-
J. fhys. Chem. 1982, 86, 1591-1596
Energy Partitioning in the Reaction 0
+ OH
H
1591
+ 0,
0. P. Glass' and H. Endo Depertment of Chemistry. Rlce University, Houston, Texas 77001 (Received: September 11, 1981)
-
The average product translational energy liberated in the reaction 0 + OH H + O2 has been mesured as 84 f 7% of the reaction exoergicity. This value was obtained by comparing the reactivity (toward Dz)of hydrogen atoms produced in the above reaction with that displayed by hydrogen atoms prepared with various known initial energies by monochromatic photolysis of HBr. The experimental measurements were made at 295 K with a discharge flow apparatus which was attached to a sensitive EPR spectrometer. The average fractional energy losses per collision suffered by the hot atoms, produced in the above reaction, in collisions with Dz,He, and,Ar have been estimated as 0.068,0.085, and 0.017, respectively. Some of the implications of these estimates to other kinetic studies have been noted.
Introduction Translationally hot atoms have been studied by using photochemical and nuclear techniques for many years.' However, little attention has been paid to their production and subsequent removal in normal thermal reactions. This neglect has been the result of a belief that, in thermal environments, such atoms are quenched before chemical reaction can occur. This is not always true. Hot hydrogen atoms, because of their light mass, lose only a small fraction of their translational energy in elastic collisions with heavier molecules and thus can remain hot for a considerable time. While hot, these atoms may react to form products other than those usually observed in studies of thermalized atoms. In addition, they may react much more rapidly than anticipated. The work reported in this paper grew out of an attempt to model the overall kinetics of the reaction between atomic oxygen and HBr. The primary purpose of the modeling was to extract a rate constant for the elementary reaction 0 + HBr -,OH + Br (1) However, it soon became apparent that the experimentally measured concentration of atomic hydrogen, which was formed as an intermediate in the overall reaction sequence, was much lower than that predicted by the model using previously established rate constants. After some effort, the cause of the discrepancy was shown to be related to the production of "hot" hydrogen atoms in reaction 2. 0 + OH H + 02 (2) In this paper a measurement of the average product translational energy liberated in reaction 2 is reported. In addition, calculations are presented to show that the hot atoms produced in this reaction retain a significant proportion of their initial translational energy (-20%) after they have suffered 100 collisions with argon or 20 collisions with helium or Dz. Some of the implications of these measurements to the study of reaction kinetics using discharge-flow systems and to modeling studies of combustion systems are discussed. +
Experimental Section The discharge flow apparatus, the EPR spectrometer, and the operating techniques used in this study have been described in detail previously.2 The 20-mm i.d. quartz (1)(a) F.S.Rowland, MTP Znt. Rev. Sci.: Phys. Chem.,Ser. One, 9, 109 (1972). (b) J. Dubrin, Annu. Reu. Phys. Chem., 24,97 (1973). (2)(a) J. E.Breen and G. P. Glass, J. Chem. Phys., 62,1082 (1970). (b) J. E.Spencer and G. P. Glass, Chem. Phys., 16,35 (1976). 0022-3654/82/2086-1591$01.25/0
flow tube was operated at pressures of 0.5-1.0 torr and at linear flow speeds of approximately 1500 cm/s. Atomic oxygen was generated 50 cm upstream of the EPR cavity by microwave discharge of dilute mixtures of O2in argon, helium, or in mixtures of these two gases. A movable double-inlet probe, whose position could be varied between 2 and 35 cm from the point of EPR detection, allowed two gases to be added simultaneously to the flow tube, one slightly upstream of the other. In these studies HBr (Matheson, 99.8%) was added at the downstream inlet, and D2 (Matheson, 99.5%) was added at the upstream inlet. Their flow rates were estimated by measuring the pressure drop in bulbs of known volume. EPR signals of O(3P), H, and D were recorded with a Varian E12 spectrometer. Absolute concentrations were determined by the method of first moments with O2as an internal calibration ~ t a n d a r d . ~The sensitivity of the spectrometer was sufficient to allow H and D to be detected at concentrations of 1011~ m - ~ . In order to prevent wall recombination of 0, H, D, and Br(2P3,2),the flow tube was coated internally with a fluorinated halocarbon wax: Before each experiment, the inertness of the flow tube to bromine atom recombination was checked by using a method described fully in a previous publi~ation.~ All measurements were made at 295 f 1 K.
