Activation energy unimolecular reactions

In the unimolecular reactions which are also of the first order, only one molecule takes part in the reaction. The process of activation in unimolecular reactions, if caused by collisions should ordinarily lead to second order reactions. How then the observed rate of reaction could be of first order. If however, the activation is by absorption of the radiant energy, this problem can be avoided. But many unimolecular reactions take place under conditions where there is no absorption of radiant energy. For example... 

With bimolecular gas reactions, as we have seen, it is plausible to assume that the kinetic energy of the impact between the two molecules provides the energy of activation, and on this assumption we find for the number of molecules reacting number of collisions x e ElRT. This equation in six out of seven known examples is as nearly true as experiment can decide. Thus there is no absolute necessity to look any further for the interpretation of bimolecular reactions. At first it seemed natural to apply an analogous method of calculation to determine the maximum possible rate of activation in unimolecular reactions this led to the result that unimolecular reactions in general proceed at a rate many times greater than the expression Ze ElRT requires, e. g. about 105 times as many molecules of acetone decompose at 800° abs. in unit time as this method of calculation would admit to be possible, f... 

Kinetic theory tells us that reactions take place because random collisions between molecules produce a small number of molecules with an energy greater than the minimum (the activation energy) for reaction to occur. For unimolecular reactions at a particular temperature, this number (and thus the rate of reaction) will be proportional to the number of molecules present in a particular space (volume), i.e. the concentration. Thus for a reaction... 

Figure 3.5 Schematic potential energy profiles for three types of unimolecular reaction, (a) Isomerization (b) dissociation where there is a high energy barrier and a large activation energy for reaction in both the forward and reverse directions (c) dissociation where the potential energy rises monotonically as for rotational ground state species, so that there is no barrier to the reverse association reaction (Steinfeld et al., 1989).

Of note is the relatively narrow temperature range over which measurements could be made due to the high activation energies for reaction, coupled with the small dynamic range of the mobility spectrometer. The narrow temperature range does not, however, preclude obtaining results with good precision. The pre-exponential factor of ca 10 S" is the maximum expected for unimolecular decompositions [45]. 

The Fundamental Constraints on Activation Energies Unimolecular Elementaiy Reactions... 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

From stochastic molecnlar dynamics calcnlations on the same system, in the viscosity regime covered by the experiment, it appears that intra- and intennolecnlar energy flow occur on comparable time scales, which leads to the conclnsion that cyclohexane isomerization in liquid CS2 is an activated process [99]. Classical molecnlar dynamics calcnlations [104] also reprodnce the observed non-monotonic viscosity dependence of ic. Furthennore, they also yield a solvent contribntion to the free energy of activation for tlie isomerization reaction which in liquid CS, increases by abont 0.4 kJ moC when the solvent density is increased from 1.3 to 1.5 g cm T Tims the molecnlar dynamics calcnlations support the conclnsion that the high-pressure limit of this unimolecular reaction is not attained in liquid solntion at ambient pressure. It has to be remembered, though, that the analysis of the measnred isomerization rates depends critically on the estimated valne of... 

By ab initio MO and density functional theoretical (DPT) calculations it has been shown that the branched isomers of the sulfanes are local minima on the particular potential energy hypersurface. In the case of disulfane the thiosulfoxide isomer H2S=S of Cg symmetry is by 138 kj mol less stable than the chain-like molecule of C2 symmetry at the QCISD(T)/6-31+G // MP2/6-31G level of theory at 0 K [49]. At the MP2/6-311G //MP2/6-3110 level the energy difference is 143 kJ mol" and the activation energy for the isomerization is 210 kJ mol at 0 K [50]. Somewhat smaller values (117/195 kJ mor ) have been calculated with the more elaborate CCSD(T)/ ANO-L method [50]. The high barrier of ca. 80 kJ mol" for the isomerization of the pyramidal H2S=S back to the screw-like disulfane structure means that the thiosulfoxide, once it has been formed, will not decompose in an unimolecular reaction at low temperature, e.g., in a matrix-isolation experiment. The transition state structure is characterized by a hydrogen atom bridging the two sulfur atoms. 

Many elementary reactions have large activation energies. For example, the isomerization of s-2-butene to trans-2-butene is a unimolecular rotation whose activation energy is 284 kJ/mol. This high value arises because a C — C 7t bond must be broken during the course of the isomerization process (see Figure IS-TT... 

While all rates of these unimolecular reactions can be fit quantitatively by LH expressions. Equation 11, the heats of adsorption determined from the temperature dependence of the adsorption equillb-rium constant. Equation 14, do not agree with the measured reaction activation energy except for NH3 where = 16 2 kcal/mole. NO... 

In general, intramolecular isomerization in coordinatively unsaturated species would be expected to occur much faster than bimolecular processes. Some isomerizations, like those occurring with W(CO)4CS (47) are anticipated to be very fast, because they are associated with electronic relaxation. Assuming reasonable values for activation energies and A-factors, one predicts that, in solution, many isomerizations will have half-lives at room temperature in the range 10 7 to 10 6 seconds. The principal means of identifying transients in uv-visible flash photolysis is decay kinetics and their variation with reaction conditions. Such identification will be difficult if not impossible with unimolecular isomerization, particularly since uv-visible absorptions are not very sensitive to structural changes (see Section I,B). These restrictions do not apply to time-resolved IR measurements, which should have wide applications in this area. 

All these reactions are endothermic and, in addition, occur with a loss of entropy. Back unimolecular reactions are exothermic and occur with an increase in entropy. So, the role of such reactions should be negligible due to high activation energy and very fast back reaction. The values of the rate constants for addition reactions CH302 + carbonyl compound, calculated by the IPM method are presented in the following table ... 

Most of our knowledge about the kinetics of the homogeneous decomposition has come from shock-tube experiments. These have been performed in several laboratories under a variety of experimental conditions. However, their results are contradictory in some respects especially with regard to activation energy and on the question of the importance of chain reactions. In some cases the experimental conditions are such that consecutive reactions have to be taken into account or at least cannot be safely excluded. Until recently, one reason for the difficulty of reconciling the results of different investigators was that, if they were interpreted in terms of the unimolecular reaction48... 

Carbon dioxide decomposes behind a shock front in accordance with the kinetics expected of a unimolecular reaction in its low-pressure region31-37. The second-order rate coefficients obtained by a number of experimentalists in the temperature range 2500-11000 °K are in reasonable agreement, but there is a considerable spread in the values derived for the Arrhenius activation energy (Table 3). Furthermore, even the highest of these values31 is much smaller than the endothermicity (D = 125.8 kcal.mole-1) of... 

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