Analytic solution of relaxation and dissociation of ozone and sulphur dioxide at low pressures

1981 ◽  
Vol 59 (17) ◽  
pp. 2569-2574 ◽  
Author(s):  
Wendell Forst
Keyword(s):  
Rate Constants ◽  
Sulphur Dioxide ◽  
Vibrational Relaxation ◽  
Analytic Solution ◽  
Thermal Dissociation ◽  
Relaxation Times ◽  
Average Energy ◽  
Collision Rate ◽  
Low Pressures ◽  
Good Agreement

The analytic solution of vibrational relaxation in a low-pressure gas is applied to the thermal dissociation of O3 in helium and of SO2 in argon. Use is made of experimental relaxation times to obtain average energy lost per collision. Calculated weak-collision rate constants are in very good agreement with experiment in the case of SO2, but only in fair agreement in the case of ozone. Several curious aspects of the ozone system, both experimental and theoretical, are discussed.

Theory of vibrational relaxation in mixtures of ortho- and para-hydrogen

1981 ◽  
Vol 59 (8) ◽  
pp. 1277-1283 ◽  
Author(s):  
Avygdor Moise ◽  
Huw O. Pritchard
Keyword(s):  
Rate Constants ◽  
Vibrational Relaxation ◽  
Numerical Study ◽  
Relaxation Times ◽  
High Dilutions ◽  
State Rate ◽  
The Mean ◽  
The Individual ◽  
Individual Rate ◽  
Very High

A numerical study of the vibrational relaxation at 500 K of a mixture of ortho-H2 and para-H2 is described. The required state-to-state rate constants were calculated from the quantum results of Rabitz and co-workers, and missing pieces of data were estimated by interpolation.It is concluded that only one relaxation time will be observed in any mixture of ortho-H2 and para-H2 and that (except at very high dilutions in a third inert gas) the relaxation rate constant will be close to the mean of the individual rate constants for relaxation, weighted according to the respective mole fractions of ortho-H2 and para-H2 present in the mixture.We find that the relaxation process can be modelled very accurately as an electrical RC network, whose time constants can be written down quite easily as sums of the appropriate microscopic rate constants, and by using this model, it is a simple matter to explore the conditions required for a mixture of two gases to exhibit two distinct vibrational relaxation times.

Temperature dependence of vibrational relaxation times in gases

1958 ◽  
Vol 244 (1237) ◽  
pp. 212-219 ◽  
Keyword(s):  
Energy Transfer ◽  
Methyl Bromide ◽  
Sulphur Dioxide ◽  
Vibrational Relaxation ◽  
Transition Probability ◽  
Relaxation Times ◽  
Methyl Chloride ◽  
Collision Theory ◽  
Ultrasonic Dispersion ◽  
Carbon Tetrafluoride

Ultrasonic dispersion measurements at varying temperatures, extending over the range 290 to 580° K, have been made on gaseous ethylene, cyclo propane, carbon tetrafluoride, methyl chloride and methyl bromide. The results are correlated with previous measurements on methyl fluoride and sulphur dioxide. The non-polar gases show a steady rise in the probability of energy transfer between translation and vibration with rise in temperature. The transition probability, P 10 , is found to vary with exp — T -½ in accordance with current collision theory, but the quantitative dependence cannot be predicted from molecular properties. The polar gases behave in a similar way at higher temperatures, but at lower temperatures the transition probability increases with falling temperature. This is interpreted as due to increasing predominance of oriented collisions, which are specially favourable for energy transfer, between polar molecules at lower temperatures.

Calculation of vibrational relaxation times in gaseous sulphur dioxide

1957 ◽  
Vol 243 (1232) ◽  
pp. 84-93 ◽  
Keyword(s):  
Specific Heat ◽  
Sulphur Dioxide ◽  
Vibrational Relaxation ◽  
Vibrational Excitation ◽  
Relaxation Times ◽  
Collision Theory ◽  
Relaxation Behaviour ◽  
Ultrasonic Dispersion ◽  
Higher Modes ◽  
Dispersion Data

Approximate vibrational relaxation times have been calculated for gaseous sulphur dioxide at 373°K using the collision theory of Schwartz & Herzfeld (1954). Two major effective relaxation times are found; the shorter associated with the relaxation of the specific heat contribution of the lowest mode and the longer with the relaxation of the total contributions of the two higher modes. The results are compared with the recent ultrasonic dispersion data of Lambert & Salter (1957), a measure of agreement being found. The mechanism of vibrational excitation in gaseous sulphur dioxide is discussed and compared with that in some similar molecules. Tentative predictions are made about the relaxation behaviour of a few selected molecules.

The influence of non-equilibrium transient effects on measurements of vibrational relaxation times and of dissociation rate constants

1982 ◽  
Vol 60 (23) ◽  
pp. 2927-2942 ◽  
Author(s):  
Heshel Teitelbaum
Keyword(s):  
Rate Constants ◽  
Vibrational Relaxation ◽  
Vibrational Energy ◽  
Relaxation Times ◽  
Dissociation Rate ◽  
Harmonic Oscillators ◽  
Dissociation Limit ◽  
Transient Effects ◽  
Rate Law ◽  
Non Equilibrium

