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OCR for page 75
THE EVALUATION OF SPECIFIC REACTION RATES IN CHAIN
REACTIONS1
G. K. ROLLEFSON
Department of Chemistry, University of California, Berkeley, California
Received May 25, 1988
One task involving photochemical chain reactions which has been under-
taken by many investigators is that of evaluating the specific reaction
rates (or rate constants) for the various steps which occur. The problems
which arise with each reaction studied are so similar that the discussion
will be simplified if we consider the three main types of processes: (~)
chain starting, (2) chain terminating, (~) chain continuing.
I. CHAIN-STARTING REACTIONS
A consideration of the mechanisms which have appeared in the literature
leads to the conclusion that chains are started by some kind of an odd
molecule, either an atom or a free radical., and are propagated by the alter-
nate formation and disappearance of such molecules. Therefore, in this
discussion, we are concerned with the rate of formation of odd molecules
as a result of light absorption. In the simple cases, such as the absorption
of light by diatomic molecules in the gaseous state in a continuous absorp-
tion band, it has been quite well established that dissociation occurs for
every light quantum absorbed. The same may be said for the truly con-
tinuous absorption by more complex molecules, although, in such cases, it
may be difficult to decide whether the spectrum is really continuous or
only appears to be so because of inadequate resolution. Very often, how-
ever, we must consider a competition between the dissociation process and
otter processes such as fluorescence, deactivation by collision, or some
reaction of the photoactivated molecule, either by itself or with other
molecules, which does not involve the formation of odd molecules. For
example, the photodecomposition of acetaldehyde at high temperatures
is a chain reaction probably involving methyl radicals (15~. From the
work on this reaction at lower temperatures we know that, in the first
stage, we have competition between fluorescence, a polymerization reac-
tion, and probably a direct decomposition into methane and carbon monox-
ide as well as the dissociation to give methyl radicals (16, 27~. It is appar-
~ Contribution No. 7 to the Third Report of the Committee on Photochemistry,
National Research Council.
75
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76
G. K. ROLLEFSON
ent, therefore, that in this case it would be definitely inaccurate to set the
number of chains started equal to the number of quanta of light absorbed.
This uncertainty is involved in every reaction in which the radicals are
produced by a predissociation process. A similar uncertainty is intro-
duced if we have two overlapping absorption bands corresponding to
transitions to two difl Brent excited states. Even with such a simple mole-
cule as chlorine, Aickin and Bayliss (1) have shown that the continuous
absorption is complex and there is a continuum underlying the sharp line
bands. In this case Bayliss (3) has shown that the observed facts con-
cerning the combination of hydrogen and chlorine caused by light absorbed
in the banded region of the spectrum can be accounted for by assuming
that only the continuous absorption starts the reaction chains.
Another source of uncertainty as to the efficiency of the dissociation
process was suggested by Franck and Rabinowitch (11~. They expressed
the view that the quantum yield of a primary dissociation process in solu-
tion must be very low, as the surrounding molecules will prevent the sepa-
ration of the parts. Rollefson and Libby (28) pointed out that such an
eject should be observed if the speed of the separating parts is small, but
most experiments have been performed with such energies that the parts
would be separating with relatively large kinetic energies and thus be able
to break through the surrounding cordon of solvent molecules, making the
dissociation practically as efficient as in the gas phase. Dickinson (8) has
discussed a number of reactions in solution and shown that they could be
most readily explained by assuming that the first step was a dissociation
of the light-absorbing molecule. Rabinowitch (22) has objected to such
arguments on the grounds that the rate considerations used by Dickinson
and others depend on the steady state concentrations of radicals or atoms
rather than on their rates of formation, and these steady state values could
be unchanged if the rates of dissociation and recombination were affected
equally by the solvent. Rollefson and Libby pointed out that such a
symmetrical modification was unlikely. Furthermore, it must be said
that it is difficult to conceive of chains which are unaffected by dilution
having a length such that the quantum yield of the overall reaction would
be 2; yet such an assumption is necessary for C102 in carbon tetrachlo-
ride solution if we do not assume a high efficiency for the primary step.
