NOTES
3377
data, and the proposed error in ICE changes the deduced AT.9 Of course, there is no reason why (AE) values magnitude of (AE) by only 10%. The error in should be identical for different substrates and systems.2 AHfo(CH2)in the second case6 is actually irrelevant What meaning is to be attached to (AE) quantities? since the thermochemistry was specified in empirical Atkinson and Thrush suggested in their concluding remanner as based on reasonably well known (within a marks, as a preferred interpretation of the data obtained by them, that most collisions with inefficient factor of 2, say) values for k E in the cyclopropane sysbath gases are elastic and that a large amount of energy, tem. Moreover, the original (AE) values for cycloperhaps an average vibrational quantum of -16 kJ p r o p a n e ~have ~ recently been reconfirmed by a reinvesmol-’, is rrmovcd on infrequent collisions, e.g., 1 in 28 tigation of the dimethylcyclopropane system,8while the for He, sag, rather than a much smaller amount on virsec-butyl data agree with a large number of recent investually each collision. On this basis, however, the retigations of other similar radical ~ y s t e m s . ~ There is no doubt that experimental error may affect maining disagreement between thc two groups becomes the question, hoJv important is elastic collision? Is the some or all of the data under consideration. For instance, there is an inconsistency between the data reelastic collision probability, p f l , closc to unity for He, for example, as suggested by .Yl’?lo ported by AT for CHT and CHT-ds.13 Some values for CHT-ds at lower energies are inaccurate but can be The Cambridge data offrr no iiiforin:btion on this matter since theirs is a “high pwsure” s t ~ d y . ~The corrected, work of the Washington gronl’ ciitcd,4J and later Acknowledgment. One of us (B. S. R.) is grateful studies,B>’were made at both “high” and “low” presfor the hospitality of Trinity College (Oxon) during sures and do providc such information, as do thermal his tenure there as a Visiting Fellow, and for that of dilution studim8 Wr niny rccall (see ref 4 and 7) that the Department of Physical Chemistry, Oxford Unithe “high pressurc” single-channel kinetics method for versity. studying energy transfer gives values of (AE’) which depend, as required input, upon the magnitude of the (9) L. D. Spicer and B. S. Itabinovitch, J . Phys. Chem., 74, 2445 inelastic collision cross section; by contrast, the “low (1970). pressure’’ method yields values of (AE) which refer (10) If this suggestion is correct, however, there should then not be nearly as much curvature in the calculated Stern-Volmer plots only to inelastic collisions and which require no knowlpresented by AT for He, COP, and SFs (Figures 5 and 6 of ref 2), edge of the inelastic collision cross section. The measince the curvature depends on the magnitude of the average energy amount transferred per inelastic collision and not on the magnitude surements to date which are diagnostic for this matter of the average amount per total number of collisions: elastic colsupply a consistent answer : “IOTV pressure” single-chanlisions do not affect the shape of the Stern-Volmer curve. ne1 reaction systems, of the kind considered above, and (11) D. C. Tardy, C. W. Larson, and B. S. Rabinovitch, Can. J. Chem., 46, 341 (1968); C. ‘CV. Larson and B. S. Rabinovitch, J . later work with multiple channel reaction systems7J1 Chem. Phys., 51, 2293 (1969). give concordant values for the behavior of a given inef(12) Y. N. Lin, S. C. Chan, and B. S. Rabinovitch, J . Phys. Chem., ficient bath gas in similar systems; these values of 72, 1932 (1968); 9. C. Chan, J. T. Bryant, L. Spicer, and B. 9. Rabinovitch, {bid., 74, 2058 (1970). (AE) when applied to the “high pressure’’ single(13) The experimental magnitudes of k~ for the two compounds channel data show that pit has no special weight. I n diverge with increase of E in a manner contrary to the theoretical short, the relative magnitudes of inelastic collision predictions for normal isotope effects in externally activated systems: see B. S. Rabinovitch and J. H. Current, Can. J . Chem., 40, 557 cross sections for all gases appear to be closely similar (1962). to those of conventionalg total kinetic collision cross section and, in the case of helium, say, is certainly not as low as l/z8 of such magnitude. This