In this paper we intend to use the considerations of a previous article [2] in a study of the decomposition of azomethane, a homogeneous gas-phase reaction which is unimolecular at high pressures. Equations referred to are in that article and the nomenclature is the same as used there

Rice, Oscar Knefler

English

Caltech Authors - Main

CHEMISTRY: 0. K. RICE
We have thus shown how to evaluate all our quantities in terms of the
thermal properties of the decomposing molecules. The application of
these considerations to a specific case, and comparison with the classical
theory, will be undertaken in another paper.
In conclusion the writer wishes to acknowledge his indebtedness to
various members of Gates Chemical Laboratory, especially to Dr. L. S.
Kassel who is attacking the same problem from another angle. He is also
indebted to Dr. H. C. Ramsperger of Stanford University.
1 NATIONAL RSsIMRcH F&Low.
2 Rice and Ramsperger, J. Amer. Chem. Soc., 49, 1617 (1927).
3Kassel, J. Phys. Chem. (in print). Rice and Ramsperger, J. Am. Chem. Soc. (in
print).
4 Tolman, Statistical Mechanics, Chemical Catalog Co., 1927, p. 261.
6 This equation and its consequences will be considered in detail in another article.
THE THEORY OF THE DECOMPOSITION OF AZOMETHANE
BY OSCAR NJIMLEIR Rice'
GAThs CEiMIcAL LABORATORY. CALIFORNIA INsTITUTIr OF TaCHNOLOGY
Communicated January 6, 1928
In this paper we intend to use the considerations of a previous article2 in a
study of the decomposition of azomethane, a homogeneous gas-phase re-
action which is unimolecular at high pressures. Equations referred to are
in that article and the nomenclature is the same as used there.
Our first task consists in the determination of n, m, and eo. Later we
shall consider B and C.
To get the various quantities we need to consider the thermal properties
of azomethane, in particular we need to know the average energy at the
temperature of reaction and higher temperatures. We have to get at this
indirectly by considering first the specific heat, and it is necessary to esti-
mate the specific heat itself by comparison with a similar compound, ace-
tone. Acetone, for the range 129°C. to 233°C. has a specific heat (Cp)
of 24 calories per mole.8 We subtract 2 to change Cp to C, and 3 more to
get the "internal" specific heat, whose maximum possible value, as in
the case of azomethane, is 51 calories per mole. We assume that at the
temperature at which azomethane reacts, about 600°C. abs. it is slightly
more excited, and estimate the specific heat at 0.5, the classical value.
Let us assume for the moment that the oscillators are all equally excited.
(We treat the rotational terms as if they were due to oscillators since they
are small in number and hence relatively unimportant.)
PROC. N. A. S.-118
CHEMISTRY: 0. K. RICE
Now from Einstein's formulas4 for the specific heat and energy of a
harmonic oscillator it will be found that an oscillator which is 0.5 excited
as regards specific heat has an energy 0.15 the classical value. This would
make the average energy at 600°C. abs. equal to about 4500 calories.
From the work of Ramsperger5 we may take e - (Eq. (7)) to be
about 52,000 calories per mole, and this would make the average energy
of the reacting molecule 56,500 calories per mole. 56,500 will be the
average energy at about 1900°C., abs., and it will be close enough to con-
sider that We has a maximum at e = 56,500 calories per mole at 1900°.
Then, from (10) we find m equal to 31 or 32.
We may investigate how m varies as we change el in equation (10) and
this will give us some idea of the error we make by setting m constant in
(6). It will be found that, in the neighborhood of 56,000, m varies about
2 per 10,000 calories, increasing with el. The effect of this is to spread the
curve W4b, against e slightly, on both sides of the maximum, but the
effect on the final results is inconsiderable. It may also be stated that
the curves for W.b. at different temperatures of reaction in the range in
which we shall be interested (290°C. to 330°C.) come near enough to
having their maxima at the same value of e so that we do not need to worry
about any difference in m between them.
