X
i
v i A i $
X
k
v
0
k A
0
k :
ðÀ2:2:1Þ
The rate of the direct processes is (2.1.9), and the rate of the reverse process is
r
0
¼ k
0
Y
k
A
0
k
 à m
0
k
:
ð2:2:2Þ
The k and k
0 (or k 2.1 and k -2.1 for the process (2.2.1, –2.2.1)) are rate constants of
direct and reverse processes. It is obvious, that what process is direct and what is
reverse is determined by which species are written in the left and right parts of an
(2.2.1, –2.2.1). In principle, one can measure the rate constants of direct and reverse
processes.
Let us analyze the reaction
2CH 3 $
M C 2 H 6 ;
ðÀ2:1:16aÞ
as an example.
One can produce CH 3 radicals by photolysis of an unsaturated hydrocarbon at
room temperature and measure the rate constant of direct reaction 2CH 3 !
M C 2 H 6 :
r 1:16a ¼ À
1
2
d CH 3
½
dt
¼ k 1:16a Á CH 3
½
2 ½M
The reverse reaction 2CH 3
M C 2 H 6 has negligible rate constants at room temperature, even if one utilizes C 2 H 6 molecule as unsaturated hydrocarbon:
[C 2 H 6 ] >> [CH 3 ], but C 2 H 6 dissociation energy is high, 3.91 eV [5], and scale
factor for energy values in molecular-scale systems for room temperature, kT %
0.03 eV (k is Boltzmann constant).
On the other hand, one can heat C 2 H 6 molecules at very high temperatures at
which their dissociation is possible using an explosive driven shock tube. A simple
shock tube utilizing in chemical physics is a tube in which a gas or a gas mixture at
low pressure and a gas at high pressure are separated using a diaphragm [6], p. 4.
The diaphragm suddenly bursts open, for example, due to an explosion of a
H 2 + O 2 mixture to produce a wave propagating through the low-pressure section.
The shock that eventually forms increases the pressure, and temperature, up to tens
of thousands of degrees (several eV) of the test gas, and induces a flow in the
direction of the shock wave. Observations can be made in the flow behind the
incident front or take advantage of the longer testing times and vastly enhanced
pressures and temperatures behind the reflected wave.
If one heats C 2 H 6 molecules using an explosive driven shock tube, their thermal
decomposition: C 2 H 6 !
M 2CH 3 (reaction (–2.1.16a)) occurs only. The CH 3 radical
concentration is low just after the explosion. Besides, recombination rate constants
decrease with temperature for an overwhelming majority of these reactions.
14
2 General Kinetic Rules for Chemical Reactions, Collisional …
i
v i A i $
X
k
v
0
k A
0
k :
ðÀ2:2:1Þ
The rate of the direct processes is (2.1.9), and the rate of the reverse process is
r
0
¼ k
0
Y
k
A
0
k
 à m
0
k
:
ð2:2:2Þ
The k and k
0 (or k 2.1 and k -2.1 for the process (2.2.1, –2.2.1)) are rate constants of
direct and reverse processes. It is obvious, that what process is direct and what is
reverse is determined by which species are written in the left and right parts of an
(2.2.1, –2.2.1). In principle, one can measure the rate constants of direct and reverse
processes.
Let us analyze the reaction
2CH 3 $
M C 2 H 6 ;
ðÀ2:1:16aÞ
as an example.
One can produce CH 3 radicals by photolysis of an unsaturated hydrocarbon at
room temperature and measure the rate constant of direct reaction 2CH 3 !
M C 2 H 6 :
r 1:16a ¼ À
1
2
d CH 3
½
dt
¼ k 1:16a Á CH 3
½
2 ½M
The reverse reaction 2CH 3
M C 2 H 6 has negligible rate constants at room temperature, even if one utilizes C 2 H 6 molecule as unsaturated hydrocarbon:
[C 2 H 6 ] >> [CH 3 ], but C 2 H 6 dissociation energy is high, 3.91 eV [5], and scale
factor for energy values in molecular-scale systems for room temperature, kT %
0.03 eV (k is Boltzmann constant).
On the other hand, one can heat C 2 H 6 molecules at very high temperatures at
which their dissociation is possible using an explosive driven shock tube. A simple
shock tube utilizing in chemical physics is a tube in which a gas or a gas mixture at
low pressure and a gas at high pressure are separated using a diaphragm [6], p. 4.
The diaphragm suddenly bursts open, for example, due to an explosion of a
H 2 + O 2 mixture to produce a wave propagating through the low-pressure section.
The shock that eventually forms increases the pressure, and temperature, up to tens
of thousands of degrees (several eV) of the test gas, and induces a flow in the
direction of the shock wave. Observations can be made in the flow behind the
incident front or take advantage of the longer testing times and vastly enhanced
pressures and temperatures behind the reflected wave.
If one heats C 2 H 6 molecules using an explosive driven shock tube, their thermal
decomposition: C 2 H 6 !
M 2CH 3 (reaction (–2.1.16a)) occurs only. The CH 3 radical
concentration is low just after the explosion. Besides, recombination rate constants
decrease with temperature for an overwhelming majority of these reactions.
14
2 General Kinetic Rules for Chemical Reactions, Collisional …