J . Phys. Chem. 1989, 93, 4010-4016
4010
Hydride-Transfer Reactions. Temperature Dependence of Rate Constants for i-C,H,+ 4HC(CH,), = C,H, C(CH,),+. Clusters of i-C,H,+ and I-C,H,+ with Propane and Isobutane
+
Jan A. Sunner,+ Kimihiko Hirao,t and Paul Kebarle* Chemistry Department, University of Alberta, Edmonton, Canada T6G 2G2 (Received: May 19, 1988; In Final Form: October 31, 1988)
The rate constant k , for the hydride-transfer reaction i-C3H7++ i-C4Hlo= C3Hs + t-C4H9+was measured between 125 and 640 K with a pulsed electron beam high-pressure mass spectrometer. The results for k , were in good agreement with earlier work of Meot-Ner and Field; however, the transition between the near-collision-limit near-temperature-independent rate constant at low temperature and the negative temperature dependence at high temperature was found to be more gradual. Theoretical calculations of the energy of the reaction complex with the STO-3G basis set, along the reaction coordinate obtained from the MNDO method, indicate that the potential does not have an internal barrier, Le., is not of the double-well type. complexes were found even at the lowest temperatures This result is consistent with the fact that no stabilized C3H7+C4Hlo used. In mixtures of propane and isobutane, three other adducts were formed: C3H7+-C3H8, C4H9+.C4Hlo, and C4H9+-C3Ha. The third-order rate constants and the AHo and ASo values for the formation of these complexes were determined. A semiempirical treatment of k l based on the assumption that the back dissociation ( k b ) of the excited collision complex (C3H7+C4Hlo)* can be approximated by that for (C3H7+.C3Ha)* leads to a prediction for the temperature dependence of the rate constant for the unimolecular decomposition of (C3H7+.C4HI0)* in the product channel ( k J . This analysis indicates that only a gradual transition is expected for k l and that the actual collision limit is reached only at very low temperatures.
Introduction A comprehensive study of hydride-transfer reactions was reported by Meot-Ner and Field'v2 some time ago. These authors showed that many hydride-transfer reactions proceed at Langevin collision rates a t low temperatures and at lower than Langevin rates at high temperatures, where the rate constant has the form k = c F , where n is negative (negative temperature dependence). The transition between the essentialy temperature-independent collision rate region and the negative temperature-dependent region indicated by the data was fairly sharp. This sharpness of transition was accentuated by the who fitted their data by two intersecting straight lines. Magnera and Kebarle3a in a survey of slow, bimolecular ionmolecule reactions tried to model the experimental results of Meot-Ner and Field1i2on the basis of the double-well reaction coordinate R R K M model of Brauman4 (see Figure l a ) or a "switching model" (see ref 3a) based on the reaction coordinate of Figure 1 b. The reaction selected was ( I ) , which had been (CH3)2CH+ + HC(CH3)3 = (CH3)2CH2
+ +C(CH3)3
(I)
studied over a wide temperature range by Meot-Ner and Field' and involves relatively less complex reactants. The calculations3 provided only a moderate fit to the experimental results. In particular, the sharp break in the transition region from collision rates to negative temperature-dependent rates was poorly reproduced by the calculation. Also, the form k = c F , which gives a linear log k vs log T plot, was only approximately reproduced by the calculation, i.e., the log k vs log T plot of the calculated rate constant in the high-temperature region had a noticeable curvature. The present experimental work was undertaken to check whether measurements in our laboratory reproduce the sharp break implied by the Meot-Ner work. Also, we wanted to examine whether collisional stabilization of the excited, intermediate adduct (C3H7+-C4Hlo)* occurs at low temperatures. The theoretical models4 did not include the possibility of collisional stabilization of the excited adduct. The occurrence of such stabilization is expected to favor the hydride-transfer reaction over back decomposition. Assuming that stabilization increasingly 'Present address: Department of Chemistry, State University of Montana, Rnieman M.T. . 59715 . -. ...-.., . . . .
*Visiting scientist. Permanent address: Department of Chemistry, College of General Education, Nagoya University, Nagoya 464, Japan.
0022-3654/89/2093-40l0$01.50/0
occurs as the temperature is decreased, an agreement of experiment with the theoretical models cannot be expected. For the case where a high barrier separates the loose from the tight complex, as in Figure la, collisional stabilization might even lead to the formation of a stabilized adduct i-C3H7+.-C4HlwStabilized reactant adducts have been observed for some SN2ion-molecule reactions3bwhere an internal barrier is known to occur (see Figure 10 in ref 4). The experimental observation of an adduct in the hydride-transfer (1 j would amount to a proof that such an energy barrier exists and demonstrate that the reaction coordinate is a double well (see type a in Figure 1). As described in the Results and Discussion, the experiments failed to show evidence for collisional stabilization. Also, the stabilized adduct was not observed even at the lowest temperatures covered. However, other adducts, C3H7+C3H8, C4H9+C4Hl0, and C4H9+.C3H8, formed due to the presence of propane and isobutane in the reaction mixture were observed, and the rate constants, enthalpies, and entropies of the adduct-forming reactions could be determined by measurement of the rates and equilibria (2j-(4). C3H7'
+ C3Hg = C3H7+*C3Hg
C4H9+ + C4Hlo = C4H9+*C4H,o C4H9'
+ C3Ha = C4H9+-C3H8
(2)
(3) (4)
The rate constants and thermochemistry of these adducts, while of interest in their own right, provided also insights into the nature of the intermediate adduct i-C3H7+4-C4Hlo that could be expected to form from the reactants of the transfer reaction ( I ) . In addition to the experimental work, a b initio calculations of the reaction coordinate for reaction 1 were performed. Of necessity, considering the complexity of the reactants, only a minimal basis set (STO-3G) could be used. Even though the results (1) Meot-Ner, M.; Field, F. H. J . Chem. Phys. 1976, 64, 277. (2) (a) Meot-Ner, M.; Field, F. H. J . Am. Chem. SOC.1978, 100, 1356.
