Transition state, composition

Just as the rate equation gives the transition state composition but not its structure, neither does it tell us the order in which the components were assembled. Thus, Schemes VII and VIII both give the same rate equation, v = A iA jCaCb CoCp, so this equation correctly identifies the rds transition state composition, but it cannot distinguish between these reaction schemes (or others that can be drawn). 

The appearance of Cd in the denominator means that D is coupled to a reversible step prior to the rds. If k, and k- were so large that the fast preequilibrium assumption is valid, then the Cd term in the denominator would drop out, and we would have v = A 2 CaObCd, giving the composition of the rds transition state. If k2 is very much larger than it, and k i, Eq. (5-59) becomes v = A CaOb the first step is now the rds, and the rate equation gives the transition state composition. 

Parallel reactions give rate equations having sums of rate terms. Each term provides the transition state composition for a reaction path. Eor example, some acid-catalyzed reactions have the rate equation... 

In a special circumstance the rate equation for parallel reactions may be misleading.If two parallel reactions are catalyzed by a common catalyst, and if a significant fraction of the catalyst is tied up in the form of intermediates, then the two reactions are not independent, and the rate equation will not give the transition state composition. King has analyzed this case in terms of enzyme-catalyzed reactions. 

Some quantities associated with the rates and mechanism of a reaction are determined. They include the reaction rate under given conditions, the rate constant, and the activation enthalpy. Others are deduced reasonably directly from experimental data, such as the transition state composition and the nature of the rate-controlling step. Still others are inferred, on grounds whose soundness depends on the circumstances. Here we find certain features of the transition state, such as its polarity, its stereochemical arrangement of atoms, and the extent to which bond breaking and bond making have progressed. 

The transition state composition is, moreover, uncertain as regards the number of solvent molecules it contains. Thus, we might write for Eq. (6-1), carried out in water, a composition of [Fe(CN)5N2H4C>33 nH20]t. The number of water molecules is of more than academic interest here, in that the net reaction extrudes one molecule of water. It has been suggested (from chemical evidence,1 not as a deduction from the rate law) that water is eliminated first, and that the reaction may occur by way of the following transition state (or intermediate) ... 

The new pathway, too, is a chain reaction Note that the first term of Eq. (8-31) does not give a meaningful transition state composition. Since the scheme in Eqs. (8-20M8-23) seems valid for the Cu2+-free reaction, we can seek to modify it to accommodate the new result. This approach is surely more logical than inventing an entirely new sequence. To arrive at the needed modification, we simply replace Eq. (8-23) by a new termination step, Eq. (8-30). With that, and the steady-state approximation, the rate law is... 

When the initiation and termination reactions are the reverse of one another, the kinetic form is usually simpler than when the two are independent. Also, the transition-state composition follows directly from the rate law, which is why the term well-behaved is applied. Imagine, for example, that the termination step in the system most recently presented was the recombination of two sulfate radical ions rather than Eq. (8-38) ... 

Does the transition state composition for the RCS, [S04 H20], really follow from Eq. (8-48) Indeed, from Eq. (8-35), that is exactly the case. There is no indication in this circumstance that a chain mechanism operates. [Keep in mind, however, that this example is fictional, in that Eq. (8-47) is not important compared with Eq. (8-38).] Fractional-order dependences are not necessarily indicative of chains when the reagent is symmetric, like S20 , although the particular examples presented do happen to feature chain mechanisms. 

The phenomenon of polymer swelling, owing to sorption of small molecules, was known even before Staudinger reported [1] in 1935 that crosslinked poly(styrene) swells enormously in certain liquids to form two-component polymer gels. The physical state of such systems varies with the concentration (C) and molecular structure of the sorbed molecules thus, the system undergoes transition at constant temperature from a rigid state (glassy or partially crystalline) at C < Cg to a rubbery state at Cg (the transition state composition). When C > Cg and the second component is a liquid, its subsequent sorption proceeds quickly to gel-saturation and of course a solution is produced if the polymer lacks covalently bonded crosslinks or equivalent restraints. Each successive physical state exhibits its own characteristic sorption isotherm and sorption kinetics. 

Since it does not, other possible reactions of RX must be considered. In some reductive cleavages of some substituted cyclopropyl halides, an electron transfer to RX appears to be required, leading to a dianionic fragmentation transition state (composition RX . with associated counterions) [110.I15. Pathway X could be such a dianionic pathway. However, no precedetU for this pathway for an aryl halide is apparent. According to the literature, aryl intermediates RX" either fragment or lose an electron, regenerating RX 117,18). 

Because the product composition is kinetically controlled, the isomer ratio will be governed by the relative magnitudes of AG, AGI, and AG, the energies of activation for the ortho, meta, and para transition states, respectively. In Fig. 4.7 a qualitative comparison of these AG values is made. At the transition state, a positive charge is present on the benzene ring, primarily at positions 2, 4, and 6 in relation to the entering bromine. 

The next level seeks a molecular description, and kinetics again makes a contribution. As will be seen in Chapter 5, the experimental kinetics provides information on both the energetics of the reaction (i.e., the height of the energy barrier on the reaction path) and the atomic composition of the transition state. Any proposed mechanism must therefore be consistent with the kinetic evidence. 

Perhaps the single most important piece of information to be derived from a kinetic study is the composition of the transition state. The basis of the inference can be developed by means of this elementary bimolecular reaction. 

We, therefore, conclude that the concentration dependence of the experimental rate gives the composition of the transition state in this example the transition state is composed of one molecule of A and one of B, for the experimental rate constant is first-order in each reactant. 

This argument can be extended to consecutive reactions having a rate-determining step. - P The composition of the transition state of the rds is given by the rate equation. This composition includes reactants prior to the rds, but nothing following the rds. Thus, the rate equation may not correspond to the stoichiometric equation. We will consider several examples. In Scheme IV a fast acid-base equilibrium precedes the slow rds. 

The kinetic dependence of the reaction was explained in terms of a reaction between PhB(OH)3 and PhHg+. From analysis of the concentration of the species likely to be present in solution it was shown that reaction between these ions would yield an inverse dependence of rate upon molecular acid composition in buffer solutions, as observed for a tenfold change in molecular acid concentration, and that at high pH this dependence should disappear as found in carbonate buffers of pH 10. The form of the transition state could not be determined from the available data, and it would be useful to have kinetic parameters which might help to decide upon the likelihood of the 4-centre transition state, which was one suggested possibility. 

The rate law reveals the composition of the transition state of the rate-controlling step that is, the species or at least the atoms that it contains and its ionic charge, if any. In addition, it may tell whether any rapid equilibria precede the rate-controlling step. Sometimes one can learn whether intermediates are involved in optimum cases their identities can be established. 

An intermediate often has the same composition as one of its adjacent transition states and perhaps both. Unlike the transition states, the intermediate has a choice of reactions. The intermediate and the transition states may well have the same overall structure and nearly the same geometry, but the intermediate requires some distortion or other activation before it becomes a transition state. 

The strong emphasis placed on concentration dependences in Chapters 2-5 was there for a reason. The algebraic form of the rate law reveals, in a straightforward manner, the elemental composition of the transition state—the atoms present and the net ionic charge, if any. This information is available for each of the elementary reactions that can become a rate-controlling step under the conditions studied. From the form of the rate law, one can deduce the number of steps in the scheme. In most cases, further information can be obtained about the pattern in which parallel and sequential steps are arranged. 

The concentration dependences in the rate law establish the elemental composition of the transition state and its charge. 

---