Mechanism of the Gas Phase, Thermal Decomposition of Ozone

For references to this early work, see

O. R.

Wulf

and

R. C.

Tolman

, , , ().

This atomic mechanism in which the oxygen atoms are at their equilibrium concentration has become known as the “Jahn mechanism.”

(a) Although Wulf and Tolman¹ are quite critical of their own results and do not claim to have proven the Jahn mechanism, there appears to be a popular misconception that their results did verify the rate law proposed by Jahn. That this is not the case may be seen by referring to Table XII of reference 1 and Table III of reference 1. The lack of reproducibility of their second‐order rate constants obtained with their “best” ozone is shown in Table V of reference 1. The earlier results of Jahn are similarly inconclusive in proving the Jahn mechanism.

(b)

D.

Garvin

, , ().

E. H.

Riesenfeld

and

W.

Bohnholtzer

, , ().

E. H.

Riesenfeld

and

H. J.

Schumaker

, , ().

E. H.

Riesenfeld

and

E.

Wassmuth

, , ().

H. J.

Schumaker

and

G.

Sprenger

, , ().

A.

Glissman

and

H. J.

Schumaker

, , ().

S. W.

Benson

and

A. E.

Axworthy

, Jr., , ().

H. J. Schumaker, Chemische Gasreaktion (Theodor Steinkopff Verlag, Dresden, Germany, 1938), p. 433.

K. H.

Geib

, , ().

Vessel I, $υ/s = 537/376 = 1.43 cm;$ Vessel II, $υ/s = 461/547 = 0.84 cm.$

This source of oxygen was abandoned for future experiments as it probably contains nitrogen which would lead to the formation of nitrogen oxides in the ozonizer.

At this point the danger of explosion is quite high (especially if sufficient ozone is present so that its initial concentration in the reaction vessel is much above 100 mm Hg). During the course of our investigation, we have encountered a total of eight explosions, three of which were quite damaging and none of which occurred at room temperature or below. One occurred upon immersing a 1‐liter vessel containing 250 mm of ozone in a liquid bath at 99 °C; four occurred during the evaporation of the ozone into the hot reaction vessel; and three occurred after this evaporation when large amounts of oxygen were bled into the reaction vessel. Approximately one hundred rapid distillations and evaporations have been made at room temperature and below without difficulty.

These second‐order rate constants were obtained by taking tangents at various points on a $1/(O3)$ vs time plot. All of the data of Glissman and Schumaker were plotted in this manner in order to obtain the most reliable rate constants their results would yield. Unfortunately, they allowed rather long time intervals to pass between readings and the accuracy of their results is greatly decreased because of this. Actually, a dead space correction should enter here also since the ozone is disappearing by two paths (reaction and flow into the dead space). The correction, however, is less than experimental error.

All 47 experiments of Glissman and Schumaker were plotted in this manner except Experiments 31, 37, and 94 which had numerical or typographical errors in the tabulated data.

Since our results at 99.8 °C without added inert gases agree well with the results of Glissman and Schumaker under the same conditions in terms of the proposed mechanism, it would appear that the large body of data presented by them is probably quite reliable. The values of the rate constants, activation energies, and a’s presented in this paper were obtained by the reinterpretation of the results of Glissman and Schumaker.

Natl. Bur. Standards Tables, Circular 500. Using the heat capacities given, the values have been corrected to the mean temperature of 90 °C to make the equilibrium constant fit the form of the Arrhenius equation in this region. For Reactions (1,2), $ΔH0 = 25.2 kcal/mole;$ $ΔE0 = 24.6 kcal = E1−E2.$

S. W.

Benson

, , ().

P.

Harteck

and

S.

Dondes

, , , ().

A similar effect has been observed by Allen and Rice in the decomposition of azomethane near the explosion limit [

A. O.

Allen

and

O. K.

Rice

, , ()].

The efficiency of oxygen compared with ozone per collision in activating ozone is about $aO2$ since the ratio of $O2−O3$ collisions to $O3−O3$ collisions in a mixture containing ozone and oxygen is twice the ratio of oxygen to ozone. $aO2 = k1(O2)/k1(O3) = βZO2/ZO3,$ where $ZO2$ and $ZO3$ are the collision frequencies of oxygen and ozone with ozone and β is the relative efficiency of oxygen compared with ozone per collision in Reaction (1). Kinetic theory gives $ZO3∼1/2ZO2$ (if we neglect the small differences in collision diameters). However, in a collision of two $O3$ molecules, there are twice as many chances of activation as in a collision $O2+O3,$ so $β∼1.$

The vessels used by Glissman and Schumaker had the following volume/surface ratios in cm: $I = 0.85,$ $II = 2.1,$ $III = 2.25,$ and $IV = 4.74.$

S. W.

Benson

, , (). Assuming deactivation at every collision, the method presented in this reference predicts that, at 200 mm total pressure, 1% of the activated ozone molecules formed would be deactivated before decomposing. As discussed later, ozone is deactivated by oxygen (for example) not at every collision but at one in 140. This method predicts, therefore, that ozone should be within 1% of its low‐pressure limit at a total pressure of 30 atmos.

