Rate constant for the reaction C₂H₅ + HBr → C₂H₆ + Br Page: 5,847
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THE JOURNAL OF
PHYSICAL CHEMISTRYpubs.acs.org/JPCA
Rate Constant for the Reaction C2H5 + HBr - C2H6 + Br
David M. Golden,*'t Jingping Peng,* A. Goumri,* J. Yuan,* and Paul Marshall*t
tDepartment of Mechanical Engineering, Stanford University, Stanford, California 94305, United States
tDepartment of Chemistry and Center for Advanced Scientific Computing and Modeling (CASCaM), University of North Texas,
Denton, Texas 76203, United States
0 Supporting Information
ABSTRACT: RRKM theory has been employed to analyze the kinetics of the title reaction, in
particular, the once-controversial negative activation energy. Stationary points along the reaction 3-- /---3
coordinate were characterized with coupled cluster theory combined with basis set extrapolation
to the complete basis set limit. A shallow minimum, bound by 9.7 kJ mol-1 relative to C2H5 +
HBr, was located, with a very small energy barrier to dissociation to Br + C2H6. The transition
state is tight compared to the adduct. The influence of vibrational anharmonicity on the kinetics
and thermochemistry of the title reaction were explored quantitatively. With adjustment of the
adduct binding energy by ~4 kJ mol-1, the computed rate constants may be brought into
agreement with most experimental data in the literature, including new room-temperature results
described here. There are indications that at temperatures above those studied experimentally, the activation energy may switch
from negative to positive.INTRODUCTION
In the past, heats of formation of several radicals R had been
determined by measuring the temperature dependence of the
reactions'
RH+X - R+HX (1)
or
RX+X-*R+X2 (2)
where X is I or Br. It was thought that the rate constant for the
reverse of reaction 1 (k_1) could be characterized by activation
energies (E_1) of 4-8 kJ mol-1 for X = I and Br, and that for
the reverse of reaction 2 could be characterized by an activation
energy (E-2) of 0-4 kJ mol-1. In addition, in many of the
studies of these first two reactions, it was often possible to
characterize the ratio of the rate constants for the reverse
reactions, and it was usually the case that the difference
between E_1 and E_2 was in the range of 4-8 kJ mol-1. All of
this notwithstanding, it has become apparent from several
direct studies2-5 of the reverse of reaction 1 that for many
species R, E_1 can be negative. (There is a study6 that indicates
a positive activation energy for R = C2H5 and X = Br, as well as
studies7'8 with R = t-butyl and X = Br and I and R = CH2Br and
CHBrCl with HBr9 that report positive activation energies.)
This negative activation energy, together with the values of E1,
has led to values of the heats of formation of several simple
radicals that are higher than first thought and that are in accord
with modern quantum chemistry calculations.'0
Understanding of the reasons for the negative activation
energy of the reverse of reaction 1 has been somewhat elusive.
Some discussions for the case where R = CH3 have been
presented."'"2 McEwen and Golden attempted an explanation
for the case of t-butyl + HI by positing a complex between
t-butyl and HI at the I atom. ' Even then, a quite deep complexwas required to accommodate the measured negative activation
energy. Notable prior theoretical work on the title reaction
C2H5 + HBr - C2H6 + Br (3)
was carried out by Chen and Tschuikow-Roux, who used MP4/
6-31G(d) energies at MP2/6-31G(d) geometries for stationary
points.'4 They concluded that a loosely bound intermediate complex
bound through the H atom of HBr caused the negative activation
energy, and they calculated rate constants k3 using transition-state
theory (TST) and RRKM theory. Their results were intermediate
between the higher and lower measured values. Recently, Sheng
et al.'5 have presented a calculated potential surface for reaction 3.
They found that there is a weakly bound (by about 13 kJ mol-1)
complex between the reactants, followed by a transition state to
products that is much lower in entropy (tighter) than, but at
essentially the same energy as, the complex. They used ICVT
(improved canonical variational transition-state theory) to explain
the rate constants. Their calculated rate constants exhibit the
negative activation energy found in many recent studies, but their
suggested fitting parameters would seem to have a typographical
error.
We have also performed quantum calculations on this
surface, with results not too different from those of Sheng et al.
(It might be noted that one of the senior authors (P.M.) sent
the other (D.M.G.) these essential results over 10 years ago, but
we did not have the wherewithal to perform the chemical activa-
tion calculations that we discuss herein. A poster was presented
at the 16th International Symposium on Gas Kinetics in 2000.)
Special Issue: A. R. Ravishankara FestschriftReceived:
Revised:
Published:September 20, 2011
January 17, 2012
January 23, 2012ACS Publications 2012 American Chemical Society
5847
dx.doi.org/10.1021 /jp209081 v I J. Phys. Chem. A 2012, 116, 5847-5855
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Golden, David M.; Peng, Jingping; Goumri, Abdellatif; Yuan, Jessie & Marshall, Paul. Rate constant for the reaction C₂H₅ + HBr → C₂H₆ + Br, article, January 23, 2012; [Washington, D.C.]. (https://digital.library.unt.edu/ark:/67531/metadc501410/m1/1/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Arts and Sciences.