J. Phys. Chem. 1984, 88, 3052-3059
3052
Intramolecular Converslon Rates over Low Barriers. 2. The Alkyl Nitrites K. I. Lazaar and S . H. Bauer* Department of Chemistry, Cornell University, Ithaca, New York 14853 (Received: June 20, 1983; In Final Form: January 10, 1984)
Relaxation times for intramolecular conversions in alkyl nitrites (syn anti) were measured via dynamic NMR spectroscopy, both in CDC13solutions and in the gas phase. The pressure range covered was 120-4.0 torr, at corresponding temperatures 293-205 K. Equilibrium constants were checked, and rates were estimated from both coalescence points (M,,T,) and broadened line shapes. A consistent assignment of chemical shifts is presented. The preponderance of data, from several sources, lead to a barrier of approximately 10 kcal mol-' for these interconversions. The magnitudes of bimolecular rate constants deduced for samples a$ the higher densities are in agreement with values calculated from appropriately corrected RRKM equations, but rate constants found for low-density samples were considerably larger than those predicted. A regional phase space model is proposed which accounts for this discrepancy. It is based on the postulate that, when the density of states is low (=40/cm-' for H3CON0at the barrier summit), nanoseconds are required for full redistribution of energy over all vibrational phase space.
Introduttion The rationale for our preoccupation with intramolecular conversion rates over low barriers (5 < E, C 15 kcal mol-') was presented in the first paper of this series.' The levels of excitation required for such reactions are so low that at 300 K the forward and reverse rates are effectively in equilibrium. In gaseous systems unimolecular processes follow second-order kinetics even at modest pressures, 10.2 atm. If the molecular species involved are relatiyely small, the density of states at E, levels are sparse (C1O2/cm-'), and one may anticipate attaining conditions when intramolecular vibrational relaxation times become significantly longer than picoseconds.* Thus, one cap explore in Boltzmannian systems (rather than on the basis of state-to-state processes) when RRKM models are no longer valid, with reference to the basic postulate that these rate constants depend only on the total vibrational energy content; irrespective of the distribution of Evlb within phase space. anti In our previous report' we deduced kbl's for the syn interconversions of methyl nitrite (I) from preliminary measurements of coalescence points (AIc, T, pairs) and N M R line shapes, over the pressure range 5-100 torr and a temperature range 240-310 K. We concluded that RRKM equations adequately accounted for those observations. Since those data were obtained while visiting two out-of-town installations, under rather restricted conditions, we recently repeated these experiments in our department by using a Bruker WM300 spectrometer. Also, measurements were extended to the ethyl (11), n-propyl (111), n-butyl (IV), and tert-butyl (V) nitrites in dilute CDC13solutions and in the gas phase. In the analysis and interpretation of the new data we encountered two problems. The first concerns the use of the generally quoted expression for the unimolecular rate constant in the second-order regime; it is applicable to strictly unidirectional processes and is not valid for reversible reactions. This question was fully analyzed and re~olved.~The second problem concerns the confusion in the current literature regarding the assignments of the chemical shifts to the various synanti isomers for the alkyl nitrites and estimates of their relative stabilities. This problem is resolved in the following, but first we present a brief review of the conflicting proposals now in the literature. That there are rotational isomers of the alkyl nitrites is well established. N M R spectra over a range of temperatures, both of the neat liquids and of solutions, showed that when the temperature was lowered the resonance line assigned to the a-carbon protons broadened and eventually split into two unequal peaks, which sharpened on further cooling. In the earlier report^^-^ the ~~
~
(1) Bauer, S. H.; True, N. S. J. Phys. Chem. 1980, 84, 2507. (2) Oref, I.; Rabinovitch, B. S. Acc. Chem. Res. 1979, 12, 166. (3) Bauer, S. H.; Lazaar, K. I. J . Chem. Phys. 1983, 79, 2808.