(b) Meot-Ner, M. In Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic Press: New York, 1979; Vol. 1, p 197. (3) (a) Magnera, T. F.; Kebarle, P. In Ionic Process in the Gas Phase; Almoster-Ferreira, M. A,, Ed.; D. Reidel Publishing: Dordrecht, Holland, 1984; p 135. (b) Caldwell, G.; Magnera, T. F.; Kebarle, P. J . Am. Chem. Soc. 1984, 106, 959. (4) Farneth, W. E.; Brauman, J. I . J . Am. Chem. SOC.1976, 98, 7891. Olmstead, W. N.;Brauman, J. I . Ibid. 1977, 99,4219. Dcdd, J. A,; Brauman, J . I . J . Phys. Chem. 1986, 90. 3559.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 10, 1989 4011
Hydride-Transfer Reactions
I""""""""'"1 t
\
C++D+
05
0
1.o
1.5
20
Time/ms. !AH
Figure 1. Potential energy diagrams for two possible cases that lead to rate constants that are lower than collision rates. (a) Double-well diagram. An internal barrier is present since transition state (AB+)* has a higher potential energy than the intermediate complex A+B. (b) Transition state (AB+)*has a somewhat lower energy than intermediate A+.B complex; however, the transition state is a bottleneck since it is a tight complex, while A+.B is loose. The columns of lines illustrate the density of states at different positions of the reaction coordinate.
obtained cannot be very reliable, a combination of the experimental data for (1)-(4) with the theoretical reaction coordinate leads to a considerable expansion of the description of hydride-transfer reactions such as (1).
Experimental Section The pulsed electron beam high-pressure mass spectrometer, PHPMS, used in the present work has been previously de~cribed.~ A quadrupole mass spectrometer and a secondary electron multiplier were used to detect the ions. The correction factors for discrimination against heavier ions in the quadrupole were obtained by comparing the low-pressure 70-eV electron impact spectrum of perfluoro-tert-butylamine measured on the quadrupole with the same mass spectrum obtained on a magnetic sector field mass spectrometer. Ultrahigh purity methane (Matheson U H P 99.97%) was mixed with small quantities of propane (Matheson RG 99.99%) or deuterated propane-d8 (MSD Isotopes) and isobutane (Matheson RG 99.96%) at atmospheric pressure in a heated Pyrex globe. The gas mixture was bled into the ion source at a pressure of 1-3 Torr. Prior to entering the ion source the gases passed a cold trap at -130 OC with n-pentane ice slush. This reduced the water content in the gas flow to negligible levels, and there was no interference in the spectra from proton transfer to HzO. Measurements were done at temperatures from 125 to 693 K. For temperatures below ambient the ion source was fitted with a cooling jacket with channels for flowing cooled nitrogen gas.s The ion source temperature was measured with iron-constantan thermocouples. The accuracy of the temperature scale was confirmed by the good agreement obtained with earlier published equilibria from this laboratory. At low ion source temperatures, extensive clustering occurred between the cations and the neutral hydrocarbon molecules. To study the hydride-transfer kinetics, the clustering must be suppressed. It was therefore necessary to use low partial pressures of propane and isobutane in the ion source. At the same time the propane pressure had to be at least 3-10 times as high as the isobutane pressure to produce a high initial concentration of the reactant C3H7+ion and a low initial concentration of the product (5) Kebarle, P. In Techniques of Chemistry Series: Techniques f o r the Study of Ion-Molecule Reactions; Sanders, W., Jr., Farrar, J. M., Eds.; Wiley-Interscience: New. York, 1988.
Figure 2. Ion intensities of major ions observed in a typical run. C2H5+ and CH,+ (not shown), the final ions of methane decrease, very rapidly due to reactions 5 and 6 with propane, which lead to C3H7+.C3H7+in turn decreases rapidly due to the hydride-transfer reaction (1) with isobutane. Reaction mixture: 3 Torr of methane, 3 mTorr of propane, and 0.3 mTorr of isobutane at 30 "C. In the initial 0.4 ms after the short electron pulse (30 ps), rapid ion-electron ambipolar diffusion contributes
noticeably to the decrease of the C3H7+(and C4H9+)intensity. C4H9+ions. A low limit to the ion source pressure of the isobutane Torr, was set by the increasing uncertainty in gas, ca. 3 X the actual partial pressure of isobutane and by an increasing interference from reactions involving impurities. In the experiments where clustering equilibria were measured, the concentration was varied from neat isobutane gas to a 5 X mole fraction in methane and the propane concentration from to 1.4 X mole fraction in methane.