Procedure In this study OH was produced in the presence of oxygen atoms by adding a small quantity of HBr to a large excess of atomic oxygen. Under these conditions the most significant reactions that occurred were
0 + HBr -,OH + Br
(1)
0 + O H + H + 02
(2)
H
+ HBr
H2 + Br
-,
(3)
Hot hydrogen atoms (those having translational energies greatly in excess of the average thermal energy) were produced by reaction 2. They were identified by their ability to react with DP, which was added to the flow tube through the central inlet probe. Their presence was confirmed by adding helium to the system. This gas efficiently quenched H* (hot atomic hydrogen), thus reducing the quantity of atomic deuterium formed in reaction 4. (3)A. A. Westenberg, Prog. React. Kinet., 7 , 24 (1973). (4)G. A. Takacs and G. P. Glass, J. Phys. Chem., 77, 1060 (1973). (5)G. A. Takacs and G. P. Glass, J. Phys. Chem., 77,1182 (1973).
0 1982 American Chemical Society
1592
Glass and Endo
The Journal of Physical Chemistry, Vol. 86, No. 9, 1982
H
+ D2
-
HD
+D
(4)
(threshold energy: 7-8 kcal/mo16) The initial translational energy possessed by the hot atoms was measured by using an adaptation of a technique frequently applied to photochemical systems? In essence, the method consisted of measuring the yield of deuterium atoms produced by the O/HBr/Dz system in the limit of infinite dilution in Dz. Then, the amount of translational energy liberated in reaction 2 was estimated by comparing thisyield, which is sometimes termed the "integral reaction probability", to yields obtained by using hydrogen atoms prepared with various known initial translational energies by monochromatic photolysis of HBr. The yield of deuterium atoms was estimated as follows. In the presence of D2,the overall reaction mechanism can be written in the sequence (1)-(7), where H* represents
-
0 + HBr
OH
+ Br
(1)
kl = 3.9 x 10-l4 cm-3 539
0 + OH
-
k2 = 3.7 H
H*(or H)
X
+ HBr
k3 = 3.7 x
+ O2
lo-" cm-3 lo
-
Hz + Br
-
+D H* + HBr Hz + Br H* + M - H + M D + HBr -DH + Br H* + D2
k7 = 1.8 x
(2)
HD
(3)
(4) (5) (6)
(7)
cm-3 l1
a hot hydrogen atom and M any physical deactivator (including Dz or HBr). At any given instant, the rate of production of hydrogen atoms from reaction 2 is k z ( 0 ) (OH). This can be set equal to k,(O)(HBr) if the steady state approximation can be applied to OH. The rate of production of atomic deuterium from reaction 4 is k4(H*)(Dz), which can be set equal to k,(D)(HBr) if the steady state condition can be applied to D. The yield of atomic deuterium, that is, the fraction of hydrogen atoms formed in reaction 2 that produces D via reaction 4, is given by the ratio of these two quantities. yield of D = k7(D)/kl(0)
(8)
In the above mechanism the steady state approximations are undoubtedly valid after some initial induction period since k2 = 1000k1,5k7 = 40kl," and the rate of reaction 4 is always less than that of reaction 1. However the validity of the approximations were tested by means of an experiment and a number of calculations. In the experiment, the concentration profiles of H, D, and 0 were monitored as a function of reaction time. As expected, the profiles (6)A.Kuppermann and J. M. White, J. Chem. Phys., 44,4352(1966). (7)(a) G. P. Sturm, Jr., and J. M. White, J. Chem. Phys., 50, 5035 (1969). (b) R. G. Gann and J. Dubrin, ibid., 47,1867 (1967). (8)R. M.Martin and J. E. Willard, J. Chem. Phys., 40,3007(1964). (9)(a) R. D.H. Brown and I. W. M. Smith, Int. J. Chem. Kinet., 7, 301 (1975). (b) D.L.Singleton and R. J. Cvetanovic, Can. J. Chem., 56, 2934 (1978). (IO) "Reaction Rate and Photochemical Data for Atmospheric Chemistry-1977", N . B. S. Spec. h c b l . (U.S.) 513,(1978). (11)H.Endo and G. P. Glass, J. Phys. Chem., 80,1519 (1976).