conclusion is furThe Reaction of Acetaldehyde and ther supported by the consistency of relative effective tert-Butyl Hydroperoxide’ cross sections found from dnergy transfer cross sections with those deduced from transport properties.9~~~ Thus, for helium, smaller amounts of energy are transby M. C. V. Sauer and John 0. Edwards* ferred on virtually every collision, rather than very Department of Chemistry, Brown Uniuersity, large amounts a t infrequent collisions. Providence, Rhode Island 02912 (Receioed M a y 7 , 1972) Finally, it was suggested by AT that the calculated Publication costs assisted by U . S . A i r Force Ofice of Scientific Research values of (AE) in (1) the sec-butyl radical system and in (2) the cyclopropane system depend strongly on the magnitudes of the theoretical ICE used in the data interThe stoichiometry and thermodynamics of the addipretation in the first case4and on an error in the value of tion reaction (eq 1) of acetaldehyde and tert-butyl AHfo(CH)2) used6 in the second case. We have reinhydroperoxide have been studied by proton magnetic vestigated this matter by detailed ad hoc stochastic calresonance spectroscopy. culations. The suggestion of AT proves to be greatly overdrawn. I n the first case, the experimental mag(1) Abstracted from a portion of the Ph.D. thesis of Maria C. V. nitudes of KR depend principally on “low pressure” Sauer at Brown University, 1970. The Journal of Physical Chemistry, Val. ‘76,N o . 21, 1971
NOTEB
3378
0
OH
I
// CH3C \
+ HOOC(CHg)3)r CH,COOC(CH,), I H H
(1)
Nmr Spectra. The nmr spectrum of pure acetaldehyde consists of a quadruplet at 6 9.68 and a doublet a t 6 2.15 (Figure 1). The quadruplet was assigned to the aldehydic proton and the doublet to the methyl group. The nmr spectrum of tert-butyl hydroperoxide consists of a singlet at 6 1.25 assigned to protons of the tert-butyl group and a quite broad resonance a t 6 7.97 assigned to the proton of the hydroperoxide group.2 The nmr spectra of mixtures of acetaldehyde and tert-butyl hydroperoxide show (in addition to the resonances of pure acetaldehyde and tert-butyl hydroperoxide) a quadruplet centered a t 6 5.35 and a doublet centered a t 6 1.24. The broad peak assigned to the hydroxy and hydroperoxy groups was shifted in this spectrum to about 6 5. The assignments of the doublet and the quadruplet of the addition product were checked by measuring the coupling constants; it was found that J d o u b l e t = J q u a d r u p l e t = 5.50 cps. Similarly, for acetaldehyde, the assignments were confirmed by the coupling constants: J d o u b l e t = J q u a d r u p l e t = 2.84 CPS. The 6 1.25 resonance due to the tert-butyl group in tert-butyl hydroperoxide appears in the mixtures spectra as a slightly broad peak and apparently overlaps with the resonance due to the tert-butyl group in the addition product. By varying the total concentration 0
TMS
of tert-butyl hydroperoxide it was found that under the experimental conditions the resonance was saturated. The saturation was noticed because with increasing concentrations of tert-butyl hydroperoxide the intensity of the peak remained unchanged and by decreasing the radiofrequency of the oscillator the intensity of the peak in a particular sample increased.a To avoid the saturation problem, solvent benzene was added to the system and, when working at low temperatures, small concentrations of tert-butyl hydroperoxide were used. Under these conditions, the 6 1.25 resonance became narrower and it was possible then to distinguish the chemical shifts of the tert-butyl group in the free tert-butyl hydroperoxide and in the addition product; these shifts are less than 2 cps apart. The product nature and stoichiometry of the reaction were checked in every spectrum by measuring the relation in intensities between the tert-butyl resonance, the methyl doublet, and the proton quadruplet of the addition product.
Results. The equilibrium constants K were calculated according to the equations [addition product], [CH3CH01, [tert-RuOOH],
K = and [CH,CHO], =
(
ICHaCHO
) [CH~CHOIO
ICH~CHO
+
I a d d i t i o n product
wherein I refers to the intensity of the nmr signal for the respective quadruplets. Similarly, from conservation of mass, we have [addition product], = [CH3CHOIo- [CH3CHO],
Ill1
and [tert-BuOOH], = [tert-BuOOHIo - [addition product],
b
IY C
I
till
1111
l
10
TMS
~
l
5
.
