J. Phys. Chem. 1987, 91, 4127-4131 b
at which the hump occurs also increases with increasing temperature. This results from the increase in the absolute value of AHo that occurs with increasing temperature. In conclusion, we have measured densities and specific heat capacities of the C10, C12, C14, and C16 TABS. These data have allowed us to calculate 4c values. We have combined these 4~ values with previously derived 6,values to determine values of C P 2 O . We suggest that, when possible, measurements should be made in the pre- and postmicellar concentration regions for surfactant solutions in order to determine quantitatively C P 2 O and ACpo values. However, in cases where this is not feasible, we suggest that enthalpy data obtained as a function of temperature can be used in conjunction with measured heat capacity data to determine ACpoand C P 2 O . W e also suggest that the 4c values to be used in this manner be determined at concentrations where C # J ~ is not changing rapidly.
c cp" 9
Ep20
cmc d, do AHdil
I
K kix
m
M2 n v20
Ax0 01
P 6
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research.
r
Y*
d 4C
Glossary A,
B,,, B ,
dr
constant in Debye-Hiickel expressions ion interaction parameters
Dynamics of the Reactions of CH,',
dL
4V
CH,',
4127
ion-size parameter specific heat capacity of solution and solvent standard partial molar heat capacity of solute critical micelle concentration expressed in molality density of solution and solvent integral enthalpy of diluting a solution from an initial concentration to a final concentration m ionic strength, mol kg-l thermodynamic equilibrium constant of eq 1 based on mo-
lalities coefficients in eq 8 and 9 defined in ref 8 total or stoichiometric molality of surfactant molecular weight of solute aggregation number standard partial molar volume of solute change in a thermodynamic property X (X= H , C,, V) for forming micelles at infinite dilution mole fraction of surfactant in micellar form fraction of counterions "bound" to the micelle shielding factor to give effective micellar charge activity coefficient product mean stoichiometric activity coefficient osmotic coefficient on a stoichiometric basis apparent molar heat capacity relative apparent molar heat capacity relative apparent molar enthalpy apparent molar volume
and CH+ with Acetylene
R. B. Sharma, N. M. Semo, and W. S . Koski* Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21 218 (Received: July 29, 1986; In Final Form: February 20, 1987) The reactions of CH3+, CH2+,and CH+ with acetylene to produce C3 ionic products were investigated by measuring the angular distributions of ion product velocities, reaction cross sections, and deuterium isotope distributions. The reactions appear to be proceeding by two different mechanisms. The lifetimes of the intermediate complexes as judged from the deuterium distributions are significantly smaller than the rotational periods of the systems. Measurements of the energies of the ionic reactants and products show that a large amount of internal energy can be present in the C3H3+ion.
Introduction The reactions of hydrocarbon ions with neutral hydrocarbons play an important role in the buildup of ionic chains in combustion processes.' They also play a key role in hydrocarbon polymerization by radiation2 and in recent years they have received considerable attention from scientists interested in explaining the origin of hydrocarbon molecules observed in ~ p a c e . ~ Most - ~ of these applications are based on laboratory work which, in the main, has been devoted to the measurement of rate constants and branching ratios." Considerably smaller number of investigations have been involved in measuring the energy and angular distribution of the products produced in hydrocarbon ion-molecule reactions. Such measurements give one a deeper insight into the dynamics and mechanism of these ion-molecule reactions than one can obtain by most other studies. They give information on the existence or nonexistence of a persistent intermediate complex which has been a point central to chemical kinetics and in turn they shed light on the nature of condensation reactions which are (1) Calcotte, H. F. Combust. Flame 1981, 42, 215. (2) Foldiak, G., Ed. Radiation Chemistry of Hydrocarbons; Elsevier: New York, 1981. (3) Herbst, E.; Adams, N. G.; Smith, D. Astrophys. J . 1983, 269, 329. (4) Schiff, H. I.; Bohme, D. K. Astrophys. J . 1979, 232, 740. (5) Smith, D.; Adams, N. G. Astrophys. J . 1977, 217, 741. (6) Szabo I.; Derrick, P.J. int. J. Mass Spectrom. Ion Phys. 1971, 7 , 5 5 . (7) Fiaux, a.; Smith, D. L.;Futrell, J. H. Int. J. Mass Spectrom. ion Phys. 1974, 15, 9. (8) Kim, J. K.; Anichich, V. G.; Huntress, W. T., Jr. J. Phys. Chem. 1977, 81, 1798.
