Constant rate qualitative picture

Comparisons of electrochemical values of surfactants 1 and 2 in microemulsions and micellar solutions helped establish qualitative pictures of dynamics at relevant electrode-fluid interfaces. Rate constants for oxidations of ferrocene (Fc) 2-Fc (1) and 5-Fc (2) were similar in homogeneous DMF and DM SO on Pt and glassy carbon electrodes [32, 33]. However, in aqueous CTAB micelles, electron transfer rates were in the order Fc > 2-Fc > 5-Fc, with tenfold differences in successive values. This was attributed to 2-Fc and 5-Fc achieving head down orientations on the electrode prior to electron transfer. Adsorbed CTA+ on the electrode seems to help order 1 and 2 on the electrode prior to electron transfer. 

Transition state theory (TST) has historically been the most important and widely used theoretical approach for describing rate constants for chemical reactions, and for qualitative pictures and order-of-magnitude estimates one does not expect this to change. However, TST is approximate - it is based inherently on classical mechanics and quantized only in an ad hoc fashion. It will nevertheless be seen in the rigorous rate theory described below that many TST-like features survive qualitatively. 

Recall that for first-order kinetics a plot of In (fraction unreacted) versus time has a slope — k. Also note that the reaction reaches an equilibrium characterized by an absorbance 0.115 the data must be corrected for this. For both the anionic and cationic micelles, qualitatively sketch, emphasizing the charge state, the micelle, the solubilized substrate, and the approaching OH" reactant. Indicate how these pictures are consistent with the experimental rate constants. 

A similar picture holds for other nucleophiles. As a consequence, there might seem little hope for a nucleophile-based reactivity relationship. Indeed this has been implicitly recognized in the popularity of Pearson s concept of hard and soft acids and bases, which provides a qualitative rationalization of, for example, the similar orders of reactivities of halide ions as both nucleophiles and leaving groups in (Sn2) substitution reactions, without attempting a quantitative analysis. Surprisingly, however, despite the failure of rate-equilibrium relationships, correlations between reactivities of nucleophiles, that is, comparisons of rates of reactions for one carbocation with those of another, are strikingly successful. In other words, correlations exist between rate constants and rate constants where correlations between rate and equilibrium constants fail. 

Of course, there is more to a chemical reaction than its rate constant the reaction path or mechanism is also of central interest. Once again, nonequilibrium solvation is crucial in describing this path. In an equilibrium solvation picture, the solvent polarization would remain equilibrated throughout the reaction course, but this assumption is rarely satisfied for an actual reaction path, because of the same considerations noted above for the rate constant. Indeed these nonequilibrium solvation effects can qualitatively change the character of the reaction path as compared with an equilibrium solvation image. Dielectric continuum dynamic descriptions thus have an important role to play here as well. Indeed, we will employ in this contribution the reaction path Hamiltonian formulation previously developed [48,49], which can be used to generate a reaction path which is the analog in solution of the well-known Fukui reaction path in the gas phase [50], The reaction path will be discussed for both reaction topics in this contribution. 

However, as pointed out by Reich and Schindler (23), this picture is not fully satisfactory. If hydrogen were a simple transfer agent then the rate of polymerization (at constant monomer concentration) would not be affected by the presence of hydrogen, whereas in fact there is a fall in rate (Figs. 11a and 11b). Schindler suggests two reasons for this. First, that the step to convert Cat—H to Cat—P is slow, and secondly, that the hydrogen displaces ethylene from the surface of the catalyst and so reduces the effectiveness of the ethylene. We believe that these factors can account qualitatively for the observed results but that the precise determination of mechanism requires more extensive and accurate data than are at present available. 

The above discussion has been based on simple qualitative ideas about how an elementary reaction may occur. The way to test this picture, of course, is to see if rates of reaction measured experimentally, using different concentrations of each reactant and at different temperatures, show the same predicted behaviour. For this purpose the experimental rate equations for a few elementary reactions involving two reactant species are given in Table 4.1. In each case the experimental rate constant is denoted by the symbol k. Comparison of the form of the experimental rate equations in Table 4.1 with Equation 4.6 makes it clear that there is a good agreement between theory and experiment. Other details also help to confirm this conclusion. For example, the experimental rate constant for the reaction between potassium atoms and Br2 molecules is found to be independent of temperature, suggesting that the energy barrier to reaction is effectively zero. By contrast, the rate constants for the other two reactions (in Table 4.1) are markedly temperature dependent. 

Clearly, by the appropriate choice of substituents, carbenic stability, reactivity, and philicity can be simultaneously varied, while the delicate interrelations of these properties can be understood in empirical and, more precisely, in theoretical terms. The kinetic range of the carbene reactions that we have considered is enormous the rate constants span 9 or more orders of magnitude. From this perspective, it is remarkable that the classical tools of physical organic chemistry, resonance and inductive effects, and Hammett relationships, provide such a satisfactory qualitative rationalization of the entire picture. Augmented by modem experimental methods such as LFP, and theoretical tools (FMO and computational methods), we are now able to understand and manipulate carbenic philicity in an intellectually satisfying and synthetically useful manner. 

The goal of extending classical thermostatics to irreversible problems with reference to the rates of the physical processes is as old as thermodynamics itself. This task has been attempted at different levels. Description of nonequilibrium systems at the hydrodynamic level provides essentially a macroscopic picture. Thus, these approaches are unable to predict thermophysical constants from the properties of individual particles in fact, these theories must be provided with the transport coefficients in order to be implemented. Microscopic kinetic theories beginning with the Boltzmann equation attempt to explain the observed macroscopic properties in terms of the dynamics of simplified particles (typically hard spheres). For higher densities kinetic theories acquire enormous complexity which largely restricts them to only qualitative and approximate results. For realistic cases one must turn to atomistic computer simulations. This is particularly useful for complicated molecular systems such as polymer melts where there is little hope that simple statistical mechanical theories can provide accurate, quantitative descriptions of their behavior. 

The microscopic picture of reactions is qualitatively consistent with macroscopic observations of the rates of reactions. Laboratory measurements of most reaction systems show a rather simple dependence of the reaction rate on the concentrations, and this is consistent with an overriding requirement for reaction, that the reacting particles collide. Our analysis of collision events shows the dependence of a rate on a concentration however, the proportionality factor between the rate and the concentration, called the rate constant, depends on temperature and on numerous properties of the reacting species and their interaction potential surface. 

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