of H and D were observed to parallel that of atomic oxygen after an induction period of 5-7 ms. The calculations involved integrating the pertinent rate equations numerically by using Euler's method with a step size of s. The steady state approximation was applied to those hot hydrogen atoms with energy in excess of the threshold energy for reaction 4 and a set fraction of the hydrogen atoms formed by reaction 2; namely, the fraction estimated from the experimental results by using eq 8 was assumed to react with Dz. Under normal operating conditions ((O), = 1015~ m -(HBr), ~, = 1014 ~ m -and ~ , (DJo = 5 x 1015~ m - ~ ) , OH was observed to approach its steady state concentration in less than 0.1 ms. Atomic deuterium was formed much more slowly but was usually within 10% of its steady state concentration in -10 ms. The integral reaction probability for reaction 4 has been measured previously by Sturm and White' using atoms produced in the photolysis of HBr at energies of 24.8,36.8, 45.3, and 65.9 kcal/mol and by Martin and Willard8using hydrogen atoms produced at an initial energy of 65.9 kcal/mol. The choice of translational energies studied by these workers was dictated largely by the availability of intense photolytic sources. No measurements have been made at energies below 24.8 kcal/mol. For this reason, a simple model was developed that allowed the integral reaction probability to be calculated at energies other than those studied. In the present investigation the model was used to determine the energy of monoenergetic hydrogen atoms that would have provided, from reaction 4, the same yield of atomic deuterium as was measured experimentally in the O/HBr/D2 discharge flow system. This energy was equated with the average translational energy of atomic hydrogen produced in reaction 2.
Calculation of Integral Reaction Probabilities In principle the integral reaction probability (IRP) can be calculated from the equation
where &(E) and S ( E ) are, respectively, the reactive and total scattering cross sections, n(E) is the steady state collision density function, Ethis the threshold energy, and E is the upper bound of energy appropriate to the experiment being performed. In practice, the major difficulty that arises in attempting to use this equation is that of finding the correct form for n(E). Porter12 has derived a formula for n(E) in terms of functions that can be estimated from the form of the nonreactive differential scattering cross section. Alternatively, n(E) can be determined via stochastic calculations.13 Unfortunately, the appropriate measurements for the application of Porter's formula to reaction 4 have not been made, and the accuracy of our discharge-flow-tube measurements does not warrant making lengthy stochastic calculations. Therefore, we have estimated integral reaction probabilities for H-D, using the following simple model. Consider a collection of hydrogen atoms, all formed with initial translational energy Eo and all undergoing collisions with D2. Assume that the fractional energy loss suffered by every H atom at every collision is equal to the aueruge fractional energy loss per collision. Then, an atom approaching the ith collision has energy Ei given by Ei = EoY(1 - € ( E L ) )
(10)
(12) R. N. Porter, J. Chem. Phys., 45,2284 (1966).
(13)C. Rebick and J. Dubrin, J . Chem. Phys., 53,2079 (1970).
Energy Partitioning
The Journal of Physical Chemistry, Vol. 86, No. 9, 1982 1593
TABLE I: Average Fractional Energy Loss in a Collision of H* with D,
a
d
04-
U
Q
/
-
t
-
initial relative energy, 16.8 25.2 37.8 56.8 kcal/mol total cross section S ( E ) ,A' a 40.7 38.7 36.7 34.9 average fractional energy loss 0.068 0.061 0.053 0.042 per collision,
-I
a
I
ENERGY,
E, (kcal/molel
Figure 1. Integral reactlon probability for reaction 4 plotted as a function of the translational energy of atomic hydrogen. The experimental points marked wlth a circle were taken from ref 7a. A correction was applied to take into account a more r m t measurement" of the ratio of abstraction to exchange for the reaction between D and HBr. The point marked wlth a square was taken directly from ref 8.
where c(Ei)is the average fractional energy loss per collision. The probability of a reaction occurring at the ith collision is i-1
pi = [I - CPiIS,(Ei)/S(Ei) i=l
(11)
where the term in parentheses gives the probability of a hydrogen atom surviving i = 1collisions without reacting and the other terms give the probability of such an atom reacting at the next (ith) collision. In eq 11, the cross sections that should be used are those appropriate for a collision between a stationary D2 molecule and a hydrogen atom of translational energy Ei; that is, they are cross sections estimated for collisions of relative energy 0.8Ei. The integral reaction probability is obtained by summing Pi over all values of i. This s u m has a small finite number of nonzero terms since the reactive cross section goes to zero when Ei is less than Eth. The calculations reported in this paper were performed by using the absolute integral cross sections measured by Gengenbach, Hahn, and Toennies.14 For ease of computation, these were evaluated by using the equation In
,"(A2) = 3.953 - 0.101 In ER (kcal/mol)
From ref 14.