0022-3654/87/2091-4127$01.50/0
important in carbon chain build up. In this later type of measurements reference should be made to the work of Herman et ale9 In the reaction of C2H4' (C2H4, CH3, H2) C3H3+they measured velocity and angular distribution of the ionic product and concluded that the reaction was proceeding through a persistent complex. On the other hand, work from the same laboratory showed that the reaction CH3+ (CH,, H2) C2H5+was proceeding by a direct process.1° Very recently an interesting crossed beam study was reported on the dynamics of the reaction of C+ with CHI to produce CH3+, C2H3+, and C2H2+." The production of CH3+involved a direct rebound collision mechanism in which hydride ion abstraction took place. C2H3' and C2H2+ proceeded through unimolecular decay of long-lived collision complexes. In the work being reported here we measured cross section and angular and energy distribution of the ionic products from the reactions of CH+, CH2+,and CH3+ with acetylene and because of the ubiquitous nature of C3H3+we have tended to emphasize reactions producing this ion and related ions.'* The ion C3H3+ is one of the abundant ions present in C2H2/02flames, in mass spectra of hydrocarbons, and in products of irradiated hydrocarbons, and it was felt that a study of the dynamics of these (9) Herman, 2.;Lee, A.; Wolfgang, R. J . Chem. Phys. 1969, 51, 452. (10) Herman, 2.;Hierl, P.; Lee, A.; Wolfgang, R.J . Chem. Phys. 1969, 51, 454. (11) Curtis, R. A.; Farrar, J. M. J . Chem. Phys. 1983, 85, 2224. (12) Smyth, K. C.; Lias, S.G.; Ausloos, P. Combust. Sci. Technol. 1982, 28, 147.
0 1987 American Chemical Society
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Sharma et al.
reactions would give us a better insight into the reactions and the nature of this ion. In view of the fact that CH3+ is isoelectronic with C H 2 one might expect some similarities between reactions involving CH3+and singlet CH2.I3 In this connection deuterium isotopic studies which were carried out in this investigation also give some interesting mechanistic insights into those reactions.
Experimental Section The instrumentation used in this study is of two types: (1) a spectrometer capable of measuring angular distribution and (2) an in-line tandem mass spectrometer. Both of these instruments have been previously d e ~ c r i b e d ' ~soJ ~only a brief description of their principal features is given here. The first instrument consisted of an ion source, a 180' electrostatic analyzer, and a quadrupole mass spectrometer as an input section. The projectile ions passed through a reaction chamber containing the target gas. The product ions exiting from the reaction chamber were energy analyzed by a second 180' electrostatic analyzer, mass analyzed by a second quadrupole mass spectrometer, and detected as a function of angle by an electron multiplier. The beam width was 0.1 eV (fwhm). Pulse counting techniques were used. The data from the angular and energy distributions for the reactant and product ions are collected, stored, and processed by using a minicomputer. The in-line tandem was used for measuring cross sections. Ions are formed by electron bombardment or chemi-ionization of a suitable gas. The ion beam was mass analyzed by a quadrupole mass filter and was energy analyzed by an electrostatic analyzer before passing through a reaction chamber. The products were then mass analyzed by a 60' Nier type mass spectrometer and detected with an electron multiplier. In preparing the projectile ions care was taken to keep the excitation energy to a minimum. This was done by a 100-eV electron bombardment of appropriate molecular species mixed with a large excess of suitable rare gas. CH3C1 + Xe+, CH3F + Kr+, and CH4 + Kr+ to give CH3+are essentially thermoneutral processes; hence one would expect the CH3+to have little internal excitation. CH2C12 in a large excess of Ar bombarded with electrons produces CH2+by a reaction which is exothermic by 9 kcal. The pressure in the ionization chamber was close to 1.0 Torr so there were many collisions before the ion left the chamber. This further helped reduce the internal excitation of the projectile. CH+ can be produced by a near-thermoneutral process by irradiating a mixture of fluoroform (CF3H) in a large excess of He with 100-eV