On the other hand, had we supposed that the specific heat of 0.5 the
classical value was due to half the oscillators being fully excited, with
the.other half completely frozen in (6) would become simply a classical
formula with m equal to 25 or 26. The value of e at 600 °C. abs. would be
about 15,000 calories.
We have not yet found B and C, but as stated B is of no interest in it-
self and C only determines the pressure at which the rate has fallen to a
certain fraction of its high-pressure value. If we plot log K/Ku, against
log p, the curve for given values of n, m, and e3 is invariable in shape with
changes of C, such a change merely shifting it along the pressure axis;
and in such a plot the distance between any two points on two curves for
different temperatures (with the same values of n, m, and eo) is invariant
under changes of C, and definitely determined, since the temperature
coefficients of all quantities involved are known. Now the experimental
points lie at fixed positions along the log p axis, but may be shifted ver-
tically, since K,,, is not exactly known. Taking C as unknown, for the
time, we may, by suitable horizontal shifting of the theoretical points and
vertical shifting of the experimental points, bring them into coincidence,
provided our theory gives the right dependence of relative rate and rela-
tive pressure. The results of such a comparison, taking m = 31 and eo =
34,000 calories per mole (found as explained in the preceding paper from
the above value of m and assuming e = 6000 calories per mole at 330°C.-
actually it makes e = 7000) is exhibited in figure 1. It is seen that the
VOL. 14, 1928 119
CHEMISTRY: 0. K. RICE
agreement is satisfactory. Though the theory holds strictly for initial
rate constants, we have used Ramsperger's average rates, the error caused
by this being small.
The effect of changing m and e is shown by figure 2. Here the curves
have been brought into the closest correspondence possible, by shifting
along the log p axis. Curves IV are the result of applying the classical
theory as originally developed by Rice and Ramsperger.6 It is seen
that the curves have much the same shape, over what may be called
reasonable variations of m and E, and the comparison with the classical
Log,loP (cim-)
FIGURE, 1
ED, upper curve, 290°C.; 0, lower curve, 330°C.
curves seems to indicate that the same is true with respect to variation
in n. All the curves can be fitted to the data about equally well. De-
viations between the various curves would probably appear over a wider
pressure range and if we used still a smaller value of n than was used in the
classical case, we would reach a point where the rate would fall off rela-
tively more rapidly with pressure, as was the case when the classical
theory was applied to propionic aldehyde.A
But the point to be emphasized is the invariability of the shape of the
curve over a considerable pressure, when the constants involved are varied
through a reasonable range. This makes the agreement with experiment
120 PROC. N. A. S.
VOL1,T128CHEMISTRY: 0. K. RICE
much more significant, since it means that, though our determination of
these constants was admittedly rough, what we have done could not be
construed as a fixing of the shape of the curve by manipulation of arbitrary
quantities.
By use of equations (3), (4), (6) and (14) we may find C in terms of I,
which is defined in equation (13). Since I can only be approximately
determined, and since small differences in I make large differences in C,
it is best to first note that from equations (3), (4) and (5), and figure 1
(taking s = 6 X 10-8 cm.) the value of C (a dimensionless constant) which
0
8
FIGURE 2
Curve n m eo e (330°C.) Curve n m eo e (330 OC.)
I 51 31 34,000 7,000 III 51 25 40,000 12,000
II 51 51 34,000 12,000 IV 25 25 51,000 15,000
makes the rate fall off at right pressure, is 3.0 X 107 at 2900C., and then
attempt to discover whether the value of I corresponding to this is a reason-
able value. Substituting (3) and (5) in (4), integrating approximately,
and using (14) we find that the above value of C makes I = -18.5.