Estimated from Natl. Bur. Standards data (reference 18) as the $ΔE00.$

(a)

T.

 

Carrington

and

N.

 

Davidson

,  , ();

(b)

H. S.

 

Johnston

,  , ();

(c)

H. F.

Cordes

and

H. S.

Johnston

, , ().,

K. E.

Russell

and

J.

Simon

, , ().

(a)

O. K.

 

Rice

,  , ();

(b)

Pritchard

,

Sowden

, and

Trotman‐Dickenson

,  , ();

(c)

Pritchard

,

Sowden

, and

Trotman‐Dickenson

, , ().,

Christie

,

Norrish

, and

Porter

,  , ().

See also

Christie

et al., , ().,

R.

Marshal

and

N.

Davidson

, , ().

Thus if we write the bimolecular rate constant in the collisional form, $sZ′P(e)$ (where $Z′$ is the familiar Collision frequency, s is the steric factor, and $P(e)$ is the Boltzman probability factor for having energy “e” distributed between the internal degrees of freedom and the relative kinetic energy along the line of centers of the colliding pair), then, although s may be of the order of $10−2$ (representing the probability that at least $e*$ of the energy wind up in the internal degrees of freedom of $O3$ after the collision), $P(e)$ has the form, $103 exp(e/RT)$ where the factor $103$ represents the probability increment arising from the number of different ways there are of having such a prescribed collision (i.e., an entropy term). The net result of these two compensating effects is to give an over‐all increase in the frequency factor above the apparent collision frequency. Such high‐frequency factors are quite common in energy transfer reactions and never occur (to our knowledge) in any other kind of bimolecular reaction. We believe that this arises from the fact that in the usual metathetical reaction like atom transfer, the requirements on energy localization are much more severe than in the energy transfer reaction where the energy may be distributed over many degrees of freedom of the activated molecule. Or, in other words, the large entropy increases usually accompany activation, not reaction.

i.e., $kb = ka/Keq(a,b) = A1 exp(−ΔS(a,b)/R)$ by setting $E1 = ΔE(a,b).$

The average energy of $O3*$ reacting does differ at the two limits, but, if we restrict our discussion to the equilibrium with $O3*$ having energies equal to the average energy of $O3*$ reacting at the low‐pressure limit, this will not affect our argument.

M. K.

Wilson

and

R. M.

Badger

, , ().

Use of the vibrational frequencies favored by Herzberg of 710, 1043, and $1740 cm−1,$ leads to an entropy of activation of 16.4 eu yielding a collisional deactivation efficiency of 1/330 [G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules (D. Van Nostrand Company, Inc., New York, 1945)].

The foregoing computation of the entropy of activation may be low since it does not include the contributions of anharmonicity or centrifugal distortion, both of which would tend to increase the internal entropy at the high average internal temperatures of the activated ozone complex. On the other hand, it is probably high by about $R ln(3250/363) = 4.4 eu$ because of the difference in average spread of energy states available in the flask vs the hypothetical 3250 °K.

The average lifetime of $O3*,$ τ, may be calculated by $τ = 1/k(c) = (Keq(c,d)k(d))−1.$ But $Keq(c,d) = Keq(1,2)/Keq(a,b) = exp[(ΔS1,2−ΔS(a,b))/R]$ on setting $ΔE(1,2) = ΔE(a,b).$ And if we set $k(d) = Z(d)$ (the collision frequency of $O+O2≈2×1011 liter/mole‐sec,$ then $τ⩾10−13 sec$ which seems very short and is probably much smaller than the real value. This arises from our neglect of the non‐equilibrium situation prevailing in the reaction which is producing “cold” (i.e., low entropy) $O2+O.$

The lowest lying known excited state, $Σu+3,$ lies at 103 kcal above the ground state and so is just barely too high for the energy balance. See G. Herzberg, Spectra of Diatomic Molecules (D. Van Nostrand Company, Inc., New York, 1950), second edition.

This seems quite reasonable if the excess energy is mainly translational since the bulk of present evidence points to the rather inefficient transfer between vibration and translation in collisions and for these processes transfer of more than one vibrational quantum at a time is not indicated.

The $O2−O2$ collision frequency is $12$ that of $I2−O2,$ but either $O2$ may be activated so that the net rate of activation should be about the same.

L. J.

Heidt

and

G. S.

Forbes

, , ().

L. J.

Heidt

, , ().

G.

Kistiakowsky

, , ().

H. J.

Schumaker

, , ().

O. K.

Rice

, , ().

C. E. Thorp, Bibliography of Ozone Technology (Armour Research Foundation, Chicago), Vol. 2, p. 30.

It may at first be considered unlikely that this is the case since the similar reaction $2 O3→3 O2$ probably has an activation energy in excess of 20 kcal. However, the two reactions are not precisely comparable because of the presence of H in $HO2$ and moreover Reaction (14) may take place via H transfer through a structure, “see pdf for the artwork” whereas the reaction of $2 O3$ can only take place via O atom transfer.

S. N.

Foner

and

R. L.

Hudson

, , (), have estimated the bond energy from appearance potential measurements of $HO2$ from $H2O2$ together with the ionization potentials of $HO2$ produced in electric discharges or thermally from $H+H2O2.$