electrons. The state of excitation of the projectile ion in ion-molecule reactions has been frequently ignored in some past work; however, it can exert a significant influence on the cross sections and branching ratios. For example, the cross section of the reaction CH3+ (C2H2,H2) C3H3+is 4 times greater if the CH3+ is prepared by electron bombardment of CHI than if it is prepared by electron irradiation of an appropriate rare gas mixture. Results and Discussion Reactions of CH3+and CD3+with Acetylene. The methenium ion, CH3+,is isoelectronic with methylene and hence some similarities might be expected between reactions of CH3+and singlet CH2.I3 In addition CH3+undergoes condensation reactions with C2H2to form C3 compounds and it is of interest to determine if long-lived persistent complexes are formed as intermediates in these reactions. In order to get some insight into these points the reaction cross sections for the CH3+and CD3+reactions and the energy and angular distributions of the ionic products were measured. An experimental criterion that the reaction is passing s) is that the distribution through a long-lived intermediate (> of the velocities of the ionic products be symmetric about a line at 90' to the beam direction and passing through the center of mass of the system. This is a necessary but not a sufficient condition. Deviation from such symmetry is generally taken as (13) Jones, M.;Moss, R. A. Carbenes; Wiley: New York, 1973. (14) Wendell, K.; Jones, C. A,; Kaufman, Joyce J.; Koski, W. S. J . Chem. Phys. 1975, 63, 750. (15) Watkins, H. P.; Sondergaard, N. A,; Koski, N.S. Radiochim. Acta 1981, 29, 87.
350 m sec
CI
Figure 1. Ion velocity distributions shown in Cartesian coordinates in the center of mass system for the reactions (a) CH,' (C2H2,H2) C3H3+,(b) CD,' (C2H2,D2) C3DH2+,and (c) CD,+ (C2H2,HD) C,D2H+. The barycentric energies are 1.30, 0.82, and 2.36 eV, respectively. (+) indicates the velocity of the center of the mass of the system.
evidence for a mechanism in which the reactants interact with each other for a time less than several rotational periods of the system. Some insight into the lifetime of a reaction intermediate can be gained by recourse to simple RRK the0ry.l' In the simplest form of this theory the lifetime is given by
L
where E is the total excitation energy of the complex, E* is the threshold energy for its decomposition and S is the number of active vibrational modes. For the reaction CH3+ (C2H2, H2) C3H3+E can be taken as the sum of the relative kinetic and internal energies of the reactants (1.3 + 0.2 eV) and the exothermicity of the process CH3+ C2H2 C3H5+(3.91 eV). We assume the lowest energy isomer, the planar allyl cation, for this product. Other possible structures and their energies have been calculated by Pople's group.18 A value for E* is not known but we take as an estimate the endothermicity of the deocmposition of the ground state of C3H5+to the ground-state products, C3H3+ + H 2 (1.35 eV). If one assumes a full complement of active oscillators (S)one obtains a lifetime of the order of 10 rotational periods. On the other hand if one assumes that only a half of the oscillators are active the lifetime is less than a rotational period. Obviously, because of the various uncertainties such as internal excitation of the various species involved, barrier to decomposition, number of active oscillators etc., one cannot expect a reliable lifetime from such considerations. However, such simple considerations suggest that it would not be too surprising if this reaction did go through a persistent complex. Typical angular distributions of the ionic products from the reactions of CH3+ and CD3+ with C2H2are given in Figure 1. All three of the angular distributions deviate from ideal symmetry and the peaks of the distributions are slightly behind the center of mass of the systems indicating that the reactions occur pre-
+
-
(1 6 ) Bernstein, R. B.; Levine, R. D. Molecular Reaction Dynamics;Oxford University Press: New York, 1974. (17) Kassel, L. S. Kinetics of Homogeneous Gas Reactions; Chemical Catalog Co.: New York, 1932. (18) Radon, L.; Hariharan, P. C.; Pople, J. A,; v. R. Schleyer, P. J . Am. Chem. SOC.1976, 98, 10. Raghavachari, K.; Whiteside, R. A,; Pople, J. A,; v. R. Schleyer, P. J . Am. Chem. SOC.1981, 103, 5649.