with the predictions of the model. This does not imply that the model is correct and therefore transferable to other systems. It is possible that errors in it are offset by errors in the reactive cross sections that were used. Indeed, there is some evidence that the cross sections calculated by Karplus, Porter, and Sharma are high." However, the agreement displayed in Figure 1does imply that the model can be used with reasonable accuracy to interpolate between experimental measurements and to extrapolate from these to moderately lower energies.
i
i
/
E
(12)
which provides a reasonable fit to the data over the relative energy range ER = 2-25 kcal/mol. Reactive cross sections, &(E),were estimated from the calculations of Karplus, Porter, and Sharma.15 These cross sections were expressed as an inverse polynomial function of the relative energy by using coefficients listed by the original authors. The average fractional energy loss per collision was determined by using a method developed by Estrup,16 which is discussed in the next section. The integral reaction probability for reaction 4, estimated as described above, is plotted as a function of initial atom translational energy in Figure 1. Various experimental measurements of the IRP are included in this figure. As can be seen, these are in excellent agreement (14)R.Gengenbach, C. Hahn, and J. P. Toennies, J.Chem. Phys., 62, 3620 (1975). (15)M. Karplus, R. N. Porter, and R. D. Sharma, J.Chem. Phys., 43, 3259 (1965). (16)P.J. Estrup, J. Chem. Phys., 41, 164 (1964).
Average Fractional Energy Loss per Collision Estrup16 has shown that when the interaction between a hot atom of mass m and a stationary moderating molecule of mass M can be described adequately by means of a spherical potential, then the average fractional energy loss per collision can be evaluated from the equation
€ ( E )= (1 - P)Q1/2S(E)
(13)
where P = [(M - m ) / ( M + m)I2,S ( E ) is the total nonreactive scattering cross section, and Q1 is an integral commonly encountered in the theory of transport properties.18
Q1 = 2 r J m ( 1 - COS 0)b db 0
(14)
In the above equation defining Q', 0 represents the angle of deflection produced in a collision of impact parameter b. Q' cannot be obtained in analytical form for any but the simplest potentials. However, the integral has been evaluated numerically, and tables of it have been prepared for use with the Lennard-Jones p ~ t e n t i a l , 'V(r) ~ = 4~[(ro/r)12- (ro/r)6],and for use with the Born-Mayer potential,20V(r) = A exp(-ar). Absolute integral cross sections for the scattering of D from H2have been measured by Gengenbach, Hahn, and Toennies.14 These have been used to test various literature interaction potentials. Although the precise form of the "correct" potential could not be determined, these measurements could be used to estimate optimal parameters for use in various model potentials. On the basis of the measurements, a new Born-Mayer-Spine-van der Waals potential, having a spherically symmetric repulsive part of the form V(r)= 55.9 (eV) exp(-3.065 (A-') rj, was proposed. This form of the potential was used in this investigation to estimate values of Q1 and thus e(H-D,) at various relative collision energies ranging from 5 to 50 kcal/mol. Some of these values, which were used to determine integral reaction probabilities for reaction 4, are listed in Table I. Integral elastic cross sections for hydrogen atoms scattered by rare-gas atoms have also been measured by Toennies and cc-workers.2l Parameters in the Lennard-Jones (17)H. R.Mayne and J. P. Toennies, J. Chem. Phys., 70,5314(1979). (18)J. 0.Hirschfelder, C. F. Curtis, and R. B. Bird, "Molecular Theories of Gases and Liquids", Wiley, New York, 1954, Chapter 8. (19)J. 0.Hirschfelder, R. B. Bird, and E. L. Spotz, J. Chem. Phys., 16, 968 (1948). (20) L. Monchick, Phys. Fluids,2,695 (1959).
