Unimolecular decomposition rate constants

Further developments in the use of kinetic chemical activation for energy transfer studies will undoubtedly be based on more detailed attention to the energy dependence of the transition probabilities and more accurately defined initial product excitation functions. Each extension wall require that the unimolecular decomposition rate constant be calculated or measured as a function of energy. In cases where adequate... 

Figure 9. Unimolecular decomposition rate constants ky for Mn(CO)x as a function of ion internal energy above threshold, Ef, calculated using RRKM theory employing Whitten-Rabinovitch state counting and bond energies listed in Table II, with log A = 15.

From these relationships, unimolecular decomposition rate constants can be calculated from termolecular reaction rate constants and equilibrium cmistants (see Table 5.3). 

Since the unimolecular decomposition rate constants for the secondary alkoxy radicals with > 4 carbons, are 10" s (Atkinson and Arey 2003), the reactions of the types (7.23), (7.24) and (7.25) can occur in parallel to give hydroxyl aldehyde, aldehyde with the same carbon number as the reactant alkanes, and aldehydes with one carbon less than the original alkane, respectively. The rate constants of for the isomerization reaction, reaction with O2, and the unimolecular... 

The decomposition is homogeneous and probably unimolecular, with rate constants given by... 

Derive an expression for the decomposition rate constant kd (e ) for the Hinshelwood theory of unimolecular reactions. 

Reaction (6-6) is a unimolecular decomposition, as written, soka will be a first-order rate constant. The magnitude of this decomposition rate constant is usually of the order of 10 -10" sec at the temperatures at which such initiators are used. 

When initiators are decomposed thermally, the rates of initiator disappearance ( d) show marked temperature dependence. Since most conventional polymerization processes require that should lie in the range 10 -10 s (half-life ca 10 h), individual initiators typically have acceptable only within a relatively narrow temperature range ca 20-30 °C). For this reason initiators are often categorized purely according to their half-life at a given temperature or vice versa For initiators which undergo unimolecular decomposition, the half-life is related to the decomposition rate constant by eq. II. 

Anharmonic corrections have also been determined for unimolecular rate constants using classical mechanics. In a classical trajectory (Bunker, 1962, 1964) or a classical Monte Carlo simulation (Nyman et al., 1990 Schranz et al., 1991) of the unimolecular decomposition of a microcanonical ensemble of states for an energized molecule, the initial decomposition rate constant is that of RRKM theory, regardless of the molecule s intramolecular dynamics (Bunker, 1962 Bunker, 1964). This is because a... 

These are the reverse of unimolecular decomposition reactions. The decomposition reaction can be analyzed by the means discussed above, and then the rate constant for the association reaction can be obtained using the equilibrium constant. When doing this, it is important to check that the rate of the association reaction does not substantially exceed the gas-kinetic collision rate. If it does, then there is probably a problem with the decomposition rate constant, the equilibrium constant, or both. 

Is best used for representing the pressure dependence of the termolecular reaction rate constant. This equation is based on the curve fitting to the pressure dependence of the unimolecular decomposition rate by the Kassel theory. In Eq. (2.54), is called a broadening factor, and it is a good experimental fitting for many termolecular reactions in atmospheric chemistry has been obtained by taking e.g. Fp = 0.6. The curve (b) in Fig. 2.9 shows the schematic pressure dependence... 

The direct meastirements of the rate constants of the reaction of hydroxymethyl cyclohexadienyl radical with O2 has been made using the UV absorption method (Sect. 5.2.10), and the values of 2.5 x 10 cm molecule for benzene (Bohn and Zetzsch 1999 Grebenkin and Krasnoperov 2004 Raoult et al. 2004 Nehr et al. 2011), 6.0 x 10 cm molecule s for toluene (Knispel et al. 1990 Bohn 2001) are reported. Therefore, most hydroxymethyl cyclohexadienyl radicals are thought to react solely with O2. Also, the unimolecular decomposition rate of cyclohexadienyl radical from benzene back to CgHg + OH has been reported as (3.9 1.3) s at 298 K (Nehr et al. 2011). 

Influence of OH concentration on the reaction rate constant. From the dependence of the observed first order rate constant on the sodium hydroxide concentration, shown in Table 3, it can be established that equation (2) holds, where ko represents the contribution due to the unimolecular decomposition process and koH is the contribution due to the base-catalysed process in alkaline medium. 