’
~
0
ppm (6)
Figure 1. The nmr spectra of acetaldehyde (a), led-butyl hydroperoxide (b), and a mixture of acetaldehyde and hydroperoxide (c) relative to tetramethylsilane; assignments are given in text. The Journal of Physical Chemistry, Vol. 76, N o . d l , 1971
~
The subscripts zero and e refer to initial and equilibrium states, respectively. The reaction was studied in the concentration range for acetaldehyde from 2.6 to 6.2 IM, for tert-BuOOH from 1.7 to 2.5 M , and benzene concentration from 3.7 to 7.4 M. At least four experiments at different concentrations were performed at each temperature. The equilibrium constants obtained, along with standard deviations, are presented in Table I. The corresponding Van’t Hoff plot showed some scatter but no deviation from linearity. The derived thermodynamic parameters for ~ ~ * l finite concentrations are as follows: AH = -8.60 (2) D. Swern, A. H. Clements, and T. M. Lwong, Anal. Chem., 41, 412 (1969). (3) J. A. Pople, W. G. Schneider, and J. H. Bernstein, “High-Resolution Nuclear Magnetic Resonance,” McGraw-Hill, New York, N. Y . , 1969.
COMMUNICATIONS TO THE EDITOR
3379
kcal mol-', AG = -0.66 kcal mol-', A S = -26.6 cal mol-' deg-l, and TAX = - 7.94 kcal mol-'. Table I: * Equilibrium Constants a t Different Temperatures for the Reaction of Acetaldehyde with tert-Butyl Hydroperoxide (Eq 1) Temp,
K ,M-1
O C
12.2 i 0 . 8 9.3 f 0.5 6 . 7 =k 0 . 5 5.6 0.5 4 . 8 i0 . 4 3 . 1 i0 . 4
-1.0 5.5 10.0 12.0 17.5 25.5
The value of K for the reaction of tert-BuOOH with acetaldehyde is slightly less (a factor of 4 a t 0"; a factor of 2 after statistical correction) than for hydrogen peroxide and acetaldehyde. Since conditions could not be made identical, the difference is only an estimate; nevertheless, it is clearly small. Also there are small differences in the values of A H and AS (more negative for HzOz addition). It seems clear that the addition process is essentially the same for HzOaand tert-BuOOH; the replacement of H by a tert-butyl group has little significance on the reaction. Acknowledgments. We are grateful to the U. S. Air Force Office of Scientific Research (Grant No. 70-1839) for continued support.
COMMUNICATIONS TO THE E D I T O R
Dependence of the Glass Transition Temperature on Heating Rate and Thermal History Publication costs assisted by Catholic University of America
Sir: In a recent paper Rasmussen and MacKenziel have reported glass transition temperatures, T,, measured by differential thermal analysis (dta) as a function of heating rate for water-alcohol solutions. Using a treatment proposed by McMillan,2 they calculated activation entropies and enthalpies for the glass transition relaxation from their data. We wish to report here some preliminary results of an analysis of heat capacity measurements in the glass transformation region which indicate that no fundamental significance can be attached to the kinetic parameters derived by the method of the above authors. l s 2 McMillan's treatment2 is in error in that he considers the heat capacity, C , rather than the enthalpy, H , to be the relaxing quantity in the glass transition region. (Mchlillan's treatment cannot account, for instance, for the maxima commonly observed3 in heat capacitytemperature plots near T,.) The correct approach is to consider the total enthalpy of a glass-forming liquid to be the sum of a nonrelaxing part, Ho, and a relaxing part, Hr
H(T,t) = Ho(T)
+ Hr(T,t)
The heat capacity changes and the breaks in the dta curves observed near T , are then associated with the
time-temperature dependence of the relaxing part of the enthalpy, for which a corresponding relaxational heat capacity may be written
C,(T,t)
=
bH,(T,t)/bT
The simplest assumption for the time dependence of the relaxational enthalpy is the first-order kinetic expression
b[Hr(T,t) - Hr"(T(t))l -= bt
-
[Hr(T,t) - Hrm(T(t)) 1 r(T(t)) (1)
is the relaxation time and H," is the equilibrium relaxational enthalpy, such that at constant temperature
Hr,~= m lim H,,T t+
m
In eq 1 it is presumed that the temperature-time schedule of the system is known, so that H," depends ultimately only on T . This, along with the assumption of linearity, also makes r a function only of T . Previous relaxation experiments have shown that eq 1 is generally inadequate both in that more than one time constant r is needed to account for the observed data and in that first-order kinetic expressions fail at fairly (1) D. H. Rasmussen and A. P. MacKensie, J . Phys. Chem., 75, 967 (1971). (2) J. -4.McMillan, J . Chem. Phys., 42,3497 (1965). (3) U. E.Sohnaus, C. T. Moynihan, R. W. Gammon, and P.B. Macedo, Phvs. Chem. Glasses, 11,213 (1970).
The Journal of Physical Chemistrv, Vol. 76, N o . 91, 2071
