Unimolecular decomposition theory

The theory of isolated resonances is well understood and is discussed below. Mies and Krauss [79, ] and Rice [ ] were pioneers m treating unimolecular rate theory in temis of the decomposition of isolated Feshbach resonances. 

Mies F H 1969 Resonant scattering theory of association reactions and unimolecular decomposition. Comparison of the collision theory and the absolute rate theory J. Cham. Phys. 51 798-807... 

Miller W H, Hernandez R, Moore C B and Polik W F A 1990 Transition state theory-based statistical distribution of unimolecular decay rates with application to unimolecular decomposition of formaldehyde J. Chem. Phys. 93 5657-66... 

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... 

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 quasi-equilibrium theory (QET) of mass spectra is a theoretical approach to describe the unimolecular decompositions of ions and hence their mass spectra. [12-14,14] QET has been developed as an adaptation of Rice-Ramsperger-Marcus-Kassel (RRKM) theory to fit the conditions of mass spectrometry and it represents a landmark in the theory of mass spectra. [11] In the mass spectrometer almost all processes occur under high vacuum conditions, i.e., in the highly diluted gas phase, and one has to become aware of the differences to chemical reactions in the condensed phase as they are usually carried out in the laboratory. [15,16] Consequently, bimolecular reactions are rare and the chemistry in a mass spectrometer is rather the chemistry of isolated ions in the gas phase. Isolated ions are not in thermal equilibrium with their surroundings as assumed by RRKM theory. Instead, to be isolated in the gas phase means for an ion that it may only internally redistribute energy and that it may only undergo unimolecular reactions such as isomerization or dissociation. This is why the theory of unimolecular reactions plays an important role in mass spectrometry. 

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. 

Both unimolecular and bimolecular reactions are common throughout chemistry and biochemistry. Binding of a hormone to a reactor is a bimolecular process as is a substrate binding to an enzyme. Radioactive decay is often used as an example of a unimolecular reaction. However, this is a nuclear reaction rather than a chemical reaction. Examples of chemical unimolecular reactions would include isomerizations, decompositions, and dis-associations. See also Chemical Kinetics Elementary Reaction Unimolecular Bimolecular Transition-State Theory Elementary Reaction... 

In the area of reaction energetics. Baker, Muir, and Andzehn have compared six levels of theory for the enthalpies of forward activation and reaction for 12 organic reactions the unimolecular rearrangements vinyl alcohol -> acetaldehyde, cyclobutene -> s-trans butadiene, s-cis butadiene s-trans butadiene, and cyclopropyl radical allyl radical the unimolecular decompositions tetrazine -> 2HCN -F N2 and trifluoromethanol -> carbonyl difluoride -F HF the bimolecular condensation reactions butadiene -F ethylene -> cyclohexene (the Diels-Alder reaction), methyl radical -F ethylene -> propyl radical, and methyl radical -F formaldehyde -> ethoxyl radical and the bimolecular exchange reactions FO -F H2 FOH -F H, HO -F H2 H2O -F H, and H -F acetylene H2 -F HC2. Their results are summarized in Table 8.3 (Reaction Set 1). One feature noted by these authors is... 

Under ordinary mass spcctrometric conditions only unimolecular reactions of excited ions occur, but at higher ionization chamber pressures bimolecular ion molecule reactions are observed in which both the parent ions and their unimolecular dissociation product ions are reactants. Since it requires a time of 10 5 sec. to analyze and collect the ions after their formation all of the ions in the complete mass spectrum of the parent molecule are possible reactants. However, in radiation chemistry we are concerned with the ion distribution at the time between molecular collisions which is much shorter than 10 5 sec. For example, in the gas phase at 1 atm. the time between collisions is 10 10 sec. and in considering the ion molecule reactions that can occur one must know the amount of unimolecular decomposition within that time. By utilizing the quasi-equilibrium theory of mass spectra6 it is possible to calculate the ion distribution at any time. This has been done for propane at a time of 10 10 sec.,24 and although the parent ion is increased by a factor of 2 the relative ratios of the other ions are about the same as in the mass spectrum observed in 10 r> sec. Thus for gas phase radiolysis the observed mass spectrum is a fair first approximation to the ion distribution. In... 