Results and Discussion ( a ) Rate Constants for the Hydride-Transfer Reaction ( l ) , C3H7++ i-C4HI0= C3H8+ t-C4H9+,at Different Temperatures and Pressures. Electron pulse (30 ps) ionization of a mixture of methane gas containing traces of propane and isobutane produces CH5+ and C2HS' ions, the well-known final ions in methane. These react predominantly with propane, which is present at a much higher concentration than butane, via the dissociative proton transfer and the hydride-transfer reactions ( 5 ) and (6).6 With
+ + CH4 + C3Hg = CzH6 + C3H7'
CH5+ + C3Hs = i-C3H7+ H 2 C2H5'
(5)
(6)
about 0.01% poropane in methane at a few Torr, the C3H7+ions formed by ( 5 ) and (6) become dominant after some 100 ps. In the presence of butane at concentrations 3-10 times smaller than those of propane, the hydride-transfer reaction ( l ) , which is the focus of this paper, is observed to occur. The changes of the ion intensities with time observed in a typical experiment are shown in Figure 2. The dominant ions over most of the time are seen to be C3H7+and C4H9+involved in reaction 1. The intensities are affected both by diffusion of the ions to the wall and by the reactive change due to (1). In the region 0.1-0.4 ms fast ionelectrpn ambipolar diffusion6%'removes C3H7+somewhat more slowly than the reactive change. A transition to the slower free diffusion occurs at t > 0.4 ms. Generally better conditions for the kinetic measurement can be obtainedS by the addition of an electron-capturing compound such as CCI4. The early conversion of e- to C1- leads to slow ambipolar positive-negative ion and free ion diffusion over mose of the observable range.s Unfortunately, this stratagem could not be applied to the present measurements ( 6 ) Ausloos, P.; Lias, S. G . In Ion-Molecule Reactions; Franklin, J. L., Ed.; Plenum Press: New York, 1972; Vol. 2, p 707. (7) Dewar, M . J. S.; Thiel, W. J . Am. Chem. SOC.1977, 99, 4899, 4907. Dewar, M. J. S.; Rzepa, H. S. Ibid. 1978, 100, 58; J . Comput. Chem. 1983, 4, 158.
4012
The Journal of Physical Chemistry, Vo/ 93, N o 10, 1989
Sunner et al.
1 3
i 0
01
02
03
05
04
06
Timehs
Figure 3. Logarithmic plot of normalized (percent of total ions) intensity of C3H7+as a function of time after a 30-ps electron pulse Ion source pressure 3 Torr, 31 OC Three different experiments are shown (a-c) with progressively higher, constant concentrations of isobutane For actual concentrations see Figure 3 Slope = v I = -kl[C4HIoI
-----
15000
I 1 I
5000
I
t 01
02
03
04
05
06
07
08
Timelms
Figure 6. Time dependence of normalized ion intensities observed with n(iso-C,Hlo)
X
(molecules cmS)
Figure 4. Plot of v, obtained from the slopes in Figure 3 versus [C4HjO]. Since v , = k,[C4HIo],the straight line observed has a slope that equals molec~le-~ cm3 s-'. k , = 3.8 X
since the electron-capturing compounds cluster more strongly with the carbocations than the paraffins C3Hs and C4HIuand thus interfere with the measurements at low temperatures. When the present ion intensities are expressed in percent of the total ionization (normalized plots), the effects of diffusion are largely r e m ~ v e d .This ~ is illustrated in Figure 3, which gives log plots of the normalized C3H7+intensity vs time. The slopes of the plots provide v l = kl[C4Hlo],the reaction frequencies or pseudofirst-order rate constants. Plotting vl obtained at different [C4Hlo] leads to a straight line with slope equal to k , (see Figure 4). Below ca. 50 "C clustering began to contribute noticeably to the loss of C3H7+and C4H9+ions. The formation of the clusters is illustrated in Figures 5 and 6. Due to the resulting more complex reaction mechanism the rate constant k l had to be determined by the "integral plot" method.5 In a situation where the ion C+ (C3H7+in the present case), see eq 7 , is removed by the C+
+B
- - (1)
D+
E+
X+
(7)
reaction of interest (eq 1 ) and also by other parallel reactions (clustering in the present case) and the product ion of (1) (D+ = C4H9+) is removed by the consecutive reaction leading to products E+ ( =C4H9+C3H8+ C4H9+.C4Hlo)whose time-dependent concentrations can be determined, one obtains k l from expression 8, where all ion concentrations are set equal to the d[P+]/dt = k,[C+][B] = v,[C+]
IP+]' t
- [p'lro = v l l:[C+] - to
dt,
where [P'] = [D']
(8)
+ [E']
experimentally obtained normalized ion intensities. The integral
a mixture of methane (1.8 Torr), propane (0.25 mTorr), and isobutane (0.05 mTorr) at -1 18 O C . The short-lived ions CH5+and CzH5+are not included in the normalization. The C3H7+ion concentration decreases due to the hydride-transfer reaction ( l ) , which leads to C4H9+,and due to formation of the propane adduct C3H7+-C3H8.