1594
Glass and Endo
The Journal of Physical Chemistty, Vol. 86, No. 9, 7982
r
I
1 1
I
I
4 --
concentration decreased when helium was added to the system. This behavior is illustrated in Figure 2. Without doubt, the deuterium atoms observed in these experiments were formed as a result of reactions of hot hydrogen atoms. The absolute concentration of atomic deuterium that was detected was 100 times greater than that predicted from the thermal reaction H + Dz HD + D,2450 times greater than that predicted from the reaction 0 + D2 OD + D,25and more than 100 times greater than that predicted from the reaction of OH with D2.26 The decrease in the concentration of atomic deuterium that occurred when He was added to the system can be explained by assuming that H* was quenched by He. The variation in the D atom concentration that occurred as the ratio of D2 to HBr was changed can be understood in terms of a competition for H* between reactions 4 and 5. The yield of atomic deuterium was estimated, with equation 8, from experimental measurements of (D) and (0)made at a reaction time of 15 ms. At 295 K, kl was cm3molecule-l s-l, the average of three taken as 3.9 X recent measurements:$ and k, was taken as 1.8 X cm3 molecule-1 s-l.ll The yield produced in the limit of infinite dilution in D2was estimated by plotting the inverse of the measured yields against (HBr)/(D2)and extrapolating the data onto the axis for which (HBr)/(D,) was equal to zero. This procedure has been used in almost all previous photochemical studies.6-8 A correction was applied to the extrapolated yield in order to account for quenching of H* by argon, which was always present in the flow tube. Most experiments were performed with mixtures containing argon and deuterium in the ratio 4:l. In such mixtures, a hot hydrogen atom collides with argon approximately 4 times as frequently as it does with Dz. After four collisions with argon, H* retains, on average, [l - c(H-A)I4 = [l - 0.01714 = 0.934 of its initial energy. After one collision with D2 it retains [l - e(H-D2)] = [ 1 4.0681 = 0.932 of its energy. Thus, H* loses approximately half of its energy in collisions with D2 and half in collisions with argon. Therefore, in such mixtures the measured, “extrapolated” yield of atomic deuterium was taken to be half of that which would have been produced in the absence of argon. As a check on this procedure, a few experiments were performed with mixtures containing 45% D2. The deuterium atom yield measured in these experiments was 1.5 times that obtained in experiments performed with mixtures containing 23 % D2. This value is very close to that estimated by using an argument similar to that presented above. The integral reaction probability for hydrogen atoms produced in reaction 2 was estimated from all of our flow tube experiments as 0.075 f 0.015. Here, the stated error represents one standard deviation. The accuracy of the measurement was, of course, not as great as this, since systematic errors could have been introduced in the extrapolation procedure and in the procedure used to estimate the relative sensitivity of the spectrometer toward 0 and D. A more realistic estimate of the yield is 0.075 f 0.025. As can be seen from Figure 1, this yield is produced by monoenergetic hydrogen atoms of initial energy 16.3 f 1.5 kcal/mol. Thus, at first sight it appears that the entire exothermicity of reaction 2 is partitioned into OH + 0 H + O2 AHo298= -16.89 kcal/mol
-
I
I1
0
1
2 [(HBr)/(D,)]
I
4
I
6
1
x 10‘
Figure 2. Concentration of atomic deuterium produced at t = 15 ms in the O/HBr/D, system. All experiments were performed at a total pressure of 0.58 torr, with (D2)0= 4.3 X l O I 5 ~ m and - ~(O), = 9.0 X 10“ ~ m - ~The . carrier gases used were pure argon (O), a 3:l Ar/He mixture (M), and a 1:l Ar/He mixture (A).
and Born-Mayer forms of the various H-rare gas interaction potentials have been fitted to this data.21 We have used these parameters, in conjunction with eq 13, to calculate the average fractional energy losses suffered by atomic hydrogen in collisions with (a) argon and (b) helium at relative collision energies of 14 kcal/mol (0.6 eV). For argon, c was estimated as 0.017 using the Lennard-Jones form of the potential. A value that differed from this by only 2% was calculated with the Born-Mayer form. For helium, c(H-He) was estimated as 0.085. It should be noted that these values are significantly smaller than those calculated from an unrealistic rigid sphere model, for which c,(H-Ar) = 0.048 and c,(H-He) = 0.320. Some estimate of the absolute accuracy of the above calculations can be obtained by considering the results of the photochemical investigations of Fass.22 In these investigations, H* was produced with an initial energy of 66.6 kcal/mol by the photolysis of HBr, and competitive reactions of it with HBr and Br2 were monitored. Fass observed that a ratio of He to HBr of at least 4 0 1 was necessary in order to avoid “hot” atom reactions with HBr. Using the value of c(H-He) estimated above, we estimate that it takes 37 collisions to deactivate H* from 66.6 kcal/mol to the threshold energy for reaction with HBr (-2.5 kcal/mol). This number is in excellent accord with Fass’s observation. In a later paper, Fass and co-worker8 compared the efficiencies of He, Ar, and D2as moderators for the D* HBr reaction. Over the energy range 2.5-46 kcal/mol, they measured the average value of a(He-D)/ cu(Ar-D) as 3.89 and the average value of a(D-D2)/a(DHe) as 0.70. At 14 kcal/mol, we estimated t(D-He)/c(DAr), which is almost identical16 with a(D-He)/a(D-Ar), the ratio of the average logarithmic energy loss, as 3.70 and t(D-D,)/E(D-He) as 0.80.
