2993
J . Phys. Chem. 1987, 91, 2993-2997
are 1 and 0.3 for pH 1.0 and 1.7, respectively, independent of [PSS]in the range (1.4-80) X lo4 M. The decay mechanism is probably similar to that in the absence of PSS. The reaction rates are several-fold higher in the PSS solutions.
Experiments at Other pH's. Some results measured at pH 11 show a general similarity to those observed at pH 4. N o systematic investigations were carried out at this pH. The decay rate (attributed to equilibrium 2') which is inversely proportional to the [PSS]is about 20-fold slower than in pH 4.0. This may be a result of changes in the acid-base equilibria of the iridium species bound to PSS. Measurements camed out at p H s 1.O and 1.7 show a first-order rate law for the decay of Ir(II)2+-PSS. The reaction rate constants
Acknowledgment. We are indebted to Dr. S. Gershuni for the synthesis of the Ir(III)2+comptex. This research was supported in part by the Balfour Foundation and by the Israel-US. Binational Science Foundation.
Reactions of Radicals with Halogen Molecules: A Frontier Orbital Interpretation Lee M. Loewensteint and James G. Anderson* Department of Chemistry and Center for Earth and Planetary Physics, Harvard University, Cambridge, Massachusetts 021 38 (Received: September 2, 1986)
The trends of reactivity of gas-phase radical-molecule reactions, where the radical is a simple atomic or diatomic species and the molecule a diatomic halogen or interhalogen, are examined. The observed trends-reactivity increasing with increasing electron affinity of the radical, and decreasing with increasing ionization potential of the halogen molecule-are explained qualitatively in terms of frontier orbital theory and Lewis electronic structure theory. The dependence of radical-halogen reaction rate constants on the difference between the ionization potential of one reactant and the electron affinity of the other indicates the importance of charge accommodation as the new chemical bond is formed. Other factors, such as electron-electron repulsions, also contribute to the activation energy, as demonstrated by the reactions of H and F atoms with halogen molecules. The proposed model is consistent with the detailed reaction dynamics ascertained from molecular scattering and energy disposal studies.
Introduction The rate constants for the reactions of radicals with molecules range over many orders of magnitude. Gas kineticists and the modelers of atmospheric and combustion chemistry have generally regarded reaction rate constants to be unknowable before exact measurements are performed, or have relied on simple assumptions based on supposed similarities of reacting species to estimate gas-phase rate constants. The importance of radical-molecule reactions in many different systems has lead to detailed rate measurements by thermal methods such as discharge flow and flash photolysis as well as by crossed molecular beam measurements. The variety of information now available on many chemical reactions makes it possible to formulate a theory relating the general properties of the individual species to both the reaction rate constants and scattering behavior. Both thermal and beam techniques provide information concerning reaction mechanisms-that is, the potential energy surfaces of the reactions; however, the more removed the measured parameters are from the individual reactive scattering event, the more difficult it is to relate the experimental findings to the reaction surface.' Nevertheless, even simple experiments can yield insights into chemical reactivity by working "backward" from the specific results of the experiment to their implications for molecular interactions. Less detailed information, such as that obtained by thermal techniques, will result in simpler inferences regarding reactive interactions. Despite this, by carefully choosing the reaction set-one where the connections between the reactions and the potential energy surfaces are as simple and direct as possible-general insights into the nature of chemical reactivity may be obtained. The traditional chemist's modus operandi, when faced with molecular complexity, is to examine the behavior of a series of related or homologous species, with the hope that any observed systematic behavior can be related to recognizable molecular properties. With this in mind, our attention will be centered on 'Present address: Materials Science Laboratory, Texas Instruments, Inc.,
P.O.Box 655936, M S 147, Dallas, TX 75265. 0022-3654/87/2091-2993$01SO/O
TABLE I: reaction^ of H,0, and OH Radicals with Halogen Molecules F2 c12 Br2 I = 15.7O I = 11.5' I = 10.5' radical a = 1.21' a = 4.61b a 6.99' H products HF + F HC1 + Cl HBr + Br k' 0.025 0.19 5.4 -45.2 -41.5 AH: -98.4 0
products FO k AHr
OH
+F
10-9 -14.7
C10 + CI 0.00042 -6.4
BrO + Br 0.14 -10.3
I2 I = 9.3' a = 12.4b HI + I 3.5 -35.2
IO
+I
1.4
products H O F + F HOCl+Cl HOBr+Br
HOI+ I
k
1.6 -20
AHr
lo-'* -14
0.00067 1.8
0.53 -9.1
'Ionization potentials in eV. *Polarizabilitiesin A'. CRateconstants in cm3 molecule-' &. "Heat of reactions in kcal mol-'. the reactions of a variety of atomic and diatomic free radicals with diatomic halogen and interhalogen molecules. The advantages of this concentration include (1) the possibility of relating molecular reactivity to some obvious property of the halogens such as electrohegativity, ionization potential, or polarizability, and (2) the availability of a large and fairly consistent data base of radical-halogen reaction studies, carried out largely by the discharge flow method in the past decade, as well as by a number of detailed studies performed by the crossed molecular beam technique. W e will first examine the data obtained from thermal measurements, in order to ascertain the systematic trends present in these reactions. We have previously described our observations of the systematic rate behavior of the reactions of OH radicals with the halogen molec~les.~9~ Electronic properties of both the radicals and molecules will be shown to influence the rates of (1) Smith, I. W. M. Kinetics and Dynamics of Elementary Gas Phase Reactions; Butttrworths: London, 1980. ( 2 ) Loewenstein, L. M.; Anderson, J. G. J . Phys. Chem. 1984,88,6277. (3) Loewenstein, L. M.; Anderson, J. G. J . Phys. Chem. 1985, 89, 5371.
0 1987 American Chemical Society
2994 The Journal of Physical Chemistry, Vol. 91, No. 11, 1987
-
I
,
,
,
-
10'0-
r
U
w r
w
3
-
0
3
g
1
-
1045
-
-
0
+
1
F2
10-22
2
C12
3 4
BrCl Br,
5
IC1
6
I2
6.70 1.49 5.28 1.97 1.57
X X X X X
lo-"
IO-"
10-1 I 0.00988 0.228 8.24 3.08 25.0
68 86 43 86 45 95
17 5.4( 3.1 1.4 1.6 0.8
A CI
8 a
TABLE 11: Rate Constants, Cross Sections, and Activation Energies of the OH + X2 Reactions at 298 K reaction halogen k' u, AZ ac, A2 Eaab
"Rate constants in em3 molecule-' s-'. bE,,, in kcal mol-', calculated from eq 3. CCorrespondsto an intrinsic activation energy of 3.6 kcal mol-', since this reaction is endothermic by 1.8 kcal mol-'.
z
G
Loewenstein and Anderson
O F
OH
00
10.20 -
DN AH
, 5
,
,
,
10 15 IONIZATION POTENTIAL - ELECTRON AFFINITY lev)
Figure 1. Plot of log k, the bimolecular rate constant in units of cm3 molecule-l s-I, vs. I - E, where I is the ionization potential of the halogen and E the electron affinity of the radical, in eV.
chemical reaction. How these molecular properties affect the activation energies of the reactions will be explained qualitatively by a new application of frontier orbital theory. Furthermore, the detailed consequences of the model will be compared to the observed energy disposal and scattering behavior of the reactions.