Figure 7. Intergral plots for evaluation of rate constants for the hydride-transfer reaction C3H7++ i-C4HI0= C4H9++ C3H8,from runs like that shown in Figure 6. The sum of the normalized intensities of' C4H9+and its subsequent product, C4H9+(C4Hio,) = XIp, is plotted against the normalized intensity of the reactant ion integrated over time. The pseudo-first-order rate constants v, are obtained from the slopes of the straight lines. The offsets in the extrapolated lines at zero time are due to direct formation of C4H9+by reactions 4 and 5. The number densities of methane, propane, and isobutane were 9.7 X IOi6, 1.4 X IO", and 2.4 X I O i 2 molecules/cm3, respectively.
at different t was evaluated by numerical integration. Examples of such integral plots are shown in Figure 7. The requisite data for the integral plots were taken from normalized ion intensitytime plots; see, for example, Figure 6. Following eq 8, the slope in the plots in Figure 7 equals v i = kl [C4Hlo]. The rate constant k , is then evaluated from the known, constant, isobutane concentration. The steeper slopes near the origin, Figure 7, are due to direct formation of C4H9+from CHS+and CzH5+and isobutane. The combined rate constant k , determinations from the procedures illustrated in Figures 4 and 7 are used in Figure 8, which
The Journal of Physical Chemistry, Vol. 93, NO. 10, 1989 4013
Hydride-Transfer Reactions
10-26
x
F
8
10-27
5
m
5
L
i
-20L ,
n
I
N
lo-12~ C4H& C3H8
48
50
52
,
,
,
,
,
,
54
56
58
60
6.2
64
WW))
1
1o - * ~ 66
Reaction Coordinate
Figure 8. Temperature dependence of rate constants (temperature in
kelvin). Curves a-d: hydride-transfer reaction, C3H7++ i-C4HIo= C4Hgt + C3Hs. (a) This work, particle density 9.7 X 10l6molecule/cm3; (b) Meot-Ner;' (c) RRKM calculations;3(d) switching model;' curves e-g: association reactions. Third-order rate constants were multiplied by number density 9.7 X 10l6to facilitate comparison with rates of the hydride-transfer reaction. (e) Reaction 10, C3H7' + C3Hs + M = C3H7+(C3H8)+ M; (f) reaction 11, C4H9+ + i-C4HI0 + M = C4Hgt(C4Hlo)+ M; (9) reaction 12, C4H9+ + C3H8 + M = C,Hg+(C,H,) + M. gives a In kl vs In T plot. The data of Meot-Ner and Field' are included for comparison. The agreement between the two sets of data is good, although near the transition region in the hightemperature range the present rate constants are some 20-30% lower than those of Meot-Ner.' As mentioned in the Introduction, Meot-Ner fitted his data by two straight lines with a sharp break between them. Meot-Ner assumed that at temperatures lower than the transition temperature -220 K the rate constants are at the Langevin collision limit and thus have no temperature dependence. At temperatures above the break the data follow relationship 9. The present data clearly indicate that there is
k , = c7n
n = -2
for T
> 220 K
(9)
a more gradual transition from straight-line negative temperature dependence as in (9) to the region where kl is essentially independent of temperature. Comparison of the actual data points from the two laboratories in the transition region shows no serious discrepancy, Le., the Meot-Ner' points (not shown in Figure 8), which are less dense in the low-temperature region, are not incompatible with the more gradual transition indicated by the points from the present work. Theoretical R R K M calculation^,^^ based on Brauman's double-well model4 shown in Figure 7, bottom curve, predict a much more gradual change of the In k versus In T curve and also fail to reproduce the linear region of the experimental curve at high temperature. The switching model calculations of Magnera3show quite a good fit in the transition region, particular with the more gradual change obtained in the present work. However these calculations also essentially fail to reproduce the linear portion at high temperature. Collisional stabilization might be considered as a possible cause for the relatively sharp break in the In k vs In T curve and/or the linear rather than curved dependence at higher In T . As the intermediate complex loses energy due to third-body collisions, the product channel (k,) due to its lower potential energy becomes favored over the back dissociation channel (kb); see Figure 1. Furthermore the probability for collisional stabilization should increase with decreasing temperature because the loose complex (C3H7+.C4H,o)* is longer lived at low temperatures. Therefore,
Figure 9. (a) Potential curve for the hydride-transfer reaction (3), along the reaction coordinate obtained by STO-3G calculation. (b) Distances R I and R2in the optimized geometries (see text).
