Kinetics and mechanisms of the thermal decomposition of propane I. The Uninhibited of reaction

1962 ◽  
Vol 270 (1341) ◽  
pp. 242-253 ◽  
Keyword(s):  
Radical Mechanism ◽  
Methyl Radicals ◽  
Methyl Radical ◽  
Third Body ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Free Radical Mechanism ◽  
Pressure Region ◽  
Initiation Reaction

The uninhibited pyrolysis of propane was investigated from 530 to 670 °C and at pressures up to 600 mm. In an unpacked vessel the reaction was of the first order at lower temperatures and higher pressures. A transition to 3/2 order at higher temperatures and lower pressures was observed. The rates were somewhat reduced in a packed vessel, and an apparent order of 1.25 was obtained. The activation energy of the reaction in its first-order region was 67.1 kcal and that of the f-order reaction was 54.5 kcal. Added carbon dioxide had no effect on the rates either in the first-order or 3/2-order region. On the basis of this evidence, and of theoretical arguments, it is concluded that the reaction is largely homogeneous and occurs by a free-radical mechanism. The initiation reaction is considered to be the dissociation of propane into a methyl radical and an ethyl radical, this reaction being in its second-order low-pressure region under the conditions of the experiments. The termination reaction when the overall order is unity is concluded to be the recombination of a methyl and a propyl radical in the presence of a third body. In the 3/2-order region the termination reaction is believed to be the recombination of two methyl radicals, also in the third-order region. These mechanisms are shown to give a satisfactory interpretation of the overall behaviour.

Studies in energy transfer I. The combination of iodine atoms

1953 ◽  
Vol 217 (1129) ◽  
pp. 271-279 ◽  
Keyword(s):  
Energy Transfer ◽  
Intermolecular Force ◽  
Third Body ◽  
Reaction Cell ◽  
Critical Temperatures ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Boiling Points ◽  
Factors Influencing

An experimental study has been made of the velocity of combination of iodine atoms in the presence of a number of added gases in order to investigate the factors influencing energy transfer. The reaction cell, containing iodine at a pressure of 0.097 mm Hg and a known pressure of third body, is irradiated with a flash from a discharge tube. The concentration of iodine atoms as recombination proceeds is determined by measuring the light absorption of the system with a photomultiplier tube. The reaction is second order with respect to the concentration of iodine atoms, and first order with respect to the third body. The third-order rate constants vary from 0.97 x 10 -32 mol. -2 cm 6 s -1 when helium is added to 224 x 10 -32 mol -2 cm 6 s -1 for mesitylene. The velocity of combination at 127° C has been found to be approximately 0.4 time the velocity at 20° C for six different additives. This factor seems to be independent of the nature of the additive. The efficiencies of the different additives is primarily determined by the magnitudes of their intermolecular force fields, which are reflected in their boiling-points and critical temperatures.

Intertextual Precision Expectations

2019 ◽  
pp. 107-116
Author(s):  
Karin Kukkonen
Keyword(s):  
Third Order ◽  
Structural Patterns ◽  
First Order ◽  
The Third ◽  
Order Probability

In the chapters that follow, the third-order probability design is developed. The third-order probability design revolves around how expectations about second- and first-order predictions are developed through structural patterns yielded by genre (III.1), textual gaps and shadow stories (III.2), and intertextual references to unfamiliar texts (III.3). The final chapter of the section, then, traces the tension between flexibility and constraint in probability designs.

scholarly journals Achieving Seventh-Order Amplitude Accuracy in Leapfrog Integrations

2013 ◽  
Vol 141 (9) ◽  
pp. 3037-3051 ◽  
Author(s):  
Paul D. Williams
Keyword(s):  
Nonlinear System ◽  
Third Order ◽  
First Order ◽  
Time Stepping ◽  
The Third ◽  
Numerical Integrations ◽  
Seventh Order ◽  
Ocean Models ◽  
Stability And Accuracy ◽  
Fifth Order

