Reaction characteristics, computing values

The standard entropy change in a chemical reaction is computed from tabulated data in much the same way as the standard change in enthalpy. However, there is one important difference The standard entropy of elements is not assigned a conventional value of zero. The characteristic value of the entropy of each element at 25 °C and 1 atm pressure is known from the third law. As an example, in the reaction... 

Computing Cumulative and Instantaneous Values of Reaction Characteristics... 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

The direct method (DM) for solution of this set of equations was proposed by Atherton et al. [5], and in a somewhat a modified form by Dickinson and Gelinas [4] who solved r sets of equations each of size In consisting of Eq. (1) coupled with a particular j—value of Eq. (2). Shuler and coworkers [5] took an alternative approach in the Fourier Amplitude method in which a characteristic periodic variation is ascribed to each a, and the resulting solution of (1) is Fourier analyzed for the component frequencies. These authors estimate that 1.2r2 5 solutions of Eq. (1) together with the appropriate Fourier analyses are required for the complete determination of the problem. Since even a modest reaction mechanism (e.g. in atmospheric chemistry or hydrocarbon cracking or oxidation) may easily involve 100 reactions with several tens of species, it is seen that a formidable amount of computation can result. 

The characteristic roots are determined by transforming experimental compositions along appropriate reaction paths into the B system of coordinates. Equations (44) and (46) are used to compute the matrix from the matrix X determined from the straight line reaction paths and the equilibrium composition. Each observed composition (<) is transformed by the matrix X into 3(0 [Eq- (40)]- The decay of each 6, with time is given by the set of Eqs. (27) and the value of — X, can be determined from the slope of the straight line obtained from a graph of In bj vs time. 

In one important respect, this derivation is not quite complete. Just as there are two ways in which the encounter complex A -B can be formed, so there are two ways in which it can react. Because the average reaction time is comparable to the time taken for the steady state to be set up, only a certain fraction w of the excited molecules will obey the Stem-Volmer equation. The remaining (1 —h ) reacts immediately after excitation and so does not contribute to the relative fluorescence yield. Put another way, if a molecule of A has a B within the reaction distance when it is excited, it may react immediately and so will not fluoresce. As may be predicted, the effect of this transient excess reactivity is more important the harder it is for A and B to diffuse apart, i.e., the greater the viscosity of the medium, and the more efficient is the reaction. Thus < >/( >o = W(1+ 2< b < o)> the stationary rate coefficient may be evaluated if w is known. The latter can be calculated from the expression w = exp(— VoCj,), where is a characteristic reaction volume surrounding A and w represents the probability that no B molecule will be found inside this space. Vjy is a function of the diffusion coefficients of A and B, the mean lifetime of A in the absence of B(xo) and the effective encounter distance. In most cases approximate values of w can be calculated and then, by successive approximations, the stationary rate coefficients and encounter distances which best lit the data are computed. 

An imponant characteristic of the reaction variable X defined in this way is that it has the same value for each molecular species involved in a reaction this is illustrated in the following e.xample. Thus, given the initial mole numbers of all species and X (or the number of moles of one species from which the molar extent of reaction X can be calculated) at time one can easily compute all other mole numbers in the system. In this way the complete progress of a chemical reaction (i.e., the change in mole numbers of all the species involved in the reaction) is given by the value of the single variable X. 

The values of redox potentials were tabulated in numerous collections [43-47], the latest collections being critically selected. The potentials of redox systems with participation of radicals and species in excited electronic states are discussed in Refs. [56, 57]. There is no need to measure the potentials for all redox pairs (and, correspondingly, AG for all known reactions). If we obtain the partial values for a number of ions and compounds, the characteristic values for any other reactions can be computed. The idea of calculation is based on the fact that the emf value only depends on the initial and final states of the system, being independent of the existence of any intermediate states. This fact is of great importance for systems, for which it is impossible, or extremely difficult, to prepare a reversible electrode (redox couples containing oxygen or active metals). From considerations of the equilibria with participation of a solvated electron, the value that determines the value of the constant in Eq. (7) was estimated - 2.87 V (SHE) [56]. 

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