we measured kl also at an approximately 3 times lower pressure, i.e., a total particle density of 2.4 X 10l6molecules ~ m - compared ~, to the 9.7 X 10l6 molecules cm-3 used in the runs of Figure 8. These data also indicated a gradual transition and a linear region at higher T , both not significantly different from those observed in Figure 8. This result is in agreement with Meot-Ner's data' (see Figure 8), which also were obtained at lower number densities ((2-4) X 10I6 molecules ~ m - ~ )Thus, . there is no pressure dependence of k , for pressures up to 3 Torr (- lOI7 molecules/cm3). Experiments that will be reported in a future publication will deal with measurements of k , at pressures up to 60 Torr. ( b ) Ab Initio Calculations of the Potential Energy Surface for the Hydride-Transfer Reaction ( 1 ) . To clarify the question whether the hydride transfer reaction (1) has an internal barrier as in Figure l a or not, points on the potential surface were calculated. Since the system is rather complex, Le., has a large number of atoms, the semiempirical M N D O method7 was used to obtain the geometries corresponding to the reaction coordinate. With fixed R l , the distance between the central atom of the isopropyl ion and the axial hydrogen of isobutane (see I), the
[
R2
H kzH=C'H3]' Rl
$..
C H 37,' CH:H3 1
remaining geometry parameters were optimized with the energy gradient method. Twelve points on the reaction coordinate were obtained in this fashion. Then, these MNDO-optimized geometries were used for STO-3G basis set calculations with standard parametema The resulting energies relative to that of the isolated reactants i-C3H7+and i-C4H10are given in Figure 9. Since the reaction coordinate is a complicated function of the geometries, the distances Rl and R2 corresponding to the different potential energies are also given in the figure. The results show that the energy changes smoothly as R 1changes gradually from a value where the intermediate is reactantlike, to a value where the intermediate is productlike, Le., from left to right in Figure 9. Thus, the calculation predicts no potential barrier for the reaction, Le., a reaction coordination of the type b (see Figure 1). It should be noted that generally speaking, the STO-3G basis set (8) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1967, 51, 2657. Hehre, W. J.; Lathan, W. A,; Ditchfield, R.; Newton, M . D.; Pople, J. A. Quantum Chemistry Program Exchange, Indiana University, 1973.
4014
The Journal of Physical Chemistry, Vol. 93, No. 10, 1989
TABLE I: Thermochemical Data for Adduct-Forming Reactions" AHa/ reaction (kcal mol-') ( 1 0) sec-CH3H7++ C3H8 = C3H7+(C3H8) 13.6 ( 1 1) r-C4H9++ C4Hlo= C4H9+(C4HIO)' 7.2 = C~H~'(C~HIO)~ 12.1 (1 2) t-C4H9+ C3H8 = C4H9+(C,H8) 6.6
+
Sunner et al.
- S O /
(cal K-' mol-])
kb( 150)
29.4 23.1 41.6 22.3
1 . 1 x 10-27 2.1 x 10-28
7.1 X IO-'' 4.2 X
4.52 7.49
3.1 x 10-29
4.2 X
6.03
&
-n
"Standard state, 1 atm. bThird-order rate constants in m ~ l e c u l e -cm6 ~ s-' at 150 K. 'Coefficients: c and n of the equation k, = CF.Due to the narrow temperature range covered and experimental difficulties, values of n and c for reactions 11 and 12 may involve considerable error (see Figure 8).
is a "soft" basis set and tends to overestimate molecular interaction energies. Thus, the presence of a barrier cannot be excluded; however, the decrease of energy is so smooth that a flattening rather than a real maximum appears more likely, and this means that the reaction coordinate is likely of type b (Figure 1). It is interesting to note that the STO-3G predicted exothermicity of reaction 1 is 18.3 kcal mol, which is close to the experimental value of 17 k ~ a l / m o l . ' . ~This ~ is due to cancellation of errors, which works particularly well for isodesmic processes," and reaction 1 is an isodesmic reaction. The absence of an internal barrier predicted by the present calculations is in line with the failure to observe a stabilized complex (i-C3H74-C4HIo)+ at low temperatures (see next section). (c) Association of Ions in Propane-Isobutane Mixtures: sec-C3H7+*C3H8, t-C4H9+*C3H8, and t-C4H9+4-C4H10.At low temperatures several adduct ions were found in the methane/ propane/isobutane mixtures used for the measurement of the hydride-transfer reaction (1) (see Figures 5 and 6). Information on the kinetics of the formation of these species and their bond energies are of interest per se; however, the information obtained is also of relevance for the understanding of reaction 1. For these reasons the kinetics and equilibria of reactions 10-12 were made
+ M = sec-C3H7+.C3H8+ M +M t-C4H9++ i-C4HI0+ M = t-C4H9+.i-C4Hlo t-C4H9++ C3H8 4- M = t-C&9+*C3H8 4- M
sec-C3H7++ C3H8
(10) (1 1)
(12)
subjects of special determinations. The rate constants for the association (clustering) reactions 10-1 2 were obtained from integral plots analogous to those shown in Figure 7 . The third-order rate constants k10-k12that were obtained are shown in the In k vs In T plots in Figure 8. The apparent values for the pseudosecond-order rate constants at a total number density of 9.7 X 10l6 molecules cm-3 are also given, for comparison with the second-order rate constants of the hydride-transfer reaction (1) which were measured at this number density. The third-order rate constants klo-klz each can be fitted to the form k = C7". The values for n are negative as expected and are -4.5, -7.5, and -6.0. k l l and k 1 2could be determined only over a very narrow temperature range so that the n values obtained are not very reliable. The c and n values are given in Table I. A search was made for the stabilized adduct s-C3H7+.i-C4Hlo of reaction 1. Such collision-stabilized complexes were observed for some slow SN2 reaction^.^ However, only barriers that lead to a small gap AE' and have a sufficiently deep first well (see Figure 1) lead to stabilizable complexes. Therefore the observation of a stabilized complex would constitute a proof that a barrier is present, but the nonobservation is not a proof for the absence of a barrier. The complex formed in reaction 1 would be of the same mass, m/e = 101, as that formed in reaction 12. It is still possible to distinguish between reactions 1 and 12 on the basis of the linearity of integral plots like that of Figure 7, since the reagent ions of ( I ) , C3H7+,and of (12), C4H9+,have a very (9) See Table IV in ref 10. Values are based on data of Baer and Rosenstock and Cox and Pilcher; see references in this table. (10) Sharma, R. B.; Sen Sharma, D. K.; Hiraoka, K.; Kebarle, P. J . Am. Chem. SOC.1985, 107, 3741. ( 1 1 ) Devlin, J. L., 111; Wolf, F. J.; Taft, R. W. J . Am. Chem. SOC.1976, 98, 1990. See also other papers by Hehre, Taft, et al., examining substituent effects.