+
Results and Discussion When large amounts of D2 ( 5 X 1015~ m - were ~ ) added to a reacting mixture of atomic oxygen and HBr in argon, atomic deuterium was detected. Its concentration increased as the ratio of D, to HBr was increased, and its (21)R. W.Bickes, Jr., B. Lantzsch, J. P. Toennies, and K. Walaschewski, Faraday Discuss. Chem. SOC.,55, 167 (1973). (22)R. A. Fass, J . Phys. Chem., 74,984 (1970). (23)R. A. Fass and D. L. Wong, J . Phys. Chem., 77, 1319 (1973).
-
-
(24)(a) A. A. Westenberg and N. deHaas, J . Chem. Phys., 47,1393 (1967). (b) K.A. Quickert and D. J. LeRoy, ibid., 53, 1325 (1970). (25)A.A.Westenberg and N. deHaas, J. Chem. Phys., 47,4241(1967). (26)(a) A. A. Westenberg and N. deHaas, J. Chem. Phys., 44,2877 (1966). (b) N.R. Greiner, ibid., 48,1413 (1968).
Energy Partitioning
The Journal of Physical Chemistry, Vol. 86, No. 9, 1982 1595
translation. This is not true. A portion of the OH formed in reaction 1 is produced in the first vibrationally excited ~ t i t eand , ~ a certain fraction of this reacts with 0 before deactivation. This fraction hm been determined previously as 0.35.% When allowance is made for it, one can estimate that 84 f 7% of the total available energy [including that vibrational energy originally present in OH(u = l ) ] is channeled into product translation. Such a partitioning of energy is not unreasonable in view of the restrictions placed on the average product rotational energy by angular momentum conservation. In a reaction between an atom and a diatomic molecule, the total angular momentum is comeosed of the orbital momentum of the incoming particles, 1, and the rotational momentum, j , of the diatomic molecule. The magnitude of the former is given by where 1 is the reduced mass of the collision pair, b is the impact parameter, g is the initial relative velocity, h is Planck's constant, and 1 is the orbital angular momentum quantum number. The magnitude of the latter is li(i 1)]1/2h/27r,where j is the rotational quantum number. For room-temperature reactions of OH, the total angular momentum is approximately equal to the orbital momentum since the most probable value of j is so small (2 at 300 K). Thus, conservation of angular momentum requires that I , + j , = 1, + j , = I ,
+
- - - - -
where the subscripts r and p refer to reactant and product, respectively. This vector equation implies that the rotational quantum number, j,, of the product molecule lies between I , + 1, and I , - 1,. For reaction 2, 1, = 11 if b = 1 A, and the initial relative velocity is taken as the average value for all possible 0-OH collisions. The value of 1, depends on the product translational energy. However, if 85% of the heat of reaction is partitioned into translation and the impact parameter for the departing fragments is again taken as 1 A, then 1, = 15. Therefore, the average value of j must be much less than 26, since the average value of &e impact parameter is undoubtedly less than 1 A. An oxygen molecule having j = 26 has a rotational energy of only 2.89 kcal/mol. This corresponds to 17% of AHoZg8for reaction 2. Our understanding of the mechanism of reaction 2 is complicated by the presence on the potential energy surface of a deep well associated with the molecule HO,. It is not clear what effect this well has on the dynamics of the reaction. However, one thing is clear. The energy of reaction is not partitioned statistically. We have determined the density of product translational-rotational energy states using a rigid-rotor-harmonic-oscillator(RRHO) energy-level scheme and have estimated the fraction of energy partitioned statistically into vibration, rotation, and translation as f, = 0.19, f , = 0.32, and ft = 0.49. If statistical partitioning is allowed subject only to the restrictions introduced by the conservation of angular momentum, then the fraction of energy partitioned into product vibration is much increased. Therefore, statistical partitioning must not occur. The extremely small value estimated for the average fractional energy loss suffered by a hot hydrogen atom in a collision with argon ( 6 = 0.017) has implications in several areas of reaction kinetics. For example, discharge-flowtube studies often are made with argon as a carrier gas. (27) J. E. Spencer and G. P. Glass,Int. J. Chem. Kinet., 9,97 (1977). (28) J. E. Spencer, H. Endo, and G . P. Glass, 16th Symp. (Znt.)Combust. R o c . 16, 829 (1976).
