Intramolecular reactions rate constants

Strictly bimolecular reaction (eq. 4.2) as would be the case for a free amino acid in solution. Rates of intramolecular reactions are usually compared to those of intermolecular reactions by determining the ratio of the first-order rate constants to the second order rate constants. The units of this ratio are concentration and the ratio is at least 5 M for simple organic reactions if no specific orientation effects are involved. Ratios of this size are generally interpreted in terms of the increased local concentration of one reactive group relative to another in the intramolecular reaction. 

In the absence of pyridine, tert-butylchlorocarbene can undergo two types of intramolecular rearrangements, react with diazirine precursor to form azine or react with solvent. It can also react with an olefinic trap to give a cyclopropane adduct. Analysis of the product mixture by Moss and Liu [25] gives the ratio of rate constants of these processes. As the alkene trapping reaction rate constant is known, the other rate constants of reaction of the invisible species tert-butyl-chlorocarbene can be deduced. 

Attempts to evaluate the rate enhancement arising from the presumed intramolecular catalysis lead to conflicting results. One way is to compare the rate constant for reaction of acetic 2-methoxy-3,5-dinitrobenzoic anhydride with acetate (25.41 mol min at 39°C) with that for reaction of 3,5-dinitroaspirin (7.9 x 10 1 mol min ) with acetate. On the assumption that the latter reaction proceeds via a mixed anhydride and that this reacts at the same rate as acetic 2-methoxy-3,5-dinitrobenzoic anhydride with acetate, the concentration of the intermediate is calculated to be 0.03 per cent [83]. On this basis the rate of hydrolysis of the mixed anhydride 52 is 17... 

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

Regardless of the nature of the intramolecular dynamics of the reactant A, there are two constants of the motion in a nnimolecular reaction, i.e. the energy E and the total angular momentum j. The latter ensures the rotational quantum number J is fixed during the nnimolecular reaction and the quantum RRKM rate constant is specified as k E, J). 

For monomers of the AB type, reactions (5.CC) and (5.DD) become AB -> and 2AB AbaB, respectively. If kj. and k are the respective rate constants for these reactions, derive an expression which gives the ring to linear ratio in the product as a function of AB concentration and the two rate constants. Criticize or defend the following proposition To obtain a test of Eq. (5.47) without the complications of intramolecular condensations, a series of otherwise identical polymeriztion reactions could be carried out on monomer mixtures at different concentrations. By... 

Derive the general expression for the observed rate constant for hydrolysis of A as a function of pH. Assume, as is the case experimentally, that intramolecular general acid catalysis completely outweighs intermolecular catalysis by hydronium ion in the pH range of interest. Does the form of your expression agree with the pH rate profile given for this reaction in Fig. 8.6 (p. 489) ... 

First-order and second-order rate constants have different dimensions and cannot be directly compared, so the following interpretation is made. The ratio intra/ inter has the units mole per liter and is the molar concentration of reagent Y in Eq. (7-72) that would be required for the intermolecular reaction to proceed (under pseudo-first-order conditions) as fast as the intramolecular reaction. This ratio is called the effective molarity (EM) thus EM = An example is the nu-... 

From this expression, it is obvious that the rate is proportional to the concentration of A, and k is the proportionality constant, or rate constant, k has the units of (time) usually sec is a function of [A] to the first power, or, in the terminology of kinetics, v is first-order with respect to A. For an elementary reaction, the order for any reactant is given by its exponent in the rate equation. The number of molecules that must simultaneously interact is defined as the molecularity of the reaction. Thus, the simple elementary reaction of A P is a first-order reaction. Figure 14.4 portrays the course of a first-order reaction as a function of time. The rate of decay of a radioactive isotope, like or is a first-order reaction, as is an intramolecular rearrangement, such as A P. Both are unimolecular reactions (the molecularity equals 1). 

A large red shift observed in polar solvents was indicative of the intramolecular charge transfer character of the triplet state. The change of dipole moment accompanying the transition Tj - Tn, as well as rate constants for electron and proton transfer reactions involving the T state of a-nitronaphthalene, were determined. The lower reactivity in polar solvents was attributed to a reduced n-n and increased charge transfer character of the triplet state... 

A series of theoretical studies of the SCV(C)P have been reported [38,40,70-74], which give valuable information on the kinetics, the molecular weights, the MWD, and the DB of the polymers obtained. Table 2 summarizes the calculated MWD and DB of hyperbranched polymers obtained by SCVP and SCVCP under various conditions. All calculations were conducted, assuming an ideal case, no cyclization (i.e., intramolecular reaction of the vinyl group with an active center), no excluded volume effects (i.e., rate constants are independent of the location of the active center or vinyl group in the macromolecule), and no side reactions (e.g., transfer or termination). 

Table 10.4 lists the rate parameters for the elementary steps of the CO + NO reaction in the limit of zero coverage. Parameters such as those listed in Tab. 10.4 form the highly desirable input for modeling overall reaction mechanisms. In addition, elementary rate parameters can be compared to calculations on the basis of the theories outlined in Chapters 3 and 6. In this way the kinetic parameters of elementary reaction steps provide, through spectroscopy and computational chemistry, a link between the intramolecular properties of adsorbed reactants and their reactivity Statistical thermodynamics furnishes the theoretical framework to describe how equilibrium constants and reaction rate constants depend on the partition functions of vibration and rotation. Thus, spectroscopy studies of adsorbed reactants and intermediates provide the input for computing equilibrium constants, while calculations on the transition states of reaction pathways, starting from structurally, electronically and vibrationally well-characterized ground states, enable the prediction of kinetic parameters. 

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