0022-3654/84/2088-3052$01.50/0
low- and high-field peaks were assigned to' the syn and anti conformers, respectively. Since the high-field peak for C H 3 0 N 0 is larger than the one at low field, Piette et aL4 concluded that tfie anti form was the predominant isomer. This was in disagreement witH Tarte's8 IR and UV studies,(gas phase), which clearly showed that the syn was more stable. Phillips et aL5 investigated several of the higher alkyl nitrites and accepted Piette's proposal. They argued that H bonding in the syn form shifts the a-proton resonance to lower fields and that the resonance position of the higher field peak was similar to those in the alcohols and ethers. Phillips reported that in isopropyl nitrite the low-high peak intensit): ratio was 0.13 (20 to -100 OCj-a questionable value. On this basis he assigned the lo%-field resonance to the syn isomer. However, at about the same time, in a similar study, Piette et aL6 found that ratio to be 16 at -75 OC. Gray and Reeves7 also studied 'H N M R spectra of I. They suggested that the relative stabilities derived from gas-phase studies (electron diffraction9and IR8 spectra) do not agree with the N M R data for solutions because of solvent effects on the higher dipole moment of the anti form.I0 Hence, they expected it to have a higher heat of solution and be the more stable isomer in the condensed phase. The enthalpy change due to isomerization for syn anti, as derived from their data, is approximately -800 cal mol-' (taken for liquid methyl nitrite, in a sealed 5-mm N M R tube, under its own vapor pressure at low temperatures). When they assumed an enthalpy increment of +350 cal mol-' for the gas-phase conversion4J0and corrected for the dielectric constant of the liquid, they estimated AH (in solution) = -100 cal mol-', rather than the observed larger negative value, but nonetheless a change in the expected direction. Brown and Hollis" also investigated a series of alkyl nitrites and nitrosamines by means of NMR. They not only claimed that all the low-field resonances of the a-carbon protons are anti and the high-field syn (on the basis of solvent and steric hindrance effects) but also questioned whether the observed kinetic phenomena were due to internal rotation. In this report we present new N M R data for both dilute solutions and the gas phase for five nitrites and propose assignments which are in agreement with the IR? LRMS,12 and other spectroscopic studies. (4) Piette, L. H.; Ray, J. D.; Ogg, R. A., Jr. J. Chem. Phys. 1956, 26, 1341. (5) Phillips, W. D.; Looney, C. E.; Spaeth, C, P. J. Mol. Spectrosc. 1957, 1 , 35.
(6) Piette, L. H.; Anderson, W. A. J. Chem. Phys. 1959, 30, 899. (7) Gray, P.; Reeves, L. W. J . Chem. Phys. 1960, 32, 1878. (8) Tarte, P. J. Chem. Phys. 1957, 20, 1570. (9) Rogowski, F. Naturwissenshuften 1940, 28, 517. (10) Chiba, Takehiko. Bull. Chem. Sac. Jpn. 1955, 28, 505. (11) Brown, H. W.; Hollis, D. P. J. Mol. Spectrosc. 1964, 13, 305. (12) True, N. S.; Bohn, R. K. J. Phys. Chern. 1982, 86, 2327.
0 1984 American Chemical Society
Intramolecular Conversion Rates over Low Barriers TO
V4"
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984 3053
Cajon joint (Voc line)
m Clamp (Nylon)
K e l - F (or
Nylon)
YO12 (Viton)
LZJ
fits
snugly
15mm
tube
Figure 2. NMR ('H)spectra of dilute solutions of R O N 0 in CDCl3at
the lowest temperature.
Figure 1. Cylindrically symmetric, light weight, vacuum valve for spinning NMR tubes. Experimental Section
Sample Preparation. The methyl nitrite was prepared by Dr. P. W. Fairchild for another inve~tigation.'~Samples of 111-V were obtained from commercial sources; I1 was synthesized following a somewhat modified procedure described by Noyes.I4 A mixture of sulfuric acid and ethanol was added dropwise to a solution of sodium nitrite. The crude product was condensed in a liquid-nitrogen trap. The bluish color of the initial product was found to be due to contamination by nitrous acid. The crude product was distilled under vacuum, first into a trap containing dry sodium carbonate (in order to free it from acid impurities), then through three more dry sodium carbonate traps, followed by two cold traps, and finally into the N M R tube. The final yellowish liquid was found to be pure ethyl nitrite on the basis of its gas-phase IR and 'H and I3C N M R spectra. All samples as well as the solvents were vacuum distilled and degassed prior to use; however, some N M R spectra of the alkyl nitrites showed that the homologous alcohol was present as a minute impurity. Solution N M R Spectra. Dilute solutions of I-V in CDC1, ( ~ 2 % 5-mm ; N M R tubes) were prepared volumetrically under vacuum manipulation. A small amount (less than 2% by volume) of tetramethylsilane (Me4Si) was added to these solutions for an internal reference before they were sealed. The proton resonances were measured on a Bruker- WM300 spectrometer, pulsed Fourier ~
~~~
(13) We thank Dr. E. R. Grant for this sample. (14) Noyes, W. A. "Organic Synthesis"; Homing, E. C., Ed.; Wiley: New York, 1943; Collect. Vol. 11, p 108.