The slow combustion reactions of acetone, methyl ethyl ketone, and diethyl ketone possess most of the features of hydrocarbon oxidation, but their mechanisms are simpler since the confusing effects of olefin formation are unimportant. Specifically, the low temperature combustion of acetone is simpler than that of propane, and the intermediate responsible for degenerate chain branching is methyl hydroperoxide. The Arrhenius parameters for its unimolecular decomposition can be derived by the theory previously developed by Knox. Analytical studies of the slow combustion of methyl ethyl ketone and diethyl ketone show many similarities to that of acetone. The reactions of methyl radicals with oxygen are considered in relation to their thermochemistry. Competition between them provides a simple explanation of the negative temperature coefficient and of cool flames. 

The reaction scheme in the QRRK theory for unimolecular decomposition can be written... 

As an example calculation using QRRK theory, we consider the unimolecular decomposition of azomethane, CH3N2CH3, from Kassel s original paper [207], Kassel tested... 

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

At the present time a number of gaseous unimolecular reactions are known. The view that none exist, although it appeared plausible for a time, has now been definitely abandoned. Nevertheless, unimolecular reactions are rather exceptional and appear to be confined to molecules of rather complex structure. It is possible that the decomposition of diatomic molecules into atoms at high temperatures is unimolecular but more probable that it is bimolecular, the reverse reaction of recombination being termolecular. Thus the rate of dissociation of chlorine would be k1 [Cl2]2 while the rate of recombination of the atoms would be 2 [Cl]2 [Clg], according to the Herzfeld theory (p. 111). 

This reaction also involves the elimination of carbon monoxide and the formation of a mixture of hydrocarbons, principally ethane and methane. It is homogeneous and conveniently measurable between 450° and 600° C. The decomposition is kinetically unimolecular over a considerable range of pressure, but at pressures below about 80 mm. Hg the velocity constant falls appreciably, in the manner which would be expected if Lindemann s theory were correct. In the region of pressure where the reaction is unimolecular the velocity constants (sec-1) are given by... 

The observation of Burk has already been mentioned, namely, that the rate of decomposition of ammonia on molybdenum, although reduced by the presence of nitrogen, does not approach zero as the surface becomes saturated with nitrogen. This is easily interpreted in terms of the theory of centres of different activity but there is also the possibility that the nitrogen film itself has some catalytic activity. The possibility that unimolecular gas films on surfaces may themselves be the catalysts in certain reactions should not be ignored, and in many examples would provide an alternative to the hypothesis of nonuniformity of the surface. But the cumulative evidence for this latter assumption is very strong. 

Fig. 9. Log-log plot of the homogeneous unimolecular rate constant vs. pressure in the decomposition of C2F40 at 126°C. The solid lines represent theoretical curves from Kassel theory with 8 and 9 effective oscillators. From Lenzi and Mele106 with permission of the American Institute of Physics.

Statistical theories treat the decomposition of the reaction complex of ion-molecule interactions in an analogous manner to that employed for unimolecular decomposition reactions.466 One approach is that taken by the quasiequilibrium theory (QET).467 Its basic assumptions are (1) the rate of dissociation of the ion is slow relative to the rate of redistribution of energy among the internal degrees of freedom, both electronic and vibrational, of the ion and (2) each dissociation process may be described as a motion along a reaction coordinate separable from all other internal... 

Density functional theory was used to show that unimolecular formation of CO2 and dihydroxycarbene from oxalic acid has a barrier of 31 kcal mol-1.33 The barrier for H-migration in dihydroxycarbene to fonn fonnic acid was shown to be less than 37 kcal mol-1 if an exchange with oxalic acid was involved (23). QRRK analysis of the pyrolytic decomposition of 2-chloro-l,l,l,2-tetrafluoroethane (F3CCFCIH) indicated that the primary route is a-climination of HC1 to form singlet F3CFC .34... 

The mechanism of unimolecular decomposition can be described semi-quali-tatively by the simple theory of Kassel156 which is adequate for this brief review. Molecules exchange energy in bimolecular collisions, and if a molecule acquires... 

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