II. CHAIN-TERMINATING REACTIONS
The best known of the chain-terminating reactions are those involving
the recombination of atoms. Many studies with atomic hydrogen have
shown that the recombination occurs at every collision during which a third
body is present to remove some of the energy (2, 10, 32~. Similarly, a
comparison of the thermal and photochemical rates of formation of hydro-
gen bromide has led to the conclusion that bromine atoms recombine by a
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REACTION RATES IN CHAIN REACTIONS
77
triple collision mechanism (5, 14~. Ritchie (23) and Hilferding and
Steiner (13) have studied the relative efficiencies of different molecules as
the third body. Some idea of the range encountered is given by rate con-
stants for the reaction
Br + Br + M = Br2 + M + k.e.
taken from the paper by Hilferding and Steiner (see table 1~. The varia-
tion is very similar to that found for the quenching of fluorescence by these
gases. On the basis of these observations it seems reasonable to assume
that any atom recombination process occurs at approximately every
triple collision if the reaction is homogeneous.
The heterogeneous recombination of atoms depends quite markedly on
the nature of the surface involved. It was found in the very first experi-
ments with hydrogen atoms that dry glass or quartz surfaces are very
much more effective in causing the recombination than ones which had
not been dried (33~. Metallic surfaces were also found to be very eff ective
in causing recombination. Experiments with the hydrogen-bromine
TABLE ~
Rate constants for Br + Br ~ M
M...............
k X 10-15.........
. . . | H2 | He | A | N2 | Br2 | HBr | HC1 | CO
... 1 1.25 1 0.47 1 0.11 1 0.82 1 2.6 2.1 1 4.7 1 6.3
reaction at such pressures that the bromine atoms recombine on the wall
show that the rate depends on the previous treatment of the walls (13~.
Another example is found in the hydrogen-chlorine reaction in which
Bodenstein and Winter (6) calculated that only one collision in six thousand
on a silver chloride surface resulted in removal of the chlorine atom. A
comparison of their quantum yields with values obtained in the presence
of glass surfaces indicates that glass is about ten times as effective. The
failure of the atoms to react at every collision with the surface does not
seem to be due to the requirement of any heat of activation, but rather to
a low value of the accommodation coefficient. This idea is supported by a
comparison of the photochemical temperature coefficients for the hydro-
gen-chlorine reaction as obtained by Hertel (12) and by Potts and Rollef-
son (21) with the value obtained by Rodebush and Klingelhoefer (24) for
the reaction of chlorine atoms with hydrogen molecules, which shows that
the latter reaction is capable of accounting for the entire temperature co-
efficient of the former. The principal difficulties in the way of securing
exact values for the rate constant of such a chain-terminating reaction are
the determination of the accommodation coefficient and the rate of ap-
proach to the wall. The latter rate is complicated by the fact that,
usually, the heat of reaction sets up convection currents which make it
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78
G. }I. ROLLEFSON
virtually impossible to decide on an average path length. On the whole,
the error in the estimation of the rate of a chain-terminating process in-
volving atoms is probably not greater than a factor of one hundred, whether
it is a homogeneous or a heterogeneous reaction.
If the chain-terminating reaction involves more complex groups, more
varieties of reaction are introduced. The surface reactions and the triple
collision mechanism for association reactions are possible here as well as
with atoms. However, it cannot be said with certainty that the associa-
tion reactions do not involve heats of activation. Furthermore, it is
possible for two radicals to combine to form a single molecule by a process
which is the reverse of predissociation without having a third body present.
In such a case, the quasi-molecule formed would have a sufficiently long
life to lose some of its energy in a collision and become a stable molecule.
Finally we have the possibility of two radicals reacting to form normal
molecules. Some examples of these types of reaction which have been
assumed are
CO Cl + Cl ~ CO + C12
CH3 + CH3 > C2H6
C2H5 + C2H5 ~ C2H4 + C2H6*
(1)
(2)
(3)
* As the concentrations of these radicals are always very low, bimolecular proc-
esses involving them must be considered improbable.
The evidence for these reactions is not very conclusive, as the experiments
have been such that other possibilities have been present. In support of
reaction 2 we may cite the formation of ethane in the photolyses of lead
tetramethyl (17), acetone (18), or methyl ethyl ketone (19~. Reaction 3
has been assumed frequently, but probably the best evidence for it is the
formation of ethane and ethylene in the photolysis of ethyl iodide (9~.
The magnitudes of the activation energies for these reactions are at present
unknown. They are probably not large, but even a small activation
energy would introduce a rather large uncertainty into the specific reaction
rate. Until further data are available, we must conclude that the constants
for reactions between two radicals are not sufficiently well known to be
used in calculating rates of photochemical chain reactions.