transform mode, operating at 300.1 MHz. Generally up to 100 scans were accumulated with a relaxation delay of 15 s. The probe temperature was controlled by using the Bruker variable-temperature unit (B-VT 1000) during the N M R scans. Readings were taken before and after each set of runs at a specified controller setting, by placing the thermocouple into a nonspinning sample tube filled with asbestos. All samples were allowed to equilibrate for about 15 min at each temperature prior to spectral acquisition. The 13Cshifts of the above samples were measured in natural abundance with a JEOL FX90Q spectrometer in pulsed Fourier transform mode, operating at 75.47 MHz, under complete proton decoupling. Typically between 5000 and 14 000 transients were recorded. The probe temperature was set by a JEOL NM-VTS variable-temperature controller. The decoupler was turned off briefly prior to reading the temperature. Gas-Phase NMR Spectra. The 15-mm reusable N M R tubes were evaluated thoroughly, degassed, filled with I-V to the desired pressure (at 296 K), and sealed. The construction of the cylindrically symmetric vacuum valves is illustrated in Figure 1. The Bruker WM300 spectrometer was shimmed at each temperture until the best fid signal was obtained by using a sealed 15-mm N M R tube containing gaseous Me4Si (400, 100, or 40 torr). Routinely fwhm of 1.5 Hz was obtained for the resonance line of the 400-torr Me,Si sample at room temperature. Typically between 200 and 6000 transients were recorded for sample pressures of 120-4 torr. Assignments of Chemical Shifts, Equilibrium Constants, and Kinetic Parameters in Solutions
-
Proton Resonances. Solutions of methyl nitrite showed 'H resonances at 4.041 4.013 ppm downfield from Me4% (at 296.5 264.5 K). The coalescence temperature (T,) was estimated to be -247 f 2 K. At the lowest temperature (212.9 K; Figure
-
3054 The Journal of Physical Chemistry, Vol. 88, No. 14, 1984
syn-anti
Lazaar and Bauer
syn-gauche
I
H
1
h.
A anti - a n t i
)\
229.6 'K
213.4
O K
anti -gauche
A
Figure 3. Conformations of C2H50N0derived from microwave data.16
2) 4 v = vSyn- vantl = 322 Hz. Below T,, the high-field resonance line (3.706 ppm) is larger and sharper than the low-field line (at 4.779 ppm). These are assigned to the syn and anti isomers, respectively. The syn isomer was demonstrated to be the more stable form via its microwave spectrum.I5 Furthermore, our gas-phase spectra of all the alkyl nitrites showed no significant differences from the corresponding solution spectra with respect to relative intensities and chemical shifts. For example, we found K,(soln; 297.5 K) = 0.454 for H,CONO; calculated for the gas phase from microwave and IR data: K,(g) = 0.655. Hence, although solvent effects are clearly present, they are not of sufficient magnitude to alter the order of relative stabilities of the isomers, as proposed by Gray and ReevesS7 A solution of C 2 H 5 0 N 0at 298 K showed resonance peaks at 4.741 ppm for the a - C protons and 1.380 ppm for the terminal CH3 group. T, for the methylene protons was -244.8 K. At the lowest temperature (212.6 K, Figure 2) A v = 334 Hz. The low-field quartet (centered on 5.190 ppm) is larger than the high-field quartet at 4.079 ppm. These resonances are assigned to the syn and anti isomers, respectively, and conform with the relative stabilities derived from microwave data (gas phase) which showed that the syn-anti conformation is the most stable one16 (see Figure 3). The methyl protons also broadened and split into two triplets when the temperature was decreased (1.500 and 1.294 ppm at 212.6 K). Because of the small 4 v , the corresponding T, = 226 K. At room temperature the proton N M R spectrum of a solution of n-propyl nitrite consists of a sharp triplet (centered at 0.979 ppm due to the methyl proton), a sharp sextet (centered at 1.768 ppm, @-protons),and a broad triplet (centered at 4.673 ppm) for the a-protons. The chemical shifts for these a-protons were slightly temperature dependent; they range d from 4.673 (296.5 K) to 4.714 (264.5 K). The assignements indicated in Figure 2 were made by comparing peak intensities and multiplicities with the ethyl homologue. These were confirmed by irradiation of the @-C proton resonance, which caused both triplets to collapse to singlets. T, for the a-protons was estimated to be 2245 K and A v 334 Hz a t the lowest temperature (Figure 2). The @-protons also broaden and split when the temperature is decreased. Spectra of n-butyl nitrite solutions were recorded over the same temperature range of 296.5-212.9 K, the corresponding chemical shifts for the a-C protons were 4.706 at room temperature to 4.730 at 264.5 K. T, was estimated to be -246 K for the a-protons with A v 336 Hz at the lowest temperature (4.008 and 5.126 ppm). The assignments indicated in Figure 2 are based on intensities, multiplicities, and irradiation experiments. A typical temperature sequence for this compound is shown in Figure 4.