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987 4129
Reactions of CH3+, CH2+, and CH+ with Acetylene dominantly from small impact parameter collisions. The resulting ionic products rebound in the backward direction, and the bulk of the available kinetic energy is carried off by the light particle. At the same time there is a significant distribution of reactive scattered products in the forward hemisphere indicating the presence of larger impact parameter collision processes. As the relative kinetic energy between the reactants increases the distribution becomes more forward as expected.I6 The near-symmetry of product ion distribution precludes a definitive conclusion as to whether the reactions are proceeding through direct or complex mechanisms primarily because these studies were carried out with a reaction chamber which prevents an as accurate determination of the position of the center of mass as one would have obtained with crossed beams. For this reason isotope scrambling experiments are also carried out in these studies. Two other reaction time scales can be considered. One is the interaction of the methenium ion with a portion or the entire acetylene molecule for a period of time corresponding to a few vibrational periods and then separating to give the final products. Such a scenario would, of course, give an asymmetric angular distribution of the products and would not be detected by means of measurements of the angular distributions of product ion velocities. If however the projectile was CD3+,collisions with C2H2 lasting several vibrational periods can lead to a scrambling of the deuteriums and the hydrogens in the complex so that an examination of distribution of the deuteriums in the final product might give one evidence for the presence of a complex which lives for a time less than the rotational period of the system. Such considerations are based on the assumption of a negligible isotope effect and complete scrambling of the hydrogen and deuterium atoms involved. Such an assumption has support in the work of Tedder and associate^.^^^^^ A final reaction time scale that can be considered is one in which the reactions take place in a time comparable to the transit time of the projectile past the target molecule. The final products can arise from a "pick-up" or stripping type of process. Under such conditions one probably would not expect a meaningful scrambling of deuteriums and hydrogens if a deuteriated projectile ion was used. In Figure 2 the cross sections for the production of C3D2H+ and C3DH2+from the reaction of CD3+with acetylene are given on a somewhat expanded scale covering the kinetic energy range 1.0-10 eV. From about 10 to 4 eV the ratio of cross sections of C3D2H+and C3DH2+is 0.99 with a standard deviation of 0.06. Starting in the 3-4-eV region this ratio starts to rise and is 1.2 at 3.0 eV, 1.3 at 2 eV, and 1.4 at 1 eV. A possible interpretation of these results is that at the higher energy the projectile ion is interacting with only one end of the acetylene molecule and a scrambling of the three deuteriums and the one hydrogen results, followed by an elimination of a hydrogen molecule and the formation of the final ionic product. In this scenario the ratio C3D2H+/C3DH2+would be expected to be unity. An insertion type of mechanism would be consistent with this picture. In the low-energy region where the ratio of the mass 41 cross section to mass 40 cross section begins to deviate significantly from unity a different reaction mechanism is probably taking place. A possibility is an addition mechanism. If the CD3+added to the triple bond of acetylene and a complex was formed in which the three deuteriums and the two hydrogens were completely scrambled one would expect a C3D2H+/C3DH2+ratio of 2. Our cross section measurements indicate that the ratio is increasing with decreasing kinetic energy and could possibly reach a value of 2 at sufficiently low energies. There is some support for this conjecture in the work of Mitchell et aLi9 In studying the CD3+ C2H2reaction using a triple quadrupole mass spectrometer these authors report a 41/40 ratio of 2. Unfortunately the energy at which these measurements were made was not reported but it is
+
(19) Mitchell, A.; Conner, J. K.; Stanney, K.; Tedder, J. M.J. Chem. Soc., Chem. Commun. 1984, 1529. (20) Batey, J. H.; Tedder, J. M. J . Chem. SOC.,Perkins Trans. 2 1983,
1263.