106 1o5 1o4
- o3 -'g 1
7.
102
c
U
y"
101
100
6;''
0 40
50
60
70
78
1 0 3 n (K-')
Figure 10. van't Hoff plots for clustering equilibria in C3H8and i-C4Hlo mixtures: (1) C3H7++ C3H8 = C3H7+(C3H8); (2) C4H9+ i-C4HIo= C4H9+(C4Hlo),(a) "loose" complex, (b) "tight" complex; (3) C4H9++ C,H8 = C4H9+(C3H8).
+
different time dependence. The analysis of the plots showed that the dominant precursor of mass 101 was C4H9+,Le., no stabilized complex was produced by (1 1). Additional experiments were performed using perdeuterated propane. In mixtures of CHI, C3D8,and i-C4H10,C3D7+is rapidly formed and subsequently undergoes the hydride transfer (13),
+ t-C4H9+
C3D7++ i-C4HI0= C3D7H
(13)
which is analogous to (1). The association products corresponding to reactions 10 and 12 C3D7.C3D8+ and C4H,.C3D8+(m/e = 109) were observed. A very minor peak at m/e = 108, which corresponds to the mass of the hydride-transfer reaction (1 3) complex C3D7+.C4HIo, was observed. However this peak could be essentially completely attributed to incompletely deuterated propane, Le., to the complex of reaction 12, C4H9+C,D7H(m/e = 108). The presence of small amounts of C3D7Hin the C3D8was manifest from the observed intensities of C3D7+and C3D6H+.Thus, these results also showed that a stabilized adduct was not produced in reaction 1 even at the lowest temperature used in the determinations (see Figure 8). Equilibrium constants for the adduct-forming reactions ( I 0)-( 12) could be determined over a considerable range of temperatures. These data were used to construct the van't Hoff plots shown in Figure IO. The thermodynamic data obtained, i.e., the AH" and AS" for the reactions are given in Table I. Most noteworthy in Figure 10 is the upward break in the plot of K , , involving the adduct C4H9+-C4Hlo.This break should correspond to a transition between a tight (unfavorable AS) and more strongly bonded adduct at low temperature and a loose and more weakly bonded adduct a t high temperature. The corresponding AS and AH values obtained from the linear regions of the plot are as follows: low temperature, A H o I I = -12 kcal mol-' = -48 cal K-' mol-I; high temperature, A H o I I = -7 and kcal mol-] and AS",I = -29 cal K-'mol-] (see Table I). The AH" and AS" values for the other two adducts indicate that
The Journal of Physical Chemistry, Vol. 93, No. 10, 1989 4015
Hydride-Transfer Reactions TABLE 11: Estimated Entropy (cal K-' mol-') of Tight C4H9(C4Hlo) Comolex at 200 K translation 38.1 21.4 overall rotation, u = 6 6.0 free internal rotation of -C4Hg+ hindered internal rotations of -CH, 1.2 X 6
~
internal vibrations in i-C4Hlo internal vibrations in t-C4H9+ sketching ( I ) , bending (2), and rocking (2) vibrations, all 250 cm-I
1.9 1.9
5
total experimentalo
81.5 11.4
"This work.