In order to find out whether this is a reasonable value or not we must
consider equation (13). Now in the neighborhood of the lower limit the
integrand of the first integral of (13) may be neglected compared with
the second. For the average energy of molecules which have an energy
greater than emax. will by either of the distributions (5) or (6) be close to
VOL. 14, 1928 121
CHEMISTRY: 0. K. RICE
Emax. + kT at a low temperature and the difference between the classical
and quantum molecules will be small compared to e - e, which we have
previously estimated to be 0.8 nkT/2 at 600°C., abs. (since e. = 6000
calories per mole) and which could only be a little more thanth is at 290 °C.
(The classical average energy ec = nkT/2.) On the other hand, if we go to
a temperature, say, 2400°C., abs., such that practically all the molecules
have energy greater than emax. (which is 58,000 calories per mole) it will
be seen that the two integrals cancel each other. Hence we may write
(for 290°C. or 563°C., abs.)
n /24OOR1= 2 - dT = R log (2400/563).
2 ~3 T 2
R is determined to make the above identical with equation (13) and, from
what we have said above, varies from about -0 . 8 to 0. 0, and R is a sort
of average in which the values at low temperatures are more heavily
weighted. We might guess it to be about -0.55. From the value of I,
-18.5, we get -0.50, which is close enough considering the nature of the
calculations. The above comparis9n is, of course, based on the values
we have chosen for mand , but is not very sensitive to changes in these
quantities.
A factor which we have heretofore neglected may now be considered
briefly. We have shown previously that our considerations resulting in
equation (1) do not hold unless almost all collisions of activated molecules
result in such a way that neither molecule after collision shall find itself
in an energy range in which the number of molecules is depleted appre-
ciably due to reaction."G Let us consider a typical case. At the lowest
pressure for which we have evaluated (1) in order to get the curve for 3300
C., in figure 1, we find that only about 22 per cent of the integral is con-
tributed by molecules whose energy is greater than 54,000 calories per mole.
Now let one of these collide with an average molecule of about 6000 calories
per mole. What is the chance that after collision either one of the mole-
cules should have an energy greater than 50,000, below which molecules
are present practically in equilibrium numbers? The sum of the energy
of the molecules being 60,000, this is equivalent to asking what is the
chance that one of the molecules should have more than 50,000 or less
than 10,000 calories. If it were just as likely to have one energy as an-
other, the chance would be one-third, and might necessitate a serious
correction of our theory. Let us try to estimate the chance that each of
the molecules shall leave the collision with energy in some small interval
near 30,000, as compared with the chance that one should have 50,000
and the other 10,000. We shall assume that statistical equilibrium is
established between the degrees of freedom of the two molecules at col-
PRoe. N. A. S.122
CHEMISTRY: 0. K. RICE
lision. Then the ratio of the probabilities is P'o/(P64P1o) where P30 is the
probability, according to the distribution law, that a molecule shall have
energy 30,000, P50 that a molecule shall have 50,000, Plo that a molecule
shall have 10,000 calories per mole.7 This quotient is independent of tem-
perature, and we may take P's at the temperature at which 30,000 is the
average energy (and about the energy, therefore, at which W. is a maxi-
mum). Let us attempt to calculate Ps0/P50. If the oscillators were all
equally excited to give a specific heat 0.5 the classical value at 600°C., abs.,
this temperature would be 1300; if half of them were completely excited
it would be 1200. Let us use the former figure to be sure we will not over-
estimate Ps0/Pr0. Then we find from (10) that we should use a value of
m equal to 25 in the neighborhood of 30,000. If we used this value of m
in a classical formula we would get P30/P50 = 6.2. If we used instead a
value of 31 for m (which seems to be at least high enough for 50,000) we
would get P30/Ps0 = 1.3. Actually it will be between these values. As
P80/P1o will also be greater than 1, it is seen that there is considerably more
chance that the molecules should have about equal, rather than widely
different energies, and as the molecule we originally considered had some-
what more than the energy of the average reacting molecule at that pres-
sure, it would seem that the effect may be neglected, although the treat-
ment cannot be made so satisfactory8 as in the classical case.6b The error
caused is in the opposite direction to that caused by using a constant
value of m in (6) for the evaluation of (1).