A hot hydrogen atom produced as an intermediate in such a system retains 42% of its initial energy after 50 collisions with argon and 18% of its energy after 100 collisions. This fraction is sometimes large enough to affect the overall kinetics of subsequent reactions. Two examples, chosen from systems studied in this laboratory, illustrate this point. As noted in the Introduction, the hot atoms produced by reaction 2 were originally identified by the rapidity of their reaction with HBr. The concentration of atomic hydrogen produced in the O/HBr/Ar system was consistently found to between 1/2 and 1/5 of the value predicted by numerical integration of the pertinent rate equations by using appropriate literature rate con~ t a n t s . ~ JThe ~ J ~greatest discrepancies between experiment and calculation were observed when mixtures rich in HBr were used. In many of these mixtures, HBr was present at mole fractions in excess of 0.01. The observed EPR spectrum of the hot atoms was entirely normal since the Doppler broadening of the EPR lines was still insignificant when compared to the pressure broadening. However, the energetic atoms were able to significantly affect the kinetics of the overall reaction because they were able to survive more than 100 collisions with argon before being quenched below the threshold for reaction 3 [ -2.5 kcal/mol"]. If the rate constant for reaction 3 had not H + HBr H2 Br (3) been determined previously, a value too low by a factor of 3 would have been reported on the basis of the experiments performed on the O/HBr/Ar system. Another that might have been affected by the presence of H* was that of the reaction between H2S and atomic oxygen. A possible mechanism for this reaction is given in reactions 17,2,18, and 19. Since the rate constant 0 + H2S OH + SH (17) 0 + OH H + O2 AH = -16.8 kcal/mol (2)
-
+
-
0 + SH
-- + + H
SO
AH
= -42.4 kcal/mol
(18)
+
H H2S H2 SH (19) for the reaction of H2S with atomic hydrogen is approximately 100 times that for the reaction with atomic oxygen,29hydrogen atoms produced in reaction 2 and 18 take part in a chain sequence (reactions 18 and 19) that oxidizes a considerable fraction of the original H2S. Hot atoms are known to be produced in reaction 2 and are probably produced also in reaction 18. Such atoms are known to react with H2S at a rate that is considerably faster than that of the thermal reaction.30 Therefore the rate of the overall oxidation could have been significantly increased if H* was not efficiently quenched. Hydrocarbon combustion might also be affected by reactions of H*. The oxidation of hydrocarbons usually proceeds via a chain-branching cycle that includes the reaction H O2 OH 0 (-2) together with other reactions that regenerate atomic hydrogen. Some examples of such reactions are31,32 CH2 + 0 -CO + 2H (20) and
+
-
+
(29) L. T. Cupitt and G. P. Glass, Trans. Faraday SOC.,66, 3007 (1970). (30) B. D. Darwent, R. L. Wadlinger,and M. J. AUard, J.Phys. Chem., 71, 2346 (1967). (31) W. M. Staub, D. S. Y. Hsu, T. L. Burks, and M. C. Lin, Symp. (Int.) Combust. R o c . , 18, 811 (1980). (32) N. Washida and K. D. Bayes, Int. J. Chem. Kinet., 8,777 (1976).
J. Phys. Chem. 1882, 86, 1596-1606
1596
CH3 + 0 -* H2CO + H
(21) Both of these reactions are sufficiently exothermic that they may produce translationally hot hydrogen atoms. if such atoms are formed, they almost certainly are quenched inefficiently by N2 and 02=and survive to react with O2 and with the fuel. According to microscopic reversibility, H* should efficiently promote reaction -2, thereby increasing the rate of the branching cycle. If H* reacts with the fuel it may form products not usually observed in thermal reactions. For example, H* may abstract from ethylene or acetylene rather than adding to them. Such reactions (with C2H2)may be responsible for the formation of the C2H fragments reported in the early shock-tube (33) Total scattering cross sections for H-N2 and H-02 have not been reported, but we W. Bauer, R. W. Bickes, Jr., B. Lantzsch, J. P. Toennies, and K. Walaschewski, Chem. Phys. Lett., 31, 12 (1975).