Abstract The leapfrog time-stepping scheme makes no amplitude errors when integrating linear oscillations. Unfortunately, the Robert–Asselin filter, which is used to damp the computational mode, introduces first-order amplitude errors. The Robert–Asselin–Williams (RAW) filter, which was recently proposed as an improvement, eliminates the first-order amplitude errors and yields third-order amplitude accuracy. However, it has not previously been shown how to further improve the accuracy by eliminating the third- and higher-order amplitude errors. Here, it is shown that leapfrogging over a suitably weighted blend of the filtered and unfiltered tendencies eliminates the third-order amplitude errors and yields fifth-order amplitude accuracy. It is further shown that the use of a more discriminating (1, −4, 6, −4, 1) filter instead of a (1, −2, 1) filter eliminates the fifth-order amplitude errors and yields seventh-order amplitude accuracy. Other related schemes are obtained by varying the values of the filter parameters, and it is found that several combinations offer an appealing compromise of stability and accuracy. The proposed new schemes are tested in numerical integrations of a simple nonlinear system. They appear to be attractive alternatives to the filtered leapfrog schemes currently used in many atmosphere and ocean models.

THE PHOTOOXIDATION OF AZOMETHANE. III

1959 ◽  
Vol 37 (9) ◽  
pp. 1546-1560 ◽  
Author(s):  
F. Wenger ◽  
K. O. Kutschke
Keyword(s):  
Carbon Balance ◽  
Bimolecular Reaction ◽  
Major Product ◽  
Performic Acid ◽  
Peroxy Radicals ◽  
Methyl Radicals ◽  
Third Order ◽  
Vibrationally Excited ◽  
The Third ◽  
High Oxygen Pressure

It is confirmed that the yields of all products in the photooxidation of azomethane at relatively high oxygen pressure depend on conversion in a manner which would be explained if a reactive hydrogen donor were produced in the early stages of the reaction. Evidence is presented which indicates that formaldehyde cannot be active as an inhibitor in the system at 162 °C. It is suggested that methyl radicals react with oxygen in two ways. The third order formation of methyl peroxy radicals leads to methoxy radicals and, eventually, to methanol, while the bimolecular reaction between methyl radicals and oxygen leads to a vibrationally excited state of formaldehyde. The latter is thought to undergo oxidization to performic acid, which acts as the inhibitor in the system. Yields of formaldehyde, of nitrogen in excess of that formed in the primary process, and of nitrous oxide are linearly related regardless of the conversion up to about 4%. Methanol is a major product of the oxidation and, if account is taken of its yield, a carbon balance of the order of 90% is obtained.

scholarly journals The free radical polymerization of the vapours of certain vinyl derivatives

1946 ◽  
Vol 187 (1008) ◽  
pp. 37-53 ◽  
Keyword(s):  
Free Radical ◽  
Radical Polymerization ◽  
Vinyl Chloride ◽  
Free Radical Polymerization ◽  
Radical Mechanism ◽  
Methyl Radicals ◽  
Kinetic Methods ◽  
Free Radical Mechanism ◽  
Vinyl Derivatives ◽  
Styrene Butadiene

The free radical polymerization of the vapours of vinyl chloride, acrylic nitrile, styrene, butadiene and methyl isopropenyl ketone has been investigated using methyl radicals from photo-decomposing acetone. Although all the reactions do not exhibit ideal behaviour it is possible by the application of kinetic methods to measure the ratio of the propagation to the termination coefficients for these polymerization reactions. In this way relative values of the quantitative tendency for a molecule to polymerize by a free radical mechanism can be computed.

scholarly journals Positive Solutions for Third-Order Boundary-Value Problems with the Integral Boundary Conditions and Dependence on the First-Order Derivatives

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yanping Guo ◽  
Fei Yang
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Third Order ◽  
Integral Boundary ◽  
First Order ◽  
The Third ◽  
Nonnegative Continuous Function

By using a fixed point theorem in a cone and the nonlocal third-order BVP's Green function, the existence of at least one positive solution for the third-order boundary-value problem with the integral boundary conditionsx′′′(t)+f(t,x(t),x′(t))=0,t∈J,x(0)=0,x′′(0)=0, andx(1)=∫01g(t)x(t)dtis considered, wherefis a nonnegative continuous function,J=[0,1], andg∈L[0,1].The emphasis here is thatfdepends on the first-order derivatives.

scholarly journals MODIFIED WAVE EQUATION FOR SPINLESS PARTICLES AND ITS SOLUTIONS IN AN EXTERNAL MAGNETIC FIELD

2013 ◽  
Vol 28 (06) ◽  
pp. 1350014 ◽  
Author(s):  
S. I. KRUGLOV
Keyword(s):  
Magnetic Field ◽  
Wave Equation ◽  
External Magnetic Field ◽  
Quantum Mechanical ◽  
Third Order ◽  
Modified Dispersion Relation ◽  
First Order ◽  
The Third ◽  
Uniform External Magnetic Field ◽  
Schrödinger Form

The wave equation for spinless particles with the Lorentz violating term is considered. We formulate the third-order in derivatives wave equation leading to the modified dispersion relation. The first-order formalism is considered and the density matrix is obtained. The Schrödinger form of equations is presented and the quantum-mechanical Hamiltonian is found. Exact solutions of the wave equation are obtained for particles in the constant and uniform external magnetic field. The change of the synchrotron radiation radius due to quantum gravity corrections is calculated.