The question still remains as to whether other satisfactory interpreta-
tions of the decomposition of azomethane could be made. Of the various
hypotheses regarding activation in unimolecular reactions, the only one
which occurs to us as likely to offer a possible alternative hypothesis is the
chain reaction of Christiansen and Kramers. This is a possibility in the
case of azomethane, since the decomposition is undoubtedly strongly
exothermic. It is hard to see how to construct a theory to take this into
account, but it must produce some disturbance. However, if some kind
of chain is an important means of activation at low pressures, and unless
the mechanism of transfer of energy is very specific, we would expect the
reaction rate to fall off during the course of a run as the reaction products
accumulate, but actually this takes place to only a very slight extent.
Certain photochemical considerations also indicate indirectly that a chain
reaction does not play a very important part in the thermal case.9
At present the evidence seems strongly in favor of the view that in the
decomposition of azomethane activation is by collision, and that the
chance of reaction of an activated molecule depends upon the energy in
about the way that one would expect if reaction is due to the energy be-
coming localized in a particular place in the molecule.
The writer wishes to acknowledge the collaboration of Dr. H. C. Rams-
123VOL. 14, 1928
CHEMISTRY: BA TES AND ANDREWS
perger of Stanford University in the calculations for the classical case, and
in the discussion applicable to that case.
1 NATIONAL REsZARCH FZLLow.
2 Rice, these PROC13EDINGS, 14, 113 (1928). A joint paper treating this case will soon
appear.6b
I Landolt, Bornstein, Tabellen, 1923, p. 1275.
4See, e.g., Reiche, Quantum Theory, E. P. Dutton & Co., New York, p. 31. Zero point
energy does not concern us.
Ramsperger, J. Amer. Chem. Soc., 49, 1495 (1927).
6 (a) Rice and Ramsperger, J. Amer. Chem. Soc., 49, 1617 (1927); (b) Ibid. (in press).
7We are using P's in this place instead of W's in order to avoid confusion.
8 In later work it has been made more satisfactory. This calculation and the similar
one made for the classical case (Ref. 6b) represent extreme differences in the assump-
tions as to the nature of the molecule, so it seems very probable that equation (1)
needs no sensible modification.
9 Ramsperger, J. Amer. Chem. Soc., 50, 131 (1928); Proc. Nat. Acad. Sci., 13,849 (1927).
FUNDAMENTAL FREQUENCIES, INTERATOMIC FORCES AND
MOLECULAR PROPERTIES
BY JOHN R. BATI3S1 AND DONALD H. ANDREWS
DEPARTMENT OF CHZMISTRY, JOHNS HOPKINS UNIVJ3RSITY
Communicated January 10, 1928
During the past three or four years the study of the spectra of molecules
has brought to light a large number of facts which have to do with the
properties of the individual molecules as contrasted with the facts of
chemistry which pertain to the properties of atoms and molecules in the
aggregate. Of these specifically molecular properties, one of the most
significant is the fundamental frequency, that is, the frequency of the vi-
bration of an atom in the molecule when it moves with an amplitude
which is small compared to its own dimensions. For this frequency there
are now available quite accurate values covering a number of compounds.
with the help of these values, we wish to point out some relations between
the frequency and the force of binding on the one hand, and such macro-
chemical properties as heats of linkage, boiling points and directive in-
fluence on substitution.
In several fields different investigators have already met with consider-
able success in interpreting chemical behavior and physical properties
with the help of the recently acquired knowledge of the behavior of in-
dividual atoms. Franck2 has related the possibility of the photochemical
decomposition of a molecule into atoms with the changes in binding and
vibrational frequency which accompany electronic excitation. He and
124 PROC. N. A. S.


The Theory of the Decomposition of Azomethane

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