The Activity Coefficient of an Activated Complex

It has been shown earlier (see section 1.4) that for any process obeying the Br nsted relation, the activity coefficient of 

For electrode processes, the Br nsted relation has been experimentally found to be valid over a wide interval of energy (a is found to 

Strictly speaking, however, the inetig activity coefficient cannot be reduced to just the ratio yH30 /Y equation for an 

A comparison of all the data compiled in groups of solutions of nearly identical composition has been given in Table 4[128]. In addition to the experimental values of the overpotential, this table contains calculated values (for more concentrated solutions) for the shifts in overpotential with respect to the first group (of the most dilute solutions). These calculations have been carried out in two different ways if the overpotential depended on the activity of water (data on water activity has been taken from [129]), and if the molar fraction were the only factor directly influencing the overpotential, i.e. if the change in the activity coefficient of water and the activated complex compensated each other. 

From a comparison of the last three columns of this table. It is apparent that only the second assumption corresponds to the experimental results within the limits of possible experimental errors. 

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THE BR0NSTED RELATION AND THE ACTIVITY COEFFICIENT OF AN ACTIVATED COMPLEX... 

Substituting all these quantities and the expression (1.36) for the, activity coefficient of an activated complex into Equation (1.40) (-f in this case will vanish and molar fraction X will replace the activities a in the equation), and expressing AGajjg as AHajjg - TASanB we obtain... 

It is with the limitation of being unable to assess the acidity of the medium independently of the type of indicator employed, that interpretation of the dependency of the rate of acid-catalysed dehydration of alcohols and hydration of olefins must be approached. As each of the various acidity functions run parallel to each other, a plot of the logarithm of the rate coefficient of an acid-catalysed reaction against an acidity function should give a linear correlation. The slope of such a plot, however, will only be unity if the ratio of activity coefficients of the substrate and its activated complex vary in the same way with changes in the reaction medium as the ratio of activity coefficients of the indicator molecule and its conjugate acid. 

The Turing mechanism requires that the diffusion coefficients of the activator and inlribitor be sufficiently different but the diffusion coefficients of small molecules in solution differ very little. The chemical Turing patterns seen in the CIMA reaction used starch as an indicator for iodine. The starch indicator complexes with iodide which is the activator species in the reaction. As a result, the complexing reaction with the immobilized starch molecules must be accounted for in the mechanism and leads to the possibility of Turing pattern fonnation even if the diffusion coefficients of the activator and inlribitor species are the same 62. 

The regioselectivity benefits from the increased polarisation of the alkene moiety, reflected in the increased difference in the orbital coefficients on carbon 1 and 2. The increase in endo-exo selectivity is a result of an increased secondary orbital interaction that can be attributed to the increased orbital coefficient on the carbonyl carbon ". Also increased dipolar interactions, as a result of an increased polarisation, will contribute. Interestingly, Yamamoto has demonstrated that by usirg a very bulky catalyst the endo-pathway can be blocked and an excess of exo product can be obtained The increased di as tereo facial selectivity has been attributed to a more compact transition state for the catalysed reaction as a result of more efficient primary and secondary orbital interactions as well as conformational changes in the complexed dienophile" . Calculations show that, with the polarisation of the dienophile, the extent of asynchronicity in the activated complex increases . Some authors even report a zwitteriorric character of the activated complex of the Lewis-acid catalysed reaction " . Currently, Lewis-acid catalysis of Diels-Alder reactions is everyday practice in synthetic organic chemistry. 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

Despite the additional complexity, all the equations in Table 5.3 are functionally equivalent. That is, the activity coefficients approach a value of 1 as the ionic strength of the solution is decreased to 0 m. Thus, in dilute solutions, w,. In other words, the effective concentration of an ion decreases with increasing ionic strength. In contrast, the activity coefficients of uncharged solutes can be greater than 1 in solutions of high ionic strength, such as seawater. 

Recall from transition state theory that the rate of a reaction depends on kg (the catalytic rate constant at infinite dilution in the given solvent), the activity of the reactants, and the activity of the activated complex. If one or more of the reactants is a charged species, then the activity coefficient of any ion can be expressed in terms of the Debye-Htickel theory. The latter treats the behavior of dilute solutions of ions in terms of electrical charge, the distance of closest approach of another ion, ionic strength, absolute temperature, as well as other constants that are characteristic of each solvent. If any other factor alters the effect of ionic strength on reaction rates, then one must look beyond Debye-Hiickel theory for an appropriate treatment. 

In practice, ideal Nemstian behavior often cannot be attained in the presence of interfering ions. The degree of interference caused by other cations is determined by the selectivity of the ion receptor for the primary ion, by the partition coefficients of the different ions over the membrane and aqueous phase, and by the relative activities of the ions in the sample solution. This imposes a second important role to the ion receptor for obtaining ion selectivity in the membrane. By selective complexation of the primary ions i, other cations j are largely excluded from the membrane, with the result that the primary ion becomes the potential determining species. When interfering ions are not completely excluded from the membrane, their contribution to the membrane potential can be treated in terms of an apparent increase of the activity of the primary ion. This is expressed in the semi-empirical Nickolsky-Eisemnan equation (Equation 4) ... 

It is an established procedure to define second-order rate coefficients in terms of concentrations rather than activities. Even if the activities of substrate and catalyst are known the rate coefficient includes the activity coefficient of the activated complex (see Vol. 2, pp. 311-312). Therefore, it is reasonable to continue to follow the same procedure no matter whether the data are obtained for solutions of strong acids or bases or for buffer solutions. (However, it is recommended to use activities rather than... 

But the symmetry factor p has been defined strictly for a single step and is related to the shape of the free-energy barrier and to the position of the activated complex along the reaction coordinate. To describe a multi step process, p must be replaced by an experimental parameter, which we call the cathodic transfer coefficient a. Instead of Eq. 41E we then write ... 

Numerous studies have appeared of the effect of added salts on the rates of reaction in solution, and the area has been reviewed (228). The key concept of the activity coefficient of the activated complex affecting the reaction rate was introduced by Brpnsted (34), which led to an expression of the type in Eq. (15), though variations exist. 

This is one of several reactions of this type in which an organic negative radical-ion and its parent molecule react in the presence of an alkali metal. It is found, rather interestingly, that the rate coefficients depend on the nature of the metal. To account for this, it has been postulated that the metal is involved in a bridging role in the activated complex, e.g., dipy.. K" ". . dipy for the case of 2,2 -dipy-ridyl (dipy) A more extreme case of this association between the radical-ion and the ion of the alkali metal used to form it occurs in the reaction of benzophenone with its negative ion. The spectrum of (benzophenone)" in dme has many hyper-fine lines caused by the interaction of the free electron with the and, when the metal is sodium, the Na nuclei. When benzophenone is added, the structure, due to the proton interaction, disappears and only the lines associated with the sodium interaction remain. To account for this, it has been suggested that the odd electron moves rapidly over all the proton positions too fast for the lines characteristic of the electron in the different proton environments to be seen), but relatively slowly from one sodium nucleus to another. Seen another way, this means that the transfer of an electron from molecule to molecule is associated with the transfer of the cation . ... 

The challenge of correcting concentrations to activities for natural waters is that the activity coefficients vary non-linearly, often in complex relations to bulk ion concentrations. For dilute electrol5fte solutions, such as some lake and river waters, it is practicable to estimate the activity coefficient of an individual ion theoretically based on that ion s charge and a general measure of the effective total ion concentration of the bulk solution. The latter measure is called the ionic... 

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