Unimolecular reactions at low pressures

Troe J 1977 Theory of thermal unimolecular reactions at low pressures. I. Solutions of the master equation J. Chem. Phys. 66 4745-57... 

J. Troe. Theory of Thermal Unimolecular Reactions at Low Pressures. II. Strong Collision Rate Constants. Applications. J. Chem. Phys., 66(11) 4758—4775,1977. 

Only two experimental investigations have been carried out to study isotope effects in unimolecular reactions at low pressures. Weston has studied the tritium isotope effect in the isomerization of cyclopropane to propylene, while Gray and Pritchard have studied the individual rates of decomposition of octadeutero-cyclobutane and unlabeled cyclobutane. Few details of the work by Gray and Pritchard are available. The isotope effect does not appear to change much with pressure. Strangly enough these authors find that the reaction exhibits an inverse isotope effect with A (QHs)/ (QD8) = I... 

Evidence for strong non-equilibrium effects has first been obtained in the investigation of unimolecular reactions at low pressures. Here, the transition from first- to second-order kinetics is caused by perturbations of the equilibrium distribution of molecules over energies close to the activation energy (see Section V.17). Furthermore, it stimulated theoretical investigations on similar effects in bimole-cular reactions. However, the study of simple models has shown that non-equilibrium effects are not very marked and corresponding corrections to the equilibrium rate constants (i.e. rate constants calculated under the assumption of the Maxwell-Boltzmann distribution) are of the order of several per cent only [339]. Yet, this conclusion is based on the assumption that the reaction cross section depends solely on the translational energy which readily relaxes. 

Rice OK, Ramsperger HC (1928) Theories of unimolecular gas reactions at low pressures. 

Quack M 1984 On the mechanism of reversible unimolecular reactions and the canonical ( high pressure ) limit of the rate coefficient at low pressures Ber. Bunsenges. Phys. Chem. 88 94-100... 

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. 

Why can unimolecular reactions exhibit second-order kinetics at low pressures ... 

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... 

As pointed out before kuni is a pseudo first order rate constant. Since kuni/[M] is independent of [M], kuni/[M] is a second order rate constant at low pressure. It is significant and important for consideration of isotope effects that this second order rate constant for unimolecular reactions depends only on the energy levels of reactant molecules A and excited molecules A, and on the minimum energy Eo required for reaction. It does not depend on the energy levels of the transition state. There will be further discussion of this point in the following section. 

The relatively long timescales of the ionization, isolation, thermalization, reaction, and detection sequences associated with low-pressure FTICR experiments are generally thought to preclude the use of this technique as a means of examining the unimolecular dissociation of conventional metastable ions occurring on the microsecond to millisecond timescale. Nonetheless, as just demonstrated (Section IIIC), intermediates with this order of magnitude of lifetime are routinely formed in the bimolecular reactions of gaseous ions with neutral molecules at low pressures in the FTICR cell, as in Equation (13). 

The isomerization of cyclopropane follows the Lindemann mechanism and is found to be unimolecular. The rate constant at high pressure is 1.5 x 10- s- and that at low pressure is 6 X 10- torr- s-K The pressure of cyclopropane at which the reaction changes its order, found out ... 

In the traditional surface science approach the surface chemistry and physics are examined in a UHV chamber at reactant pressures (and sometimes surface temperatures) that are normally far from the actual conditions of the process being investigated (catalysis, CVD, etching, etc.). This so-called pressure gap has been the subject of much discussion and debate for surface science studies of heterogeneous catalysis, and most of the critical issues are also relevant to the study of microelectronic systems. By going to lower pressures and temperatures, it is sometimes possible to isolate reaction intermediates and perform a stepwise study of a surface chemical mechanism. Reaction kinetics (particularly unimolecular kinetics) measured at low pressures often extrapolate very well to real-world conditions. 

The only example of all the unimolecular reactions known where such a difficulty has actually arisen in an acute form is the decomposition of nitrogen pentoxide. It appears that at low pressures nitrogen pentoxide reacts at a rate which is considerably greater than the maximum possible rate of activation by collision, however great a value of n be assumed. There is a limit to the maximum rate theoretically possible, since, when n is increased beyond a certain point, the increase in the term E — EArrhenius + n- )RT produces a decrease in the calculated rate which more than compensates for the increase due to the term (E/RT)1l2n 1 multiplying the exponential term. 

At these low pressures the reaction is in the second-order region of the unimolecular falloff, and low-pressure-limit rate coefficients, k0, are obtained. A master equation calculation was used to obtain the critical energy, E0, and average energy transferred per collision, from which an expression for the high-pressure rate coefficient was obtained. 

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