01
I
I
I
I
I
I
I
I
I
I
I
I
LAB ENERGY (eV)
Figure 2. Reaction cross section as a function of projectile laboratory kinetic energies: (a) CD3+(C2H2,HD) C3D2H+( 0 )and CD3+(C2H2, ( X I , CD2+ (C2H2, D) D2) C@Hz+ (VI;(b) CD2+ (C2H2, HD) C3DH2+(v),and CD2+(C2H2,H) C,D2H+ ( 0 ) ;(c) CD+ (CzH2,HD) C3H+(O), CD+ (C2H2,H,D) [C3D++ C3H2+](v),and CD+ (C2H2,H) dashed line gives the estimated position of C3H2+. C3DH+(0);
not unreasonable for the measurements to be carried out at energies much lower than ours. We might conclude, therefore, that the reaction of CH3+ with acetylene to produce C3H3+is proceeding through complex formation in which the complex has a lifetime corresponding to less than or approximately equal to the rotational period of the system. In addition the reaction appears to be proceeding by insertion of the CH3+ into a C-H bond at high energies and by addition of the CH3+to the acetylene triple bond at low energies. The mechanisms are reminiscent of the mechanisms of the reaction of methylene with unsaturated hydrocarbons. l 3 It may appear that there is some ambiguity in the interpretation presented here because of the potential contribution of C3D2+to the mass 40 peak. However, the reaction CH3+ (C2H2,H,, H)
4130
The Journal of Physical Chemistry, Vol. 91, No. 15, 1987
Sharma et al.
1800
c-
LAB ENERGY (eV)
Figure 3. Translational exoergicity for the reaction CH,+ (C2H2,H2)
. TflO --. _ _ _ rn/FC,-
C3H3+.
C3H2+is endothermic with a threshold of about 2 eV and a small cross section; consequently C3D2+ would not be expected to contribute to the mass 40 peak in the low-energy region and its contribution to the peak in the higher energy region is small. Correcting the mass 40 peak for its C3D2+content changes the ratio of 41 /40 by about 0.1. In the higher energy region it can also be argued that if the mechanism consists of the attack of CD3+ on one end of the C2Hzmolecule the picture presented above makes it unlikely that C3D2+would be produced. This appears to be supported by the 41/40 ratio of unity. The fact that a t low energies our 41/40 ratio appears to be increasing and has been interpreted as indicative of a complex where the two hydrogens and three deuterium scramble suggests that we should see C3D3+as a product. A careful search for C3D3+ failed to give convincing evidence for the presence of this ion. We believe that it is present; however, the intensity is expected to be small since statistical considerations of the deuterium distribution in CX3+ions (where X is either H or D) indicate that the intensity of C3D3+is expected to be about one-sixth of C3D2H+. In addition the branching ratio between the high-energy and low-energy mechanisms was not known and the contribution of 13Cto the mass 42 peak further complicated matters. Attempts to take these various correction factors into considerations gave us a small residue for C3D3+which we felt was not strong evidence for its presence. Another interesting question that arises with this reaction is the internal energy residing in the product ion, C3H3+. From conservation of energy one gets the following expression for Q, the translational exoergicity Q = T p- T R = UR -
Up
- AH
where T is the translational energy, U is the internal energy, P and R refer to products and reactants, respectively, and AH is the heat of reaction. Conservation of energy and momentum permit one also to derive an expression for Q in terms of experimentally measured parameters such as the projectile kinetic energy, product ion kinetic energy and the angle that the product ion path makes with the beam d i r e ~ t i 0 n . lThe ~ Q values determined in this manner are plotted as function of incident ion kinetic energy in Figure 3. Q is a measure of the internal energy residing in the C3H3+ion. Figure 3 shows that as the projectile kinetic energy increases the internal energy increases until one reaches a Q value of about -10
1-900
Figure 4. Ion velocity distribution shown in Cartesian coordinates in the center of mass system for the reactions (a) CH2+(C2H2,H) C3H3+;(b) CH2+(C2H2,H2)C3H2'; (c) CD2+(C2H2,D) C3DH2+;and (d) CD2+ (C2H2,H) C3D2H+.The barycentric energies are 1.34, 1.34, 1.87, and 1.86 eV, respectively. (+) indicates the velocity of the center of mass of the system.