-
-
(15) Ghosh, P. N.; Bauder, A.; Gunthard, Hs. H. Chem. Phys. 1980, 53, 39. (16) Turner, P. H. J. Chem. SOC.,Faraday Trans. 2 1979, 75, 317.
296.5
O K
Figure 4. Progression of NMR (solution) spectra of n-butyl nitrite. TABLE I: Chemical Shifts for "C in CDCL Solutions
temp,' 41 42
R-ON0 MeONO" MeONO"
RT
43 44
EtONOb EtONOb
RT
45 46
n-PrONOb RT n-BuONOd RT
no.
K 215.4 215.4
C&,-Cp-C,-ONO 6, 53.532 52.083, 57.982 64.061 60.485, 66.862 70.020 68.173
8R
8,
ha
14.480 11.858, 15.970 22.466 10.428 31.047 19.129 13.645
'I. bII. cIII. dIV. 'RT = room temperature.
tert-butyl nitrite exists in the anti form only.I2 As expected on the basis of the above assignments the position of the resonance line of the methyl protons is close to that for the higherfield peak (anti) of the @-protonsin I11 and IV. In brief, our assignments are in agreement with those made in ref 5, 6, and 8 for 11-IV. However, in I the position of the syn resonance is not consistent with this general pattern. These protons appear to be strongly shielded, as are the 13C nuclei to which they are bound. It is interesting to note that CH,ONO and EtONO respond in significantly different ways to multiphoton irradiation at 10.6 pm. Whereas the methyl derivative generates rotationally hot N O (Trot 2100 cm-'), EtONO yields NO'S which are at room temperature.17 I3CResonances. 13Cspectra of I-IV are presented in Figures 5 and 6. Their shifts and assignments are listed in Table I. The low-field line of the split pair for I (no. 42) is smaller and broader than the one at the high field and is assigned to the anti conformer. However, for I1 (no. 44) it is the low-field line which is larger and sharper and is therefore assigned to the syn isomer. The switching of the relative positions is strictly parallel to that observed for the 'H NMR spectra, both in solution and in the gas phase. At 215.4 K, 4 v was found to be 132.7 and 143.4 Hz for I and 11, respectively; this is another feature in which the ethyl and methyl isomers differ. Equilibrium Constants. Equilibrium constants were estimated from positions of the 'H resonances recorded for these solutions. For an intrnmolecular conversion: s a, Ksla= [a]/ [SI = T,/T,, where T , and T~ are the mean residence times in the a and s forms. The observed chemical shifts above the coalescence temperature are the corresponding weighted residence times. Thus, 6obsd = (6aTa + &sTs)/(Ta. + 7:) or Ks/a 7 (6s - 6obsd)/(60bsd - 6,). This procedure for estimating K,,, s yields more accurate values than
-
(17) Professor Curt Wittig, private communication.
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984 3055
Intramolecular Conversion Rates over Low Barriers TABLE II: Equilibrium Constants in C W l 3 Solutions ('H Resonances)
&/a
temp, K 296.5 285.8 273.4 264.5 eu
IV
I11
0.454 0.450 0.428 0.401
0.676 0.661 0.637 0.629
0.590 0.562 0.554 0.502
606.5 130 0.51 0.47
352.8 f 32 0.41 f 0.12
706.4 f 186 1.3 f 0.66
**
AH',,,, cal mol-' M's/a,
I1
I
I
I
0.603 0.583 0.568 0.549 440.0 f 31 0.48 f 0.11
"
6
I
I
Y
.
T
Figure 6. Comparison of "C spectra for MeONO and EtONO at room temperature and at 215.4 K. T
6
( O K )
-0.43
CH3-CH2-CH2-CH -ON0 2 6
y
B
a
-0.55 I
0
-
-0.59
-0.63
n Pr ON0
3.2
3.6
4.1
1 0 ~( O K1- ' ) ~
Figure 7. Dependence of equilibrium constants on temperature, for dilute solutions of the alkyl nitrites in CDC13.