C3H7+.C3H8is relatively tight while C4H9+eC3Hshas a relatively loose structure at the temperatures of the measurements in Figure 10. The entropy values in Table I give some information on the structures of the two C4H9+C4Hlocomplexes. The unusually large entropy loss associated with the formation of the tight complex indicates that this complex has a hydrogen bridge between the tertiary carbons. The following calculations show this assumption to be reasonable. Using the standard entropy of isobutane at 200 K, 62.5 cal K-' mol-','* for isobutane and for t-C4H9+,and the A S o I I = -47.6 cal K-I from Table I, one evaluates the entropy of the tight complex as So = 77.4 cal K-I mol-'. The entropy contributions from the various degrees of freedom of the tight complex are estimated in Table I1 and lead to a So = 8 1 cal K-I mol-'. A second comparison can be made by considering the compound 2,2,3,3-tetramethylbutane, which is structurally similar to the tight complex. The So = 78 cal K-I mol-',I2 is seen to be close to the So = 77.4 cal K-I mol-' obtained for the tight complex. Given the reasonable model for the tight C4H9+C4Hlo complex described above, what then is the structure of the Ioos complex? The entropy difference between the loose and tight complex predicted by the experimental results is 23.9 cal K-' mol-' (see Table I ) . This large increase is compatible with the following changes. Two free internal rotations replace two rocking vibrations, one very loose stretching vibration replaces a tight vibration, and some further loosening of internal motions in C4H9+and C4Hjo occurs also. These changes are expected for the case where the two species become essentially independent of each other but are kept within a certain distance by the essentially nondirectional ion-molecule polarizability attraction and the exchange repulsion. To summarize, the evidence is that these weakly bonded carbocation-hydrocarbon complexes may exist in a "tight" structure, where the bonding is "site-specific", Le., the relative orientation of the ion and the molecule are locked by the favorable bonding interaction between two specific sites. They may also exist in a "loose" structure, where both the ion and the molecule may undergo relatively free rotation, while bonded to each other through ion-induced dipole and dispersion forces. The tight C4H9+C4Hlo structure should correspond to the one at the bottom of a symmetric double well, where the barrier between the two wells corresponds to transfer of the bridging H from one to the other C4H9groups. Unfortunately, information on the magnitude of this barrier is not provided by the present result. ( d ) Semiempirical Treatment of Hydride- Transfer Reaction ( I ) : sec-C3H7+ i-C4Hlo= C3Hs t-C4Hg+.The mechanism ~ . eq ~ 14, written of the bimolecular reaction 1 can be e x p r e ~ s e dby for a general case, and eq 15, written specifically for (1).
+
+
C3H7++ C 4 H l o
k $ (A+B)*
-
C+
+D
(C3H7+.C4Hlo,loose)*
-
A+ + B
kP
(14)
kP
(12) Scott, D. W. U S . Bureau of Mines Bullefin 666; US.Government Printing Office: Washington, D.C., 1974.
The loose and excited chemically activated complex indicated with an asterisk is formed via the Langevin rate constant k,. The complex can back decompose via kb or form the products via k,. The bottleneck in the product channel determining the value of k , occurs at the entrance of a narrow funnel in the multidimensional potential energy surface. Even though the potential energy of the reaction coordinate continues downward through the funnel, a large tightening of the complex occurs at the funnel, and the resulting decrease of the density of states constitutes the bottleneck (see also Figure 1b and subsections b and c). Applying the steady-state assumption on the (A+B)* complex, one obtaines eq 16, where k , is the rate constant for the overall reaction and corresponds to k , for the present reaction.
kov = kl
(17)
Very approximate experimental values for kb can be deduced from the third-order rate constants k, for formation of adducts C3H7+-C3Hs,C4H9+-C3H8,and C4H9+-C4Hl0obtained in the preceding section. The k, could be measured because for these adducts there is no product channel but only back dissociation kb or collisional stabilization by a third body M (see eq 18). It
can be ~ h o w n ' ~ that J ~the third-order rate constant in the strong collision assumption has the form of eq 19. Thus, kb can be kt
=
kcks/kb
(19)
kb
=
kcks/kt
(20)
evaluated from k, see eq 20), provided that k, and k, are known. Generally k , is assumed equal to the Langevin rate, which is temperature independent, and ks is also assigned a temperature-independent value close to k,. Assuming that one can find an adduct (A+B)* whose kinetic properties regarding both dissociation (kb) are expected to be very similar to those for (C3H7+-C,Hl0)*of reaction 1 and for which experimental k, at different temperatures are available, one can use eq 22 and experimental values for k,, = k , to obtain ap-
kovkb k, = k , - kov
kovk k , = -, k,
for high T , k,
>> k,,
proximate values and temperature dependence for k,. Equation 21 is a rearranged form of (16), while (22) is obtained by substituting eq 20 into eq 21. We have chosen to represent kb for reaction 1 via the k, for the adduct (C3H7+-C3H8), Le., k, for reaction 10 (see Table I):
k l o = 7.13
X
10-18T".52 molecule-2 cm6 s-'
(24)
Obviously only a very approximate correspondence can be expected. The k I owas selected since we believe that matching the ion (C3H7+)in reaction 1 is more important than exactly matching the molecule. The kb values for reaction 1 obtained with the assumption that kb = k , k , / k l o is probably uncertain by about a factor of 5 . Shown in Figure 11 are data for k , for reaction 1 evaluated with this procedure. The experimental k,, = k , used are from (13) Durden, D. A.; Kebarle, P.; Good, A. J . Chem. Phys. 1969, 50, 805. Payzant, J. D.; Cunningham, A. J.; Kebarle, P. J . Chem. Phys. 1973,59, 5615. (14) Herbst, E. J. Chem. Phys. 1982, 68, 323. Jennings, K. R.; Bass, L. Inf. J . Mass Spectrom. Ion Proc. 1984, 58, 307. Lui, S.; Jarrold, M. F.; Bowers, M . T. J . Phys. Chem. 1985, 89, 3127, and references therein.
