Unimolecular reaction—gases

In the case of bunolecular gas-phase reactions, encounters are simply collisions between two molecules in the framework of the general collision theory of gas-phase reactions (section A3,4,5,2 ). For a random thennal distribution of positions and momenta in an ideal gas reaction, the probabilistic reasoning has an exact foundation. Flowever, as noted in the case of unimolecular reactions, in principle one must allow for deviations from this ideal behaviour and, thus, from the simple rate law, although in practice such deviations are rarely taken into account theoretically or established empirically. 

An important example for the application of general first-order kinetics in gas-phase reactions is the master equation treatment of the fall-off range of themial unimolecular reactions to describe non-equilibrium effects in the weak collision limit when activation and deactivation cross sections (equation (A3.4.125)) are to be retained in detail [ ]. 

Piiiing M J and Smith i W M (eds) 1987 Modern Gas Kinetics. Theory, Experiment and Application (Qxford Biackweii) Giibert R G and Smith S C (eds) 1990 Theory of Unimolecular and Recombination Reactions (Qxford Biackweii) Fioibrook K A, Piiiing M J and Robertson S Fi (eds) 1996 Unimolecular Reactions 2nd edn (Chichester Wiiey)... 

Troe J 1975 Unimolecular reactions experiments and theories Kinetics of Gas Reactions ed W dost (New York Academic) p 835... 

Collisional energy transfer in molecules is a field in itself and is of relevance for kinetic theory (chapter A3.1). gas phase kmetics (chapter A3.4). RRKM theory (chapter A3.12). the theory of unimolecular reactions in general,... 

Quack M and Tree J 1976 Unimolecular reactions and energy transfer of highly excited molecules Gas Kinetics and Energy Transfer mo 2, oh 5, ed P G Ashmore and R J Donovan (London The Chemical Society) pp 175-238 (a review of the literature published up to early 1976)... 

Detailed reaction dynamics not only require that reagents be simple but also that these remain isolated from random external perturbations. Theory can accommodate that condition easily. Experiments have used one of three strategies. (/) Molecules ia a gas at low pressure can be taken to be isolated for the short time between coUisions. Unimolecular reactions such as photodissociation or isomerization iaduced by photon absorption can sometimes be studied between coUisions. (2) Molecular beams can be produced so that motion is not random. Molecules have a nonzero velocity ia one direction and almost zero velocity ia perpendicular directions. Not only does this reduce coUisions, it also aUows bimolecular iateractions to be studied ia intersecting beams and iacreases the detail with which unimolecular processes that can be studied, because beams facUitate dozens of refined measurement techniques. (J) Means have been found to trap molecules, isolate them, and keep them motionless at a predetermined position ia space (11). Thus far, effort has been directed toward just manipulating the molecules, but the future is bright for exploiting the isolated molecules for kinetic and dynamic studies. 

Decomposition and Decarboxylation. Maleic anhydride undergoes anaerobic thermal decomposition in the gas phase in a homogeneous unimolecular reaction to give carbon monoxide, carbon dioxide, and acetylene [74-86-2] in equimolar amounts. The endothermic... 

S. W. Benson and H. E. O Neal, Kinetic Data on Gas Phase Unimolecular Reactions, NSRDS-NBS 21, U.S. Government Printing Office, Washington, 1970. 

The concoitradon of CHjNO decreased monotonically with temperature, but even at 800 °C a small concentration could be detected. The decrease could be due to unimolecular reactions, to biomolecular reactions with either CH,- or NO, or to a reverse reaction, CH3NO - CHj + NO. It is reasonable to assume that similar gas phase reactions would occur at much higher pressures however, we have not detected CH3NO during our catalytic experiments over the Sr/LajOj catalyst. Perhaps at much larger concentrations of NO the reaction CHjNO + NO - N O + CHjO- rapidly removes the nitrosomethane. 

Gas-phase SN2 nucleophilic substitution reactions are particularly interesting because they have attributes of both bimolecular and unimolecular reactions.1 As discovered from experimental studies by Brauman and coworkers2 and electronic structure theory calculations,3 potential energy surfaces for gas-phase SN2 reactions of the type,... 

Though statistical models are important, they may not provide a complete picture of the microscopic reaction dynamics. There are several basic questions associated with the microscopic dynamics of gas-phase SN2 nucleophilic substitution that are important to the development of accurate theoretical models for bimolecular and unimolecular reactions.1 Collisional association of X" with RY to form the X-—RY... 

Benson, S. W., and O Neal, H., "Kinetic Data on Gas Phase Unimolecular Reactions" National Bureau of Standards, NSRDS-NBS 21, 1970. 

According to the transition state theory, the rate constant of unimolecular reaction (at high pressure in the gas phase) is the following [5] ... 

For temperatures in excess of 320 °C the gas-phase decomposition of anhydrous H0C103 (or of its dihydrate) is a homogeneous, unimolecular reaction close to its first-order limit at pressures in excess of 20 torr440. Levy440 obtained a value... 

If rates in solution and in gas phase are to be equal, the activity coefficient factor, i.e./A/B//x must be equal to unity. For unimolecular reactions, where the reactant and activated complex have similar structures and/A and /x do not differ widely, the rate of reaction in solution will be quite similar to that in the gas phase. 

In the following section, the RRKM mechanism for gas phase unimolecular reactions will be introduced and the corresponding theoretical framework, including isotope effects, will be outlined. Subsequent sections will deal with some applications of this theoretical framework to systems which have been studied experimentally. 

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. 

The QET is not the only theory in the field indeed, several apparently competitive statistical theories to describe the rate constant of a unimolecular reaction have been formulated. [10,14] Unfortunately, none of these theories has been able to quantitatively describe all reactions of a given ion. Nonetheless, QET is well established and even the simplified form allows sufficient insight into the behavior of isolated ions. Thus, we start out the chapter from the basic assumptions of QET. Following this trail will lead us from the neutral molecule to ions, and over transition states and reaction rates to fragmentation products and thus, through the basic concepts and definitions of gas phase ion chemistry. 

Beynon, J.H. Gilbert, J.R. Energetics and Mechanisms of Unimolecular Reactions of Positive Ions Mass Spectrometric Methods, in Gas Phase Ion Chemistry, Bowcts, M.T., editor Academic Press New York, 1979 Vol. 2, Chap. 13, 153-179. 

Bowen, R.D. Williams, D.H. Non-Concerted Unimolecular Reactions of Ions in the Gas-Phase the Importance of Ion-Dipole Interactions in Carbonium Ion... 

To calculate the site density, L, for a given reaction step we use Eq. (6). [Equation (6) is for a unimolecular reaction the appropriate change is made when the reaction is not unimolecular.] Suppose that the reaction step is the adsorption of a gas (B) on a catalytically active site (D) ... 

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