50
d
PPm
Figure 5. N M R ("C) spectra of dilute solutions of RON0 a t room temperature.
one based on the ratio of intensities of the split pairs below the coalescence temperature. Equilibrium constants at four temperatures were evaluated for I-IV. The corresponding Ke9 were plotted in Figure 7; enthalpies and entropies of isomerization (in
CDC13 solution) are listed in Table 11. Rate Constants. Rate constants (kf")for the syn anti conversion were derived, by using a line-shape analysis program for a number of spectra recorded in the vicinity of coalescence: rochem-' = kf"(1 K e i l ) (1)
+
where Keq = r a / r s .Then, the activation energy and the A factor were derived from the slope and intercept of a plot of In kf" vs
3056
The Journal of Physical Chemistry, Vol, 88, No. 14, 1984
Lazaar and Bauer
TABLE III: Coalescence Temperatures ('H)for Gas-Phase Alkyl Nitrites I ~ ( 2 9 6K)' 120 90 60 40 25 12 7
T,' 264.0 267.0 270.5 276.6 281.0 288.0 293.1
Mb 6.501 X lo-) 4.875 X 3.250 X 2.167 X lo-) 1.354 X 6.501 X 3.792 X 10"
D'
Mb
60 39 26 12 7 4.5
3.250 X 2.113 X lo-) 1.409 X lo-' 6.501 X 10" 3.792 X 10" 2.438 X Au(204.6 K) = 329 Hzd
Av(225.7 K) = 321 Hzd
T,C
'P
T (OK) 5.81
250
240.4 I
I
c
t t
c
6.501 4.875 3.250 2.167 1.354 6.501 3.792
A' I
I
4.00
I
+
P 7 425 11 894 10028
TABLE V Gas-Phase Rate Constants from Coalescence Conditions for svn-I "i anti-I [MI, mol cm-3 T,, K k$, cm3 mol-' s-l
,
5.0
a
-33.12 -53.73 -48.1 1
R n-C3H7
Y
5*2
T,C
R/ T.
1
\ 5.4
Mb
mol L-I. cIn kelvin; estimated precision within &2 K. d A v was measured
C2H5
-J
'P
4.875 X 3.250 X 2.113 X 1.300 X 5.959 X 12.5 6.772 X lo4 3.521 X 10" 244.8 2.167 X 247.0 4.5 2.438 X Av(227.6 K) = 328 Hzd
CH3
8-
T,C
TABLE I V Least-Squares Coefficients for the Relation In M = (Y
247.5
I
90 60 39 24 11 6.5 4
248.0 249.1 252.0 257.0 11 5.959 X lo4 246.7 260.0 6 3.250 X 250.0 253.0 261.0 4 2.167 X Au(226 K) = 327 Hzd
In torr; estimated precision within h0.5 torr (sealed at room temperature). for the lowest pressure sample at the lowest temperature.
Mb
Pa
T,e
@
V
IV
111
I1
I
4.04
I
4.08
lO?T
I
I
4.12
I
\ I
1
]
4.16
(OK-')
Figure 8. Intramolecular conversion rate constant (high-pressurelimit)
for MeONO-solution data.
X X X X X
10"
X
lo-'
10"
10" x 10-7
7.955 x 1.070 X 1.623 X 2.475 X 4.015 X 8.487 X 1.483 X
264 267 270.5 276.5 28 1 288 293.1
107 lo8 lo8 lo8 lo8 10' lo9
these to be less accurate. A reading error of 0.01 ppm introduces an uncertainty in Keq of about 10%. Coalescence curves (Mc,T,) for I-IV are plotted in Figure 12. The coefficients for the least-squares-fitted linear expressions (In M, = a /3/T,)are listed in Table IV. As expected for intramolecular conversions in the second-order regime, for a sequence of homologous reactants with a common E,, the larger the number of effective oscillators the shorter the chemical relaxation time.