The first step in Mechanism I is the unimolecular decomposition of NO2. Our molecular analysis shows that the rate of a unimolecular reaction is constant on a per molecule basis. Thus, if the concentration of NO2 is doubled, twice as many molecules decompose in any given time. In quantitative terms, if NO2 decomposes by Mechanism I, the rate law will be Predicted rate (Mechanism I) = [N02 ] Once an NO2 molecule decomposes, the O atom that results from decomposition very quickly reacts with another NO2 molecule. 

As the system pressure is decreased at constant temperature, the time between collisions will increase, thereby providing greater opportunity for unimolecular decomposition to occur. Consequently, one expects the reaction rate expression to shift from first-order to second-order at low pressures. Experimental observations of this transition and other evidence support Linde-mann s theory. It provides a satisfactory qualitative interpretation of unimolecular reactions, but it is not completely satisfactory from a... 

In addition to this reaction, many other reactions of hydroperoxide decay occur in solution and they will be discussed later. This is the reason why the unimolecular decomposition of hydroperoxides was studied preferentially in the gas phase. The rate constants of the unimolecular decomposition of some hydroperoxides in the gas phase and in solution are presented in Table 4.11. The decay of 1,1-dimethylethyl hydroperoxide in solution occurs more rapidly. This demonstrates the interaction of ROOH with the solvent. 

Rate Constants of the Unimolecular Decomposition of Hydroperoxides and Peracids... 

Upon addition of a solution of sulfuric acid in D20 the reaction of A-acetoxy-A-alkoxyamides obeys pseudo-unimolecular kinetics consistent with a rapid reversible protonation of the substrate followed by a slow decomposition to acetic acid and products according to Scheme 5. Here k is the unimolecular or pseudo unimolecular rate constant and K the pre-equilibrium constant for protonation of 25c. Since under these conditions water (D20) was in a relatively small excess compared with dilute aqueous solutions, the rate expression could be represented by the following equation ... 

Dependent Rate Constants of Multichannel Unimolecular Decomposition of Gas-phase a-HMX An Ab Initio Dynamics Study. 

For a temperature of 1000 K, calculate the pre-exponential factor in the specific reaction rate constant for (a) any simple bimolecular reaction and (b) any simple unimolecular decomposition reaction following transition state theory. 

The reported decomposition of ammonium nitrate indicates that the reaction is unimolecular and that the rate constant has an A factor of 1013 8 and an activation energy of 170kJ/mol. Using this information, determine the critical storage radius at 160°C. Report the calculation so that a plot of rcrit versus T0 can be obtained. Take a temperature range from 80°C to 320°C. 

Oae (251,252) as well as Darwish and Datta (253) investigated the process of thermal racemization of chiral alkylarylsulfimides and diarylsulfimides. It was found to proceed at temperatures as low as 65 to 100°C with a rate constant of the order 1 to 10 X 10" sec" , which corresponds to an activation energy of about 23 to 30 kcal/mol. These data indicate that the thermal racemization of sulfimides is much faster than that of analogous sulfoxide systems. The racemization of sulfimides is a unimolecular reaction practically independent of the polarity of the solvent this property, coupled with the absence of decomposition products, supports the view that racemization of sulfimides occurs by pyramidal inversion. 

The thermal unimolecular decomposition of ethoxy radicals (C2H5O ) was investigated at different temperatures and pressures. Under these conditions the fi-C—C scission CH3CH2O -f M CH2O - - CH3 - - M is the dominant decomposition channel. Excellent agreement between the experimental and calculated rate constants has been found. ... 

Since both of these reactions proceed through similar transition states, their rate constants have similar pre-exponential factors, and the AH, corresponds to activation energies. Consequently, at process temperatures, i.e., T X 1000°C or less, the ratio of the rate coefficient of reaction (20) to that of (21) will be the order 10 or more. Therefore, C-Cl bond scission, i.e., reaction (20), will always dominate the unimolecular decomposition of CH3CI. 

At high temperatures and low pressures, the unimolecular reactions of interest may not be at their high-pressure limits, and observed rates may become influenced by rates of energy transfer. Under these conditions, the rate constant for unimolecular decomposition becomes pressure- (density)-dependent, and the canonical transition state theory would no longer be applicable. We shall discuss energy transfer limitations in detail later. 

Following the determination of the geometry and the thermochemistry of transition states, the rate parameters for the two silane decomposition pathways can be obtained directly by the TST formulation presented earlier. These calculations have led to unimolecular rate constant expressions 10 exp(-91000/RT)s-S and 10 exp(-62000/l r)s" for Si-H bond scission and H2 elimination reactions, respectively. These results clearly... 

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