IlI. CHATN-CONTINUING REACTIONS
The direct measurement of the rate constants for reactions of the type
involved in the propagation of chains has been limited to a very few cases
involving atoms. Most of these reactions involve hydrogen or one of the
halogen atoms.
The specific rate of the reaction
Br + H2~HBr + H
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REACTION RATES IN CHAIN REACTIONS
79
can be obtained from the thermal rate of formation of hydrogen bromide if
we assume that bromine atoms and molecules are in equilibrium in the
reaction mixture. On the basis of data obtained from the experimental
study of both the thermal and photochemical formation of hydrogen
bromide, Bodenstein and Lutkemeyer (5) give for the rate constant
log k = - 38T9 + 13.862
which corresponds to an activation energy of 17,640 cal. The reaction
is endothermic to the extent of 14,500 car., so the activation energy is only
slightly greater than the energy required to offset the endothermicity of
the reaction. The study of the rate of formation of hydrogen bromide
also tells us that the ratio of the rate constants for the reactions
H + Bra >HBr + Br
and
H + HBr~H2 + Br
is 8.6 over a very wide temperature range. This fact suggests that the
heats of activation for these reactions are zero, the only difference being in
the so-called "steric factor".
The rate of the reaction
Cl + H2 > HCl + H
was measured directly by Rodebush and Klingelhoefer (24), who used a
known concentration of.chlorine atoms produced by an electric discharge
in chlorine gas. They found that the rate was given essentially by the
number of collisions multiplied by e-6000/RT with the uncertainty in the
numerator of the exponent being approximately 1000 cal. A similar value
was obtained from the measurements by Hertel (12) and by Potts and
Rollefson (21) of the temperature coefficient of the photochemical reaction
of oxygen-free mixtures of hydrogen and chlorine, if it was assumed that
the chain-terminating step involved no heat of activation.
A number of reactions of hydrogen atoms have been studied by preparing
a measurable concentration of the atoms by means of an electrical dis-
charge and passing these atoms into some other gas. The most important
reaction studied by this method is the transformation of pare-hydrogen
into or/ho-hydrogen. The fraction of the collisions between hydrogen
atoms and hydrogen molecules which result in reaction is 2 X 10-6 and
the heat of activation is approximately 7000 cal. Other reactions which
have been tried include those with oxygen, water, the halogens, the hydro-
gen halides, some hydrocarbons, hydrogen sulfide, and methyl halides.
Under these conditions most of these reactions proceed too fast to obtain
accurate measurements, so the only conclusion which can be drawn is that
the hydrogen atoms are destroyed in less than one hundredth of a second,
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80
G. K. ROLLEFSON
which means that at least one collision in 104 is effective.
energy is therefore either zero or very small.
The activation
Other methods which have been used to obtain estimates of the rates
of the steps in a chain process are (1) studies of the overall rate with appro-
priate assumptions concerning the chain-starting and chain-terminating
reactions, and (2) studies of systems in which two reactions compete for
the same reactive intermediate. The validity of both of these methods
depends on the assumption that the mechanism used in the calculation is
correct. It is essential therefore that any other mechanisms be excluded
on the basis of the experimental evidence before rate constants obtained
by these methods may be considered valid. We may illustrate the first
method by referring to the formation of hydrogen chloride from the ele-
ments. The mechanism which seems to explain the behavior of oxygen-
free mixtures of hydrogen and chlorine is expressed by the following
equations:
k3 Cl2+hY >2C1 (1)
k2 Cl + H2 > HCl + H
k3 H + Cl2 ~ HC1 + Cl
k4 C1 > 1/2 C12 (on the walls of the reaction vessel)
This leads to the rate expression
(2)
(3)
(4)
d(HCl) kik2
dt — k Iabs.(H2)'
If the light absorbed corresponds to the continuum in the chlorine spec-
trum, there is plenty of evidence to support the assumption that ki = 2.
The constant k4 is subject to much greater uncertainty. Usually, it is
assumed that every collision of an atom with a surface is effective in causing
recombination, but recently Bodenstein and Winter (6) have presented
data which indicate that only one collision in six thousand of chlorine
atoms with a silver chloride surface leads to the formation of molecules.