eV. We were not able to follow this curve further because of the rapid decrease of the cross section with kinetic energy. In simpler cases it has been observed that the Q curve reaches a limiting value and flattens off at a value related to the dissociation energy of the product ion.21 It may appear surprising at first sight that so much energy can be stored in C3H3+;however Pople's group carried out quantum chemical calculation on the C3H3+cations and they report energies for eight isomers of C3H3+with the most excited one having 7.6 eV of energy above the lowest energy isomer, the cyclopropenyl cation.18 The use of a reaction chamber instead of crossed beams can also introduce errors in the measurement of Q especially if a heavy target is used. This is a possibility here. However, we have used the same equipment to measure Q for reactions using heavy targets such as C+(02,O)CO+ where one can compare the limiting value of Q with that obtained from known thermodynamics data and the results were satisfactory. Reactions of CH,+and CD2+with Acetylene. The CH2+ ion also undergoes condensation reactions with C2H2to produce C3 products. Questions similar to the one that arose in connection with CH3+ also arise in this case. In answer to these questions we have measured the angular distributions for the ionic products and also studied the isotopic scrambling for these reactions. If one applies the RRK equation above to this reaction using 5.17 eV for exothermicity of the process CH2++ C2H2 C3H4+and 1.74 eV for the endothermicity of the process C3H4+ C3H3+ H one obtains shorter lifetimes than that for the CH3* reaction because of the higher exothermicity of the first process. The angular distributions of the ionic products arising from the reactions of CH2+ and CDZ+with acetylene are given in Figure 4. The distributions in all four reactions are similar. The peak of the distribution is well behind the center of mass, indicating that this portion of the reaction occurs from low impact parameter
+
(21) Tully, 1730.
--
J. C.;Herman, Z.; Wolfgang, R. J . Chem. Phys. 1971, 54,
Reactions of CH3+, CH2+,and CH+ with Acetylene TABLE I: Cross Sections of C3DH2+and C3D2H+for the Reaction CD,+(C,H,. X) C2X2+Where X Is either H or D
enerev. eV ~~
cross sections, A2 CIDH,+ (cor) C,D,H' lexpt)
The Journal ofPhysica1 Chemistry, Vol. 91, No. 15, 1987 4131
(a)
t
ratio"
~
8 6 4
0.34 0.7 1.4
2
3.0
1
3.4
0.40
0.8 1.3 2.7 3.7
1.12 1.14 0.93 0.90 1.09
R = C,D2H+/C3DH2+
collisions. There is also a significant distribution of ionic products in the forward hemisphere arising form larger impact parameter collisions. At any rate, all four contours deviate from the required symmetry for complex formation and one may conclude that the reactants are within reactive proximity of each other for a time less than the rotational period of the system. We have also examined the cross section for the production of C3DH2+and C3D2H+from CD2+ reacting with C2H2. If the reaction is proceeding by CD2+ interacting with one end of the C2H2molecule and if one has complete scrambling of one hydrogen and two deuterium atoms with a negligible isotope effect, a ratio of 0.5 would be expected for C3D2H+/C3DH2+.If both the hydrogen atoms on the C2H2molecule scramble with the two deuteriums on the projectile a ratio of unity is expected. The mass 40 peak has contributions from C3DH2+and C3D2'. Both of these ions arise from exothermic reactions and contribute significantly to the peak. In order to get a C3D2H+/C3DH2+ ratio, correction has to be made for the C3D2' contribution. This correction was carried out in the following manner. In the reaction CD2+(C2H2, X,) C3X2' (where X is either H or D) the cross sections for product ions C3D2+, C3DH+, and C3H2' are expected to have statistically the relative intensities 1:4: 1 respectively. Since the C3DH+curve is free of complications we take one-fourth of the C3DH+ cross sections and subtract it from the cross section of the composite mass 40 peak. This gives us a measure of the yield of C3DH2+which is given in the column headed corrected in Table I. The ratio of C3D2H+to C3DH2+so obtained is, to within experimental uncertainty, unity and suggests that CD2+ on interacting with C2H2forms a complex which lives less than the rotational period of the system but long enough