Perturbation treatment of the Hartree–Fock equations for the ground states of the boron-like ions

1969 ◽  
Vol 47 (7) ◽  
pp. 699-705 ◽  
Author(s):  
C. S. Sharma ◽  
R. G. Wilson
Keyword(s):  
Ground State ◽  
Atomic System ◽  
Ground States ◽  
Great Accuracy ◽  
Second Order ◽  
Expectation Values ◽  
Third Order ◽  
First Order ◽  
Hartree Fock ◽  
The Third

The first-order Hartree–Fock and unrestricted Hartree–Fock equations for the ground state of a five electron atomic system are solved exactly. The solutions are used to evaluate the corresponding second-order energies exactly and the third-order energies with great accuracy. The first-order terms in the expectation values of 1/r, r, r2, and δ(r) are also calculated.

scholarly journals Solitons, Rogues and Interaction Behaviors of Third-Order Nonlinear Schrodinger Equation

2022 ◽  
Author(s):  
Ren Bo ◽  
Shi Kai-Zhong ◽  
Shou-Feng Shen ◽  
Wang Guo-Fang ◽  
Peng Jun-Da ◽  
...  
Keyword(s):  
Bilinear Form ◽  
Rogue Wave ◽  
Soliton Solutions ◽  
Ultrashort Pulses ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Femtosecond Regime ◽  
Wave Limit

Abstract In this paper, we investigate the third-order nonlinear Schr\"{o}dinger equation which is used to describe the propagation of ultrashort pulses in the subpicosecond or femtosecond regime. Based on the independent transformation, the bilinear form of the third-order NLSE is constructed. The multiple soliton solutions are constructed by solving the bilinear form. The multi-order rogue waves and interaction between one-soliton and first-order rogue wave are obtained by the long wave limit in multi-solitons. The dynamics of the first-order rogue wave, second-order rogue wave and interaction between one-soliton and first-order rogue wave are presented by selecting the appropriate parameters. In particular parameters, the positions and the maximum of amplitude of rogue wave can be confirmed by the detail calculations.PACS numbers: 02.30.Ik, 05.45.Yv.

scholarly journals Influence on The Level Riders Motorcycle Accident Traffic with Traffic Methods of Conflict Technique (TCT) (Case Study: Jalan Raya Narogong Bekasi City)

2020 ◽  
Vol 2 (2) ◽  
pp. 184-189
Author(s):  
Andri Irfan Rifai ◽  
Finsa Aziz Fernanda
Keyword(s):  
Traffic Accidents ◽  
Observation Data ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Motorcycle Accident ◽  
Transportation Sector ◽  
Side Collision ◽  
Traffic Rules

The increasing number of traffic accidents can be caused by drivers, vehicles, highways, and the environment. In Indonesia, traffic accidents become one of the problems in the transportation sector. Prevention is done during this time to anticipate accidents only based on the data of the accident quantity that has occurred. Though factors or incidents that can cause accidents to become the biggest contributor in the event of accidents. For example, driving a vehicle in an unorderly manner, the pace of the vehicle with the above-average velocity set traffic rules, and sudden vehicle maneuvers. This research is done by identifying and analyzing the behavior of motorcyclists who affect accidents and applying TCT methods to observation data at points that become potential locations Against accidents. The research location is on the Narogong Highway which is divided into 2 segments. In Segment 1 begins at junction four Cipendawa (after the flyover Simpang Cipendawa) until the junction of the three Gg. Sawo (Bantar Gebang Market). Next, in Segment 2 starts from junction three of Gg. Sawo (Bantar Gebang Market) until the three houses of Vida housing. The results showed that the research location had potential that could cause the accident to be front-side on the first order, collision front-front on the second-order, and side-by-side collision on the third order. The speed of vehicles has an impact on accidents.

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