This efl ect does not seem to be due to a heat of activation but rather is an
accommodation coefficient analogous to the steric factor for bimolecular
reactions. Collisions with glass or quartz surfaces are much more effec-
tive, but it is probable that the erratic rates of formation of hydrogen
chloride that have been reported are at least partially due to the variation
of this k4 in different experiments. If we assume that reaction 4 has no
heat of activation, then the entire heat of activation for the overall rea¢-
tion is due to reaction 2. The value of k2 may be calculated approximately
by multiplying the collision number by e-Q/T, where Q is the heat of
activation. The efficiency factor for collisions between molecules possess-
ing the necessary energy cannot be determined any more exactly than we
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REACTION RATES IN CHAIN REACTIONS
81
know k4. Usually in systems of this type the uncertainty in the heat of
activation is sufficient to mask any uncertainty in the collision number or
efficiency factor.
This type of calculation may be applied, with the same degree of approxi-
mation, to any other chain reaction involving atoms in the initial and final
steps and having the rate determined by one step in the chain process.
If radicals are involved in the initial or final steps, both of the uncertainties
become much greater particularly on account of the activation energy of
the chain-term~nat~ng step. Thus a reaction such as
2CCl3 + Cl2- > 2CCl4
which Schumacher and Wolf (31) assumed to be the chain-term~nat~g
step in the chlorination of Chloroform probably requires some heat of
activation, but the magnitude of this heat is not even approximately
known. The same statement can be made about the other processes which
we have discussed in the section on chain-terminating processes.
A further complication arises frequently owing to the complexity of the
assumed mechanism. Thus, instead of having the overall rate constant
expressed in terms of the constants for initial and final steps and one step
of the chain (k2 in the case of the formation of hydrogen chlorides we find
that the constants of two or more steps of the chain appear in the rate
equation. Such constants are indeterminate from rate measurements
alone, and up to the present time no one has determined the constants for
any system of this type from experimental data.2
The second method for evaluating the constants of steps in a chain, the
use of competitive reactions, has not been used very extensively as yet.
We have already cited the competition between hydrogen bromide and
bromine for hydrogen atoms in the formation of hydrogen bromide. Other
examples which have been studied quantitatively include the competition
of carbon monoxide and hydrogen for chlorine atoms (4, 26), of oxygen
and chlorine for COCl (25, 29), and of ozone and oxygen for oxygen atoms
(30~. The experiments determine only the ratio of the two rate constants
but if one rate constant, as, for example, that for the reaction between
atomic chlorine and hydrogen, is known from other studies, then the other
can be calculated. We have already seen that the rate constant for the
reaction
Cl + He > HCl + H
2 Bodenstein and his students claim to have made such determinations for the
formation of phosgene, but the details of their calculations have not been published.
It may be remarked here that in their published work they have neither proven their
mechanism to the exclusion of others nor listed enough independent equations based
on experimental data to determine all of the constants involved in their rate equa-
tions. See, however, contribution No. 9 to this Report.
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82
G. E. ROLLEFSO~-
;s pretty well known, therefore we may use this reaction as a means of
measuring chlorine-atom concentrations in reaction mixtures and thus the
specific rates of other reactions. Naturally this method is limited to those
systems in which the chlorine atoms react at a rate comparable with that
with hydrogen. Thus, the observation that in mixtures of ethylene,
hydrogen, and chlorine the halogen adds to the ethylene with no appreci-
able formation of hydrogen chloride tells us that the first step in the addi-
tion reaction is very fast but does not permit an exact calculation of its
specific rate.
Many reactions of hydrogen atoms have been studied by determining
the concentration of the atoms by the rate of the conversion of para-hydro-
gen to or/ho-hydrogen. This is essentially the method of competing rates,
except that the atoms are not destroyed by the test reaction. The rate
constant for this conversion has been given as 2 X 109Te-7°°°/RT, which
indicates the order of magnitude of the rates which may be studied by this
method. One point which has been overlooked in some investigations is
that if the hydrogen atoms react very rapidly with other substances in the
reaction mixture the concentration of the atoms may not be great enough
to cause appreciable conversion of pare-hydrogen to or/ho-hydrogen.
This method has been applied by Cremer, Curry, and Polanyi (7) to the
study of reactions of atomic hydrogen with alkyl halides. Their results
were only semiquantitative and their experimental method limited them
to reactions for which the activation energy was in the range 2800 < Q
HOe and H +
CO > HCO. They concluded that the former occurred once in seven
hundred fifty triple collisions and the latter once in ten triple collisions.
