to entropy of the other eight degrees of freedom was calculated by using five frequencies from Jacox, M. E. (J. Phys. Chem. Ref. Data 1984,13,1011) and the other three frequencies from Curtiss (private communication, MP2/6-31G* X 0.94), which are close to those given by Saeb0 et al. In particular, the major contributor of those eight frequencies is the smallest one (735.5 cm-1 (Curtiss), 765 cm-1 (Saebta et al.)), which Jacox14 originally gave as 569 cm-I, but withdrew (Jacox, private communication). The vibrational entropy of these eight degrees of freedom is 1.782 J/(K mol), of which 1.115 J/(K mol) comes from w = 735.5 cm-l. The total entropy at 298 K = 228.302 9.8 1.782 5.763 = 245.6 i 0.9 J/(K mol). Using this approach, we have also calculated S0349(CH20H)= 253.6f0.9 J/(Kmol),H298-HO= 12.0fO.l kJ/mol and H349- HO= 14.5 f 0.1 kJ/mol. Thus, beginning with Seetula and Gutman's AF"349 = -29.9 f 1.3 kJ/mol, we deduce AHf0298(CH20H)= -12.2 f 1.5 kJ/ mol and AHHfOo(CH20H) = -6.1 f 1.5 kJ/mol.
+ +
+
(1) Ruscic, B.; Berkowitz, J. J . Chem. Phys. 1991, 95, 4033. (2) Refaey, K. M. A.; Chupka, W.A. J . Chem. Phys. 1968,48, 5205. (3) Ruscic, B.; Berkowitz, J. Prepr.-Am. Chem. Soc.,Div. Pet. Chem. 1991, 36, 1571. (4) Seetula, J. A.; Gutman, D. J . Phys. Chem. 1992, 96, 540. (5) D6W, S.Z . Phys. Chem. (Munich) 1992, 175, 123. (6) Traeger, J. C.; Holmes, J. L. J. Phys. Chem. 1993, 97, 3453. (7) Glushko,V.P.;Gurvich,L.V.;Bergman,G.A.;Veitz,I.V.;Medvedev, V. A.; Khachkuruzov, G. A.; Yungman, V. C. Termodinamicheskie Svoistva Individuarnikh Veshchestv; Nauka: Moscow. 1919. (8) Pitzer, K. S. Quantum Chemistry;Prentice-Hall: Englewood Cliffs, NJ, 1953. (9) Haarhoff, P. C. Mol. Phys. 1963, 7, 105. (10) Guyon, P.; Berkowtiz, J. J . Chem. Phys. 1971, 54, 1814. (11) DeFrees, D. J.; McLean, A. D. J. Chem. Phys. 1985,82, 333. (12) Botschwina, P. In Ion and Cluster Ion Spectroscopy and Structure; Maier, J. P., Ed.; Elsevier: Amsterdam, 1989; p 94. (13) Tsang, W. J. Phys. Chem. Ref, Data 1987, 16, 471. (14) Jacox, M. E. Chem. Phys. 1982,59,213. (15) Saebe, S.; Radom, L.;Schaefer, H. F., 111. J . Chem. Phys. 1983,78, 845. (16) In order for the hindered rotation of CHzOH to have an entropy q u a l to that found by Traeger and Holmes6 for a torsional vibration, the barrier height to hindered rotation would have to be 16 kcal/mol, about a factor 4 larger than the value calculated in ref 15 and used here. (17) Burcat, A. In Combustion Chemistry; Gardiner Jr., C. W., Ed.; Springer-Verlag: New York, 1984; p 488. (18) Buckley, E.; Whittle, E. Tram. Faraday SOC.1962, 58, 536. (19) Lias, S.G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref, Data 1988, 17, Suppl. No. 1. (20) McMillen, D. F.; Golden, D. M. Annu. Rev. Phys. Chem. 1982,33, 493. (21) Curtiss, L. A.; Kock, L. D.; Pople, J. A. J . Chem. Phys. 1991, 95, 4040. (22) Bauschlicher, C. W., Jr.; Langhoff, S. R.; Walch, S. P. J . Chem. Phys. 1992,96, 450. (23) Espinosa-Garcia, J.; Olivares del Valle, F. J. J . Phys. Chem. 1993, 97, 3377. (24) Gordon, M. S.;Truhlar, D. G. J . Am. Chem. Soc. 1986,108,5412. (25) Feenberg,E.Ann.Phys. (A")1958,3,292; Wilson,S. Int. J. Quanfum Chem. 1980, 18,905. (26) Smith, B. J.; Radom, L. J. Am. Chem. Soc. 1993, 115,4885. (27) Lias, S. G.; Liebman, J. F.; Levin, R. D. J. Phys. Chem. Ref. Data 1984, 13, 695. (28) Although CHzOH is distinctly an asymmetric rotor, with the CHI axis deviatingsignificantlyfrom the CO axis, we have used the simple expression IR = I&/(& + I#),where I. and I8 are the moments of inertia of CHI and OH about the CO axis. The more complicated expression IR = 1.[1 &I A&/I,], where I. is the moment of inertia of the symmetric top, I, are theprincipalmomentsofinertia for theentiremolecule,and Atarethedirection cosinesof the symmetry axis of the top a,would be appropriateif CHzsatisfied more closely the criterion of a symmetric top. However, in this Case the CHI axis is tilted 26.4' from the CO axis. The differences in S O 2 9 8 and H291- HO resulting from these two equations for calculating IR amount to about 0.9 J/(K mol) and 0.1 kJ/mol, respectively. Theuncertainty in the barrier height is very likely a larger source of error. An uncertainty of f l kcal/mol in the barrier height contributes *1.3 J/(K mol) toS'298, and *0.16 kJ/mol to Hzgs -Ha.
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