+
AH* = E, - RT = 10.1 kcal mol-'
Bimolecular Rate Constants for the Conversion syn -I anti4 In our first report' we demonstrated that when the barrier for interconversion is low, the system is in the second-order regime:
AS* = R(ln A - In (ekBT/h)) = -6.3 eu
-(ds/dt) = kbJOIM][s] - kbi(l)[M][a]
1 / T (Figure 8): Ea = 10.55 f 1 kcal mol-' and In A = 27.09 f 0.3. The enthalpy and entropy of activation are
Gas-Phase NMR Spectra Proton resonances were recorded for many gaseous samples over the temperature range 297.9-204.6 K. A typical temperature sequence for I1 is shown in Figure 9, and a pressure sequence in Figure 10. Coalescence conditions were determined for each sample (Table 111). The low equilibrium vapor pressures of I11 and IV prevented determination of coalescence conditions at higher pressures. These spectra were similar to but not identical with those obtained for the solution phases. For I, the low-field peak was smaller and slightly broader than the one at the high field and was assigned to the anti isomer. For the other alkyl nitrites, with the exception of V, the low-field peak of the split pair for the a-C protons was larger than the one at high field and was assigned to the syn isomer (Figure 11). For V at low temperatures, no splitting of the methyl proton resonances was observed, as expected: 1.568 ppm at 236 K. Equilibrium constants for the gas-phase syn-I anti-I were calculated from ratios of partition functions3for the syn and anti isomers, assuming AHo = 314 cm-', which was derived from microwave spectra.15 The equilibrium constants deduced from the resonance line positions above the coalescence points were somewhat lower, and over the small temperature range (307-283 K) had a steeper slope. We consider
Since only infinitesimal departures from equilibrium contribute to N M R line broadening, 7,hem-l = kbi(' [ MI { 1 + Kq-'). Two sets of rchem'scan be derived from N M R spectra: from a sequence of coalescence points and from an analysis of line shapes recorded in the vicinity of coalescence. In the following we treated these as two distinct sets of data. The relations that we used are valid when Kes is close to unity: 7NMR-l
rm1
=
= 2rAv/2lI2 rsTa/(Ts
+ 7),
sz
l/(T2)
+ l/~,,,l
Keq =
(3)
Ta/rs
We proposed' that ( T 2 )for HCONO should be approximately + 2.52 X lo4 equal to that for H3COCH3 (T2 = 6.6 X pltorr), for which pressure-dependent line widths can be measured without perturbation due to site exchanges, on the N M R time scale. When experimental values for T2are used, determined for a model compound under comparable pressures and temperatures, corrections for line broadening due to diffusion are automatically included.
The Journal of Physical Chemistry, Vol. 88, No. 14, I984 3057
Intramolecular Conversion Rates over Low Barriers
a-rryn
Figure 10. Gas-phase 'H spectra of CH3-CH2-ONO; a pressure sequence at 257.6 K. TABLE VI: Gas-Phase Rate Constants from Line-Shape Analysis for syn-I * anti-I 6.501 4.876 4.876 6.501 1.354 6.501 6.501
X X X X X X X
10" 10" 10" lom7 10"
265.5 265.5 268.1 271.1 282.4 282.4 293.1
1050 890 1010 250 910 610 1300
5.882 X 6.648 X 7.604 X 1.424 X 2.568 X 3.583 X 7.890 X
lo7 lo7 lo7 lo8 lo8 lo8 lo8
TABLE VI1 Gas-Phase Rate Constants for Ethyl Nitrite from Coalescence Data IM1. mol T,, K kh,", cm3 mol-' s-' 3.250 2.113 1.409 6.501 3.792 2.438
X 10" X X 10" X X X
248 249.6 252 257 260 26 1
1.686 2.600 3.916 8.560 1.475 2.298
lo8 lo8 10' X lo8 X lo9 X lo9 X X X
TABLE VIII: Gas-Phase Rate Constants for Ethyl Nitrite from Line-Shape Analysis Tc, K 7chem-1, s-I kbi(o,cm3 mol-' s-] [MI, mol ~ r n - ~ 3.250 1.409 3.250 2.113 1.409 1.409 3.792 6.501 2.438
7
1
s
#
3
I
.
Figure 9. Gas-phase 'H spectra of CH3-CH2-ONO; a temperature sequence at 4.5 torr.