A semi-empirical analysis based on a rate law for vibrational relaxation of dissociating simple harmonic oscillators allows for a detailed study of measurements of vibrational relaxation times τ and of steady dissociation rate coefficients k0. It is shown that non-equilibrium populations of vibrational energy levels prevent attainment of the thermodynamically expected equilibrium energy. Even under near-isothermal and mild conditions, [Formula: see text], serious experimental errors result when the Bethe–Teller relaxation rate law is used. Closed form expressions are given which permit evaluation of these errors. Measurements should be analyzed using the rate law[Formula: see text]where ε is the vibrational energy per molecule, τ the relaxation time, kd the non-equilibrium rate coefficient, ετ the thermodynamically expected vibrational energy at temperature T, and (ε* + hv) the energy just above the dissociation limit. It is also shown that if[Formula: see text]a local minimum and maximum are predicted for measured density gradients in shock tube dissociations of diatomic molecules, where tine is the incubation time, D′ the effective dissociation energy, and x0 the mole fraction of dissociating molecules in an inert diluent. Expressions are given for extracting incubation times and rate constants from such studies when [Formula: see text]. Analysis of experimental data actually showing such phenomena (J. Chem Phys. 55, 4017 (1971)) is carried out. There are indications that any analysis which does not explicitly account for transient effects could result in errors in measured k0's of factors of 2 or more.

Étude expérimentale et modélisation théorique de la décomposition du radical éthyle

1988 ◽  
Vol 66 (9) ◽  
pp. 2142-2150 ◽  
Author(s):  
Yves Simon ◽  
Jean François Foucaut ◽  
Gérard Scacchi
Keyword(s):  
Experimental Data ◽  
Rate Constants ◽  
Critical Analysis ◽  
Reaction Rate ◽  
Closed Vessel ◽  
Reaction Rate Constants ◽  
Theoretical Approaches ◽  
Lower Limits ◽  
Low Pressures ◽  
Good Agreement

A bibliographical study of the thermal decomposition of the ethyl radical shows that the kinetic parameters for the upper and lower limits of the pressure are rather scattered. This observation explains why we have carried out a new study of this elementary process in the pyrolysis of ethane, around 800 K, in a closed vessel and at pressures of the hydrocarbon varying from 1 to 300 Torr. The experimental results have been treated according to three theoretical approaches: the RRKM theory and two methods proposed by Troe. In each case, an excellent fit of the theoretical curves with the experimental data is obtained, as well as Arrhenius expressions for the reaction rate constants at high and low pressures. A detailed critical analysis of our results as well as those found in the literature shows that as yet there is no good agreement between recent studies on this subject. However, it is possible to present two Arrhenius expressions for the reaction rate constants at high and low pressures; these expressions represent a good compromise for the results obtained by various authors:[Formula: see text][Journal translation]

Computational Study on the Kinetics and Mechanisms of Unimolecular Reactions of (Z)-(Z)-N-(λ5-phosphanylidene) Formohydrazonic Formic Anhydride: Intramolecular aza-Wittig Reaction in Competition with Mumm Rearrangement

2020 ◽  
Vol 17 (11) ◽  
pp. 884-889
Author(s):  
Somayeh Mirdoraghi ◽  
Hamed Douroudgari ◽  
Farideh Piri ◽  
Morteza Vahedpour
Keyword(s):  
Rate Constants ◽  
Density Functional ◽  
Wittig Reaction ◽  
Computational Study ◽  
Single Step ◽  
Low Energy ◽  
Coupled Cluster ◽  
Unimolecular Reaction ◽  
Single Step Reaction ◽  
Good Agreement

For (Z)-(Z)-N-(λ5-phosphanylidene) formohydrazonic formic anhydride, Aza-Wittig reaction and Mumm rearrangement are studied using both density functional and coupled cluster theories. For this purpose, two different products starting from one substrate are considered that are competing with each other. The obtained products, P1 and P2, are thermodynamically favorable. The product of the aza-Wittig reaction, P1, is more stable than the product of Mumm rearrangement (P2). For the mentioned products, just one reliable pathway is separately proposed based on unimolecular reaction. Therefore, the rate constants based on RRKM theory in 300-600 K temperature range are calculated. Results show that the P1 generation pathway is a suitable path due to low energy barriers than the path P2. The first path has three steps with three transition states, TS1, TS2, and TS3. The P2 production path is a single-step reaction. In CCSD level, the computed barrier energies are 14.55, 2.196, and 10.67 kcal/mol for Aza-Wittig reaction and 42.41 kcal/mol for Mumm rearrangement in comparison with the corresponding complexes or reactants. For final products, the results of the computational study are in a good agreement with experimental predictions.

Singlet Methylene Removal Rate Constants from the (0,1,0) Vibrational Level: Enhancement via Complex-Mediated Vibrational Relaxation

2001 ◽  
Vol 215 (6) ◽  
Author(s):  
M.A. Buntine ◽  
G.J. Gutsche ◽  
W.S. Staker ◽  
M.W. Heaven ◽  
K.D. King ◽  
...  
Keyword(s):  
Vibrational Level ◽  
Rate Constants ◽  
Vibrational Relaxation ◽  
Flash Photolysis ◽  
Laser Flash Photolysis ◽  
Removal Rate ◽  
Laser Flash ◽  
Laser Absorption ◽  
Photolysis Laser ◽  
Singlet Methylene

The technique of laser flash photolysis/laser absorption has been used to obtain absolute removal rate constants for singlet methylene,

Vibrational Relaxation Times in Oxygen

1959 ◽  
Vol 30 (6) ◽  
pp. 1614-1615 ◽  
Author(s):  
Morris Salkoff ◽  
Ernest Bauer
Keyword(s):  
Vibrational Relaxation ◽  
Relaxation Times

Vibrational Relaxation Times in Nitrogen

1957 ◽  
Vol 27 (5) ◽  
pp. 1149-1155 ◽  
Author(s):  
S. J. Lukasik ◽  
J. E. Young
Keyword(s):  
Vibrational Relaxation ◽  
Relaxation Times
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