Unimolecular processes rates

Quack M and Tree J 1974 Specific rate constants of unimolecular processes. II. Adiabatic channel model Ber. Bunsenges. Phys. Chem. 78 240-52... 

Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides... 

The rate constant ke corresponds to the reciprocal of the lifetime of the excited state. Internal conversion The excited state can do other things, such as convert some of the original electronic excitation to a mixture of vibration and a different electronic state. These are also treated as unimolecular processes with associated rate constants ... 

Now, let us discuss the rate equations embodied in eq.(74). To do this, there is need of a statistical analysis. If the system is kept coupled to a thermostat at absolute temperature T, and assuming that w(i - >if) contains effects to all orders in perturbation theory, the rate of this unimolecular process per unit (state) reactant concentration k + is obtained after summation over the if-index is carried out with Boltzman weight factors p(if,T) ... 

The apparent first-order rate coefficient is 1.5x 1010 exp(—28,200/RT ) sec-1. This expression has undoubtedly been obtained for a pressure-dependent region. If, as an extreme case, it is assumed that the unimolecular process occurred in the second-order region and if approximately one half of the classical degree of vibrational freedom are active, an upper limit of kx — 1.5 x 1015 exp(—46,000/Rr) sec-1 is obtained. The mean Pb-CH3 bond dissociation energy in tetramethyl lead19,142 is 37.6 kcal.mole-1. Dx should therefore be about 40 kcal.mole-1. 

As far as propagation is concerned, comparison of rates is hazardous because under some conditions the rate-determining step for isobutene [85], like propene [86], may be a unimolecular process, i.e., of zero order with respect to monomer (see sub-section 5.2). Moreover, comparison is complicated further by the consideration that in every system free cations and cations forming part of an ion-pair or higher aggregate may participate in the polymerization, and that therefore the extent of such participation must be ascertained before meaningful rate constants can be evaluated. This matter will be discussed in Section 6. 

If the surface complex is the chromophore, then the photochemical reductive dissolution occurs as a unimolecular process alternatively, if the bulk iron(III)(hydr)-oxide is the chromophore, then it is a bimolecular process. Irrespective of whether the surface complex or the bulk iron(IIl)(hydr)oxide acts as the chromophore, the rate of dissolved iron(II) formation depends on the surface concentration of the specifically adsorbed electron donor e.g. compare Eqs. (10.11) and (10.18). It has been shown experimentally with various electron donors that the rate of dissolved iron(II) formation under the influence of light is a Langmuir-type function of the dissolved electron donor concentration (Waite, 1986). 

The formalism for treating primary isotope effects on unimolecular processes follows analogously to the development above, once due account is taken of the difference in zero point energies on isotope substitution at the reaction site (which is reflected in an isotopic difference in the threshold energy Eo). For thermal activation the rate ratio in the high pressure limit is straightforwardly obtained from Equation 14.25. For H/D effects... 

The comparison has to be made between a first-order rate constant for the unimolecular process and a second-order rate constant for the corresponding intermolecular reaction (Sec. 6.1.1). One may arbitrarily decide on a 1 M concentration of reagent NHj, in which... 

On the grounds that furanosides anomerise and hydrolyse very much more readily than do the corresponding pyranosides. Bishop eind Cooper assumed that the first step in the glycosidation process is the methanol-ysis of the furanose form of the free sugar, and they visualised, without evidence, a unimolecular process proceeding by way of a stabilised cyclic ion (1). In support of this they observed 5) that for xylose, lyxose and ribose the furanoside formation rates (3,1,12 respectively) correlated with the furanoside contents at equilibrium (see Table 3) and hence, presum-... 

The rate constant (sometimes called the specific reaction rate) is commonly designated by k. The SI unit of time is the second (symbolized by s). Thus, unimolecular rate constants are typically expressed in s and unimolecular processes are by definition concentration-independent reactions. A slight difficulty arises regarding SI units and bi- and termolecular rate constants. Concentrations in the SI system would be mol per cubic meter, but in chemistry concentrations are expressed in mobdm (or more commonly mol-L or simply M ). Thus, a bimolecular rate constant typically has units of M s whereas a termolecular rate constant is expressed with units of... 