Since the N M R tubes were filled a t 296 K, [M]/(mol cmd3) = 5.418 X lO-*p (in torr). Values for kb,(ocare listed in Table V. A line-shape resolution program was written for computing broad profiles, given 6, and 6, for the fully resolved spectrum, K,( T ) and the intrinsic fwhm for each of the resonances. The computed profiles were matched to the recorded spectra (after scale adjustment). The best fitted rchen-lwere then converted
X X X X X X X X
X
10" 10" 10" 10" 10" 10"
246 252.5 249.6 249.6 253.5 257.6 257.6 257.6 257.6
760 970 990 870 1050 1450 670 890 630
8.733 2.601 1.145 1.548 2.820 3.922 6.734 5.217 9.848
X lo7 X lo8 X lo8 X lo8 X lo8 X lo8
lo8 lo8 X lo8 X X
to rate constants, summarized in Table VI. The two sets were found to be in good agreement as illustrated in Figure 12. A least-squares line for In kbr(ovs. 1 / T with equal weighting of all the points gave an apparent activation energy of 14.89 f 1.04 kcal mol-'. Bimolecular rate constants for the conversion syn-II+ anti-I1 were also deduced from a sequence of coalescence points as well as from line-shape analysis of spectra in the vicinity of coalescence. For the latter, equilibrium constants were used as parameters with Kq solution values for I1 as a guideline. ( Tz)'s for I1 were also used as parameters to obtain the best-fitted ~ , ~ ~ The ~ - lresulting . values are listed in Tables VI1 and VIII. Here again the two sets were found to be in reasonable agreement (see Figure 12). A least-squares line for In kbl(' vs. 1 / T with equal weighting of all the points yielded an apparent activation energy of 23.87 f
3058
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984
Lazaar and Bauer
I
1
2 1 , 5 ~ e O ~ 0
\
\,.I
\ 0 4 5
1
EtONO ',
I
34
I
, 3.6
I
3.8
I'
4.0
1 4.2
lo3/ T ( O K - [ )
Figure 12. In kf's derived from coalescence points (-0-) and from line-shape fittings(==) for CH20N0 and CzHSONOvs. 103/T. The pressure at which each sample was sealed (at room temperature) is given. The expected dependence, based on an activation enthalpy = l o kcal mol-', is indicated by - -. Equation 7, ref 3: kf = (XZ)([M]/ Q,)(aO/(l + ao))Q,*.Equation 11, ref 3: an expression for the longest relaxation time of a reversible system, near equilibrium, which involves the partition functions of both the reactants and the products. Note that the slopes of lines (solid) which connect equidensity points are close to the 10 kcal mol-' slope. The vertical dashed lines which connect equitemperature points demonstrate that the lower the pressure, the higher the deduced bimolecular rate constant.
Et ON0 4.5 Torr 204.6
2.59 kcal mol-'. The near parallel slopes of the In M , vs. l/Tc lines in Figure 2 (ref 3) indicates that similar values apply for the other nitrites.
O K
Discussion The large apparent activation energies of 15 and 24 kcal mol-' for the syn * anti conversions of I and I1 are not acceptable. (i) To account for the microwave spectra one would have to postulate a potential function with relatively flat bottoms and high narrow peaks, an unusual ad hoc shape. (ii) For I the enthalpy and entropy of activation in CDC& solutions were found to be 10.1 kcal mol-' and -6.3 eu from NMR line-shape analysis (Figure 8). A 50% increase in the gasphase over that in a polar liquid is difficult to justify. (iii) A d&ect measurement of the location of the lowest band of free-rotating
CH3-CH2-OH
Me ON0 12 Torr 240.9 OK
b
*
I
c
3
I
,
Figure 11. N M R ('H) spectra of gaseous R O N 0 at the lowest pressures and temperatures used. Resonances due to slight amounts of the corresponding alcohols are indicated.
states in H,CONO via the TD technique'* gave 11.5 2.5 kcal mol-'. (iv) The strongest argument is that with a 15 kcal mol-' barrier for I the calculated values for kbi(Oare more than 3 orders of magnitude lower than those observed. (v) Inspection of the points in Figure 12 shows that when bimolecular rate constants are evaluated from line shapes, for several pressures at the same temperature, the kh(% from the higher pressure values are smaller than those from lower pressures, which suggest that the simple bimolecular rate law (eq 2) is inadequate. Note that the 1/T slopes in Figure 12 which connect equipressure points indicate =10 kcal mol-'. To account for these observations we proposed a regional phase space model.3 We postulate two regions in phase space: (i) A states from which transitions to A, or A* states require collisions, and (ii) (18) Ruschin, S.; Bauer, S. H. J . Phys. Chern. 1980, 84, 3055.
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984 3059
Intramolecular Conversion Rates over Low Barriers
/ h
ka2/kal i= 7.5 X lo-’. Since kal i= 5 X lOI3, ka2 = 3.7 X lo7 s-I and the characteristic time for energy redistribution from a phase s. space to A* is about 2.7 X
Conclusions L?