Xa!
work of Kistiakowsky and co-workers,34and implicated in the soot-forming processes monitored by Bonne, Homann, and Wagner.35 Other examples of reactions possibly influenced by the presence of H*could be given. However, those discussed above should be sufficient to suggest that great care must be taken when studying reactions, or when modeling processes, that produce hot hydrogen atoms as intermediates.
Acknowledgment. We thank the Robert A. Welch Foundation of Houston (Grant C-312) for their support of this work. (34) J. N. Bradley and G. B. Kistiakowsky, J. Chem. Phys., 35, 264 (1961). (35) V. Bonne, K. H. Homann and G. G. Wagner, Symp. (Int.)Combust. Roc., 10, 503 (1964).
Multiple Scattering Calculations on Copper, Silver, and Gold Porphines Stephen F. Sontum and David A. Care' Department of Chemlstiy, University of Callforn&, Davls, California 95818 (Recelved: September 15, 1981)
X a calculations are presented for copper, silver, and gold porphines, and the results are compared to other calculations and to experimental data. Particular attention is paid to comparisons of electron spin resonance and ENDOR data on the copper and silver complexes. These results show that the nominally d-like odd electron has much more ligand character in the silver than in the copper complexes. The anisotropicparta of the hyperfine tensors for the metal, nitrogen, and hydrogen nuclei are in excellent agreement with measured values; spinpolarization effects give a good qualitative account of the nonaxial character of the nitrogen hyperfine tensor. The calculations underestimate the Fermi contact contributionsfor the metal and pyrrole hydrogens by 30430%; smaller errors in the opposite direction are found for the nitrogens. The calculated 14Nquadrupole coupling constants are also in poor agreement with experiment. Orbital energy trends (including relativistic corrections) for the series copper-silver-gold can be used to rationalize electrochemical and spectroscopic studies, but there is evidence that the d-orbital energies in these calculations are too low relative to the porphyrin orbital energies. Finally, the details of the calculated spin distribution are used to indicate the limitations and ambiguities inherent in the usual ligand field interpretations of ESR and ENDOR spectra.
Introduction Metalloporphyrins have been prepared with most of the elements of the transition series, and the study of their comparative bonding patterns forms an important chapter of organometallic chemistry. Among the best characterized are the d9 square-planar complexes of copper and silver, whose electron spin resonance (ESR) spectra have been studied for a quarter of a century.l Recently, electronnuclear double resonance (ENDOR) investigations have provided the complete hyperfine tensors for the metal, the nitrogens, and the pyrrole protons, along with quadrupole coupling tensors for the nitrogens.2 This detailed knowledge of the electron distribution provides a fundamental experimental reference system for theoretical descriptions of bonding and spin delocalization. Such a theory can be used to provide a more fundamental basis (1) Manoharan, P. T.; Rogers, M. T. 'Electron Spin Resonance of Metal Complexea";Yeh, T. F., Ed.;Adam Hilger: New York, 1969;p 143. For a review of ESR work on copper complexes, see: Lau, P. W.; Lin,W. C. J . Znorg. Nuel. Chem. 1975, 37, 2389. For more recent work, see: Clark, C. 0.;Poole, C. P., Jr.; Farach, H. A. J. Phys. C 1978, 11, 769. Bohandy, J.; Kim, B. F. J. Magn. Reson. 1977, 26, 341. (2) Brown, T. G.;Hoffman, B. M. Mol. Phys. 1980,39, 1073. 0022-3654/82/2086-1596$01.25/0
for the interpretation of the spectra than is available from the usual ligand field arguments; additionally, these systems are important test cases for theoretical models that may be used to study more biologically relevant metalloporphyrins. Some time ago we presented an X a multiple scattering study of copper p ~ r p h i n econsidering ,~ its excited states and oxidation-reduction behavior as well as the electronic spin resonance spectra. Since that time the ENDOR results of Brown and Hoffman2 have appeared, and in this paper we extend our previous description in several directions. First, we have added calculations on silver and gold porphines in order to study bonding trends down the periodic table. The silver(I1) porphyrin complex is well characterized, but the analogous gold moiety has not been prepared and is probably unstable, oxidizing easily to a Au(II1) ~ o m p l e x . ~The reasons behind this change in chemistry appear to involve relativistic energy shifts in the gold complex; these are discussed below. Second, we have (3) Case, D.A.; Karplus, M. J. Am. Chem. SOC.1977, 99, 6182. (4) Antipas, A.; Dolphin, D.; Gouterman, M.; Johnson, E. C. J. Am. Chem. SOC.1978,100, 7705.
0 1982 American Chemical Society