Patat (20) has also used this method to determine the concentrations of
hydrogen atoms present during the decompositions of a number of organic
compounds. On account of the complexity of such systems only qualita-
tive results concerning rate constants were obtained.
In conclusion, it must be stressed that the great need at present is the
determination, by methods free from assumptions, of a few rate constants
for reactions of the type we have discussed. No matter how reasonable
assumptions may seem, any rate constants based on them are little better
than guesses. This is especially true in complex systems as, under such
conditions, usually several mechanisms are capable of describing the facts,
and hence there is no certainty that we are dealing with the right set of
reactions. The constants which have been calculated for such systems in
the literature must be looked upon as reasonable interpretations rather
than as established facts.
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REACTION RATES IN CHAIN REACTIONS
REFERENCES
83
(l) AICKIN AND BAYLISS: TranS. FaradaY SOC. 33, 1333 (1937~.
(2) AMDUR AND ROBINSON: J. Am. Chem. soc. 56, 1395, 2616 (1933~.
(3) BAYLISS: TranS. FaradaY SOC. 33, 1339 (1937~.
(4) BODENSTEIN, BRENSCHEDE, AND SCHUMACHER: z. physik. Chem. B28, 81 (1935~.
(5) BODENSTEIN AND LUTKEMEYER: z. physik. Chem. 114, 208 (1925~.
(6) BODENSTEIN AND WINTER: Sitzber. preuss. Akad. wise., Physik.-math. ~lasse
I (1936~.
(7) CREMER, CURRY, AND POLANYI: Z. physik. Chem. B23, 445 (1933~.
(8) DICKINSON: Chem. Rev. 17, 413 (1935~.
(9) EMSCHWILLER: Ann. chim. 17, 413 (1932~.
(10) FARKAS AND SACHSSE: z. physik. Chem. B27, 111 (1934~.
(ll) FRANCK AND RABINOWITCH: Trans. Faraday Soc. 30, 125 (1934~.
(12) HERTEL: z. physik. Chem. B16, 325 (1931~.
(13) HILFERDING AND STEINER: z. physik. Chem. B30, 399 (1935).
(14) JOST AND JUNG: z. physik. Chem. B3, 83 (1929~.
(15) LEERMAKERS: J. Am. Chem. soc. 66, 1537 (1934).
(16) LEIGHTON AND BLACET: J. Am. Chem. soc. 64, 3165 (1932~; 6B, 1766 (1933~.
(17) LEIGHTON AND MORTENSON: J. Am. Chem. soc. 58, 448 (1936~.
(18) NORRISH AND APPLEYARD: J. Chem. soc. 1934, 874.
(19) NORRISH AND KIREBRIDE: Trans. Faraday Soc. 30, 103 (19341.
(20) PATAT: z. physik. Chem. B32, 274, 294 (1936).
(21) POTTS AND ROLLEFSON: J. Am. Chem. soc. 67, 1027 (1935~.
(22) RABINOWITCH AND WOOD: Trans. ]?araday Soc. 32, 547 (1936~.
(23) RITCHIE: Proc. Roy. soc. (London) A146, 828 (1934~.
(24) RODEBUSH AND KLINGELHOEFER: J. Am. Chem. soc. 65, 130 (1933~.
(25) ROLLEFSON: J. Am. Chem. soc. B5, 148 (1933).
(26) ROLLEFSON: J. Am. Chem. soc. 66, 579 (1934~.
(2?) ROLLEFSON: J. Phys. Chem. 41, 259 (1937~.
(28) ROLLEFSON AND LIBBY: J. Chem. Phys. 5, 569 (1937~.
(29) ROLLEFSON AND MONTGOMERY: J. Am. Chem. soc. 65, 142 (1933~.
(30) SCHUMACHER: z. physik. Chem. B17, 405 (1932~.
(31) SCHUMACE[ER AND WOLFF: z. physik. Chem. B26, 161 (1934~.
(32) SMALLWOOD: J. Am. Chem. soc. 51, 1985 (1929~.
(33) WOOD: Phil. Mag. 42, 729 (1921~; 44, 538 (1922~.
OCR for page 84
Representative terms from entire chapter:
hydrogen atoms