n o .n x
c
-1
/
v
37.0-
8
36.8 I
I
I
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I
I
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I
Study of rates of intramolecular conversions over low barriers was initiated to determine whether the RRKM formulation, in the second-order regime, adequately accounts for cases wherein the density of states is low at the barrier summit. The expectation, more readily seen in terms of RRK theory, is that not all portions of vibrational phase space are coupled on a time scale of picoseconds when the effective number of oscillators is of the order of 2-4. Our initial rough measurements1indicated that RRKM was an adequate approximation; the current much more precise data indicate that, indeed, at low pressures when the mean time between collisions is sufficiently long, an additional channel for reaction (1 (Y *) becomes available through a portion of vibrational phase space which is not well coupled to the reaction coordinate. We emphasize that in RRKM theory the statement k(E) is not meaningful unless a specified time scale is incorporated, such as, k ( E ) for t > T,,, where the intravibrational relaxation time is dependent on the barrier height, the density of states at E I Eo,and the coupling parameters between the molecular oscillators. Note Added in Proof. Subsequent to the submission of this manuscript and after the appearance of our paper on second-order rate constants for reversible intramoleuclar conver~ions,~ Chauvel and True published their results under the title “Conformational Kinetics of Methyl Nitrite. 11. Phase Dependence of Kinetic Parameters” (J. Chem. Phys. 1984,80, 3561), which was a sequel to paper I on “ N M R Spectral Evidence for Statistical Intramolecular Vibrational Redistribution” (Chauvel et al. J. Chem. Phys. 1984, 80, 1469). They found, as we did, that at low pressures their deduced bimolecular rate constants increased as the pressure decreased, but ascribed that to an artifact (surely not due to wall collisions). If it is an artifact, it is surprisingly consistent for diverse molecular species and for different N M R apparatuses, operating over a range of frequencies. Nonetheless they argued that their results are compatible with R R K M predictions. If the crucial low-pressure data are perturbed by an undetermined but clear trend, then they cannot be used to demonstrate that intramolecular vibrational energy redistribution occurs at the statistical limit. Reanalysis of their tabulated k,ik for C H 3 0 N 0 and SF4(Spring, C. A,; True, N. S. J. Am. Chem. SOC.1983,105,7231) show that in spite of considerable scatter these “constants” have a clear trend, from 120 torr down to the lowest pressures measured, as predicted by our eq 6:
--
A
B
The set of reactions 5 differs in a significant feature from the Gill and Laidler sugge~tion’~ (mixed RRKM-Slater) in that k2,, ka2, k,, kb4are not collisionally induced. With the further postulate that k23, k34 >> k21[M], k2,, etc., this system reduces to four differential equations with four relaxation times, of which the longest (observed) depends not only on the ambient pressure [MI, but also on the magnitudes of the internal energy redistribution rates. At modest pressures, k12[M][A]> kaz[A,], while at low pressures kI2[M][A] < (or comparable) k,,[A,]. Then the CY channel contributes to the net rate to an extent determined by the relative efficiencies for populating A, vs. A*. One may readily demonstrate, by using a simplified analysis, that this model does account for our data. Suppose k32 is very small; k23 > kzl[MI; allow A, and A* to be at steady state. Then -(dA/dT) = k23A*: -(dA/dT)
i=
[Al[Mlki2 + k1,/{1
+ (k,i/ka2)[Mll
=
[Mlkbi(oexptl (6)
-
We presume that A, and A* have the same mean integral energies rI2exp(-10000/RT) and kl, = I?’, exp(1OOOO/R T ). Then
so that k12
For these experiments, (k,,/k,,)[M] > 1. Hence, a plot of the from left member vs. 1/M, extrapolated to M-+ m, gives In r12 the intercept. In Figure 13, the two sets of rate constants were plotted in this manner. Extrapolated slopes to 1/M = 0 gave for r12= 2.3 X 10l6 (coalescence points) and 9.8 X loi5(line-shape analysis). These are reasonable values for the preexponential factors in the second-order regime. Assuming comparable collision = ria), the mean of the limiting slopes gives efficiencies (r12 (19) Laidler, K. J. “Theories of Chemical Reaction Rates”; McGraw-Hill: New York, 1969; p 142.
kkptl-+ k h i t +
K/
[MI
We conclude that indeed their data, for both C H 3 0 N 0 and SF4, support the regional phase space model. For these reversible conversions over low barriers, at low temperatures, intramolecular vibrational relaxation appears to be incomplete at =1 ns. Clearly, when kexptl’sare pressure dependent, plots of In k:ip vs. 1/T do not give correct activation energies, and one may question whether they have demonstrated a phase dependence. Acknowledgment. These studies are funded by the AFOSR under Grant No. AFOSR-80-0046. We acknowledge the National Science Foundation Instrumentation Program (CHE-79-04825 and PCM-80-18643) for support of the Cornel1 Nuclear Magnetic Resonance Facility. Also, we thank Dr. N. S. Chiu for writing the line-shape program.