4016
The Journal of Physical Chemistry, Vol. 93, No. 10, 1989 loL
'
0.1 5.0
,
5.2
1
5.4
5.6
58
6.0
62
of the inflection points in Figure 1 1 . These consideratiorls and the results in Figure I 1 make it clear that the approximately horizontal portion of k, = 1 X molecule-i cm3 S K I , observed experimentally in Figure 8 at low temperatures, probably does not correspond to k, as previously assumed] but is smaller by a factor of -2. A very gradual increase of k l to k, is expected with further decrease of temperature. Evidence was presented in subsection a that reaction 1 is pressure independent at total pressures up to 3 Torr. We will examine now whether the values for k, obtained here are consistent with this evidence. The condition for pressure independence is given in eq 28. Selecting the temperature T = 270 K, which falls
I
1
,
6.4
6.6
Ln(T(K))
Figure 11. Estimated unimolecular rate constant k , for hydride-transfer reaction. See eq 22. Numbers given in the plot correspond to choices for 109k, Assumed k , = IO9. Units for second-order rate constants k, and k , are molecule-' em's-'.
Figure 8 and were taken from the smooth (interpolated) experimental curve. At low temperatures, Le., near the transition region for kl in Figure 8, the value of k, = kl approaches that of k, and the value of k, is very strongly dependent on the choice of k,, due to the form of eq 22. Therefore, k, was treated as parameter. The k, calculated by the Langevin equation (25) is given in (25). k, = 2 ~ e ( ( u / p ) I / ~ a(C,Hlo) = 86
X
cm3 (25)
= 1.4 x I 0-9 molecule-' cm3 s-I
Therefore, k, = (1.2, 1.4, 2.0, and 2.5) X molecule-] cm3 s-l molecule-i were used, and the resulting shapes with k, = I X cm3 are shown in Figure 11. At high temperatures where k, >> k,,, (22) reduces to (23), and since k, has the approximate form (26) in this region and k, = 5.6 X 10-5T206 ( T = high)
Sunner et al.
(26)
k l o the form given in (24), the predicted k, for that region has the approximate form shown in (27). The low-temperature region
k , = k l k , / k l o = k,(7.9 X 1 0 1 z p 4 6 ) ( T h i g h ) = 7.9 X 1 0 3 p 4 6 for k, = 1 X molecule-' cm3 s-l (27) of k, in Figure 1 1 shows inflection points for k, values that are less than approximately 2 X molecule-' cm3 SKI.Since such inflection points are not expected on physical grounds, values for k, = 2 X 1 0-9 molecule-] cm3 s-' or somewhat higher are indicated. These values are still close to the Langevin value of 1.4 X molecule-' cm3 s-] and are considered not unlikely also on this ground. Furthermore. for the case where the measured value of kl is somewhat high, due to experimental error, values for k, higher than the theoretical value would be required for the elimination
k, = k,(7.5 X lo1*SKI),k,[M] = k, X lo1' at T = 270 K (29) in the region where k, is not strongly dependence on the choice of k,, we can use eq 27 for k, as shown by the first expression in eq 29. The stabilization rate predicted for [MI = 10'' molecule-] cm3 s-] (-3 Torr) is almost 2 orders of magnitude lower than k, (see values given in (29)). This result is in agreement with the assumed pressure independence of reaction 1. Since kp decreases with temperature, while k, does not, it is clear that at lower temperatures the stabilization will begin to compete. For 3 Torr of pressure stabilization may be expected to occur close to but below the lowest temperature used in Figure 8. It should be noted that the regime where k l is close to k, is not suitable for studies of pressure effects since the upper limit of k, with pressure increase is k,, and thus very accurate determinations of k, with pressure would be required. Much better suited are higher temperatures like T 1 300 K. But to see pressure effects at this temperature, pressures in the 50-Torr range will be required. Minor modifications to the PHPMS are needed to be able to do kinetic measurements at such pressures. Measurements at such pressures are presently under way, and the results will be reported in the near future. The approximate functional forms for kb and k , deduced from the present experiments should be useful also for further theoretical modeling of the hydride-transfer reaction (1) and other similar reactions. Also, the theoretical reaction coordinate in Figure 9 will be useful in modeling. Thus, for the switching model calc u l a t i o n ~ information ,~ of the potential energy of the reaction coordination is required. At the time,3 the energy was estimated on the basis of the classical ion-molecule polarizability interaction, which is an unsatisfactory procedure. Acknowledgment. This work was supported by a grant from the Canadian Natural Sciences and Engineering Research Council (NSERC). Registry No. Isopropylinium, 19252-53-0; rerr-butane, 75-28-5; propane, 74-98-6: isobutane, 75-28-5.