Elementary reactions (also termed monomolecular reactions) that involve only a single entity in the formation of an activated complex. Unimolecular rate constants, k, are concentration-independent and are typically expressed in units of sUnimolecular reactions are expected to be first order (i.e., -dc/dt = kc where c is the concentration and t is time). Examples of unimolecular processes include radioactive disintegrations, isomeriza-tions, disassociations, and decompositions. Reactions in solution are unimolecular only if the solvent is not covalently incorporated into the product(s). 

Here we see that the rate is strongly inhibited by adsorbed oxygen, which blocks sites for NO to adsorb into. This is the reason that NO cannot be decomposed in a unimolecular process at moderate temperatures in the presence of O2. 

A major source of acceleration in enzymic reactions is approximation, that is to say, the bringing together of two or more reactants in the active site. Once the reagents are in contact, the subsequent reaction is intra- rather than intermolecular. Comparisons of the rates of intermolecular and intramolecular reactions are, however, difficult because the rate constants for bimolecular reactions have the units of M "1 s-1, whereas rate constants for unimolecular reactions have the units of s l. The best one can do in comparing them is to state the molarity at which the reactants would have to be present in the bimolecular reaction to achieve the rate of the unimolecular process when the effective molarity is large-say 1000 M or more-one has some measure of the power of approximation to accelerate chemical reaction. 

Rate constants of unimolecular processes can be obtained from spectral data and are useful parameters in photochemical kinetics. Even the nature of photoproducts may be different if these parameters change due to some perturbations. In the absence of bimolecular quenching and photochemical reactions, the following reaction steps are important in deactivating the excited molecule back to the ground state. 

The El mechanism has, as the rate-determining step in solution, the ionisation of the reactant forming a carbonium ion which then decomposes rapidly. For heterogeneous catalytic reactions, the important features are the occurrence of the reaction in two steps and the presence on the solid surface of carbonium ions or species resembling them closely. Again, the kinetic characterisation by way of an unimolecular process is of little value. Even the relative rates of the two steps may be reversed on solid catalysts. A cooperation of an acidic and a basic site is also assumed, the reaction being initiated by the action of the acidic site on the group X. 

Such a reaction is described as first order and the proportionality constant k is known as the rate constant. Such first-order kinetics is observed for unimolecular processes in which a molecule of A is converted into product P in a given time interval with a probability that does not depend on interaction with another molecule. An example is radioactive decay. Enzyme-substrate complexes often react by unimolecular processes. In other cases, a reaction is pseudo-first order compound A actually reacts with a second molecule such as water, which is present in such excess that its concentration does not change during the experiment. Consequently, the velocity is apparently proportional only to [A]. 

ES (Eq. 9-14). Formation of the complex is normally reversible. ES can either break up to form enzyme and substrate again or it can undergo conversion to a product or products, often by a unimolecular process. Three rate constants are needed to describe this system for a reaction that is irreversible overall. A complete... 

This effect of N08 ion is quantitatively consistent with a reaction mechanism (43) in which N08 interacts with an electronically excited water molecule before it undergoes collisional deactivation by a pseudo-unimolecular process (the NOs effect is temperature independent (45) and not proportional to T/tj (37)). Equation 1, according to this mechanism, yields a lifetime for H20 of 4 X 10 10 sec., based on a diffusion-controlled rate constant of 6 X 109 for reaction with N08 Dependence of Gh, on Solute Concentration. Another effect of NOa in aqueous solutions is a decrease in GH, with increase in N08 concentration (5, 25, 26, 38, 39). This decrease in Gh, is generally believed to result from reaction of N08 with reducing species before they combine to form H2. These effects of N08 on G(Ce+3) and Gh, raise the question as to whether or not they are both caused by reaction of N08 with the same intermediate. 

In case (a), R and I interconvert by unimolecular processes, and then I is converted into product in a bimolecular reaction with reagent X. Such reactions are expected to be first order in [R], but order with respect to [X] will varybetweenO and 1 depending on the relative magnitudes of k2[X] and k Since X is consumed during the reaction, the variation may be detectable as downward drift in the rate constant when monitoring disappearance of R. 

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