for both hydrogens and deuteriums to completely scramble. We have also measured the Q value for the reaction of CH2+ (C2H2,H) C3H3+and the plot of Q vs. kinetic energy is indistinguishable from the results given in Figure 3 for the reaction CH3+ (C2H2,H,) C3H3+. Reactions of CH+ and CD+ with Acetylene. The criteria which decide whether a reaction proceeds through a persistent complex have been reviewed by Wolfgang.22 The most obvious requirement was that the system have accessible a deep potential well. Measurements of Q, mentioned earlier, for the reaction CH3+ (C2H2,H,) C3H3+showed that a large amount of energy can be stored in C3H3+so a deep potential well may be accessible to the CH+-C2H2system. Some interesting questions arise at this point. Will an addition product be formed? Do the condensation products formed, C3H2' and C3H+, arise form unimolecular decomposition of C3H3+or do they result from some sort of a direct mechanism? Using the RRK equation for the lifetime and the exothermicity of 8 eV for the process CH+ C2H2 C3H3+and 2.04 eV for the endothermicity of C3H3+ C3H2+ H coupled with the relative kinetic energy of reactants of 1.37 eV, one obtains lifetimes shorter than times required to give a symmetric angular distribution of the ionic product suggesting that a direct reaction might be expected. An additon product would not be expected and none
- -+
+
(22) Wolfgang, R. Acc. Chem. Res. 1970, 3, 48.
~
350 m/sec 1-900
Figure 5. Ion velocity distributions shown in Cartesian coordinates in the center of mass system for the reactions CH' (C2H2.H) C3H2+and CH' (C2H2,H,)C3Ht. The barycentric energy is 1.37 eV. (+) indicates the velocity of the center of mass system.
was found. It should be mentioned that there is considerable uncertainty about the heat of formation of C3H2'. In order to get the endothermicity of the dissociation of C3H3+we used our own value of AHf(C3H2') of 276 kcal/mol obtained from the threshold of the reaction CH3+ (C2H2,H,, H) c3H2+.23 The angular distributions of the velocities of the ionic products C3H2' and C3H+ are given in Figure 5 which shows the peaks of the distributions to be behind the center of mass indicating a rebound type of mechanism. These ions are produced with sizable cross sections. At 2 eV the cross section for the production of C3H+ from the reaction of CH+ with C2H2is about 5.5 AZand for C3H2' the value is 2.8 I%,. Cross section measurements with the deuteriated projectile ion, CD+, reacting with C2H2were carried out with the hopes that information of the type obtained with CD3+and CD2+would be realized. The cross sections obtained for the mass peaks 39 (C3DH+), peak 38 (C3D+ + C3H2+), and peak 37 (C3H+) are shown in Figure 2. If the mass 38 was only due to C3H2' one would expect its cross section to be smaller than that of C3DH+; however, the reverse is the case. This is due to the presence of C3D+. In order to obtain an estimate of the position of the C3H+ cross section curve we assume an isotope effect of 20-30% for the production of C3H+and C3D+. Then using the procedure outlined above we subtract the C3D+ contribution to mass peak 38 and obtain C3H2' as a residue. This is represented by the dashed line in Figure 2. The ratio of the C3DH+cross sections to that of the estimated C3H2+ values is approximately 2 which is the value expected if CD+ + C2H2formed a complex in which complete scrambling occurs followed by dissociation into the other ionic products in a time shorter than the rotational period of the system.
Conclusion The reactions of CH3+, CH2+, and CH' with acetylene to produce C3 products are proceeding through intermediates whose lifetimes are long enough to produce complete isotopic scrambling and in some cases near symmetry of the angular distributions of the ionic products. Indication has been obtained that two different mechanisms are in operation in the CH3+ (C2H2,H,) C3H3+case. It is suggested that both insertion and additon mechanisms may be playing a role in these reactions. It is found that a large amount of energy can be stored in C3H3+. Acknowledgment. This work was supported by the U S . Department of Energy. (23) The thermodynamic data used in this study were taken from: Rosenstock, H. M.; Draxl, K.; Steine, B. w.; Herron, J. T. J . Phys. Chem. Re$ Data, Suppl. 1977, 6, 1.
