CH3 + HBr Reaction Kinetics
J. Phys. Chem. A, Vol. 103, No. 40, 1999 8019
combinations are often directly derived from experimental data
and have better accuracy than the individual rate constants or
cross sections.
After normalization of all variable components to the initial
concentration of one (the “reference”) transient species (methyl
radicals in our case) and introduction of dimensionless combina-
tions, the ODE system becomes
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(
(
(
1
12, 1347.
dY /dt ) Abs
B Σiej ν r Y Y + Σ ν k (Y A + A Y )
ijk ij i j iej ijk ij i j i j
k
CH ,0
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3663.
(E14)
(
(
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The initial conditions are
Y ) B /B ) (Σ σ1 φ A )/(Σ σ1 φi,CH3Ai)
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(
(E15)
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5, 9900.
k0
k0 CH ,0
i
i
ik
i
i
i
3
9
(
21) Seakins, P. W.; Pilling, M. J.; Niiranen, J. T.; Gutman, D.;
In this work, the “reference” concentration is the initial
concentration of methyl radical. The dimensionless combinations
are Yi ) Bi/[CH3]0, the normalized variable component of the
ith species, AbsCH ,0 ) σ2CH [CH3]0L, the initial absorption of
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3
3
methyl radicals, B ) k3/σ2CH L, the combination of the
3
recombination rate constant, absorption cross section, and the
reactor length (which is directly measured in additional experi-
ments), and rij ) kij/k3, the normalized rate constants of
bimolecular reactions.
The set of differential equations (E14) together with the set
of the initial conditions (E15) completes the formulation of the
problem for numerical solution.
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(
The specification of the initial conditions requires only the
initial concentrations of the “permanent” species, their absorp-
tion cross sections for the laser light, and the quantum yields
of the relevant photodissociation routes. No laser energy is
required to fit the absorption kinetic curve, if the parameter B,
the initial concentrations of the “permanent” species, and the
ratios rij are known. The initial absorption of one of the free
radicals (methyl in this case) is used as a fitting parameter. The
absolute concentration of free radicals enters indirectly, via the
initial absorption and the absorption cross sections.
The variable absorption and the intensity of the monitoring
light are given by eqs E16 adn E17.
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(
41) International Thermodynamic Tables of the Fluid State. Helium-4.
Abs(t) ) Abs
(Σ (σ2 /σ2 )Yi)
(E16)
(E17)
CH ,0
i
i
CH3
IUPAC Division of Physical Chemistry Commission on Thermodynamics
and Thermochemistry Thermodynamic Tables Project; Angus, S., de Reuck,
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I(t) ) I (t) exp(-Abs(t))
0
1
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where I0(t) is the monitoring light intensity without the laser
pulse entering the reactor. The absorption of the permanent
species is automatically accounted for in eq E17.
(
9
(
(
(
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Acknowledgment. This work was supported by the Sepa-
rately Budgeted Research Support program at NJIT. Acknowl-
edgment is made to the donors of the Petroleum Research Fund,
administered by the American Chemical Society, for partial
support of this research (Grant 31640-AC6).
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