Entropies activated complexes

The main difficulty in calculating this value normally lies in the determination of the activated complex entropy. 

It is given from table 1, that an activation free energies, activation enthalpies, activation entropies and pre-exponential factors are satisfactory compared with experimental ones. Complex activation entropy is increasing, but that factor is not contradicted with well-known ideas. Changing is occurred with increasing of vibration part of active complex entropy. Rotation part of active complex entropy is changed lightly (table 2). 

Here we have the formation of the activated complex from five molecules of nitric acid, previously free, with a high negative entropy change. The concentration of molecular aggregates needed might increase with a fall in temperature in agreement with the characteristics of the reaction already described. It should be noticed that nitration in nitromethane shows the more common type of temperature-dependence (fig. 3.1). 

The insignificant alterations of the geometry, the charge distribution (see Fig. 13), the frontier orbitals, and the bond orders introduced as the educt is transferred into the activated complex point out that the latter is educt-like. However, as the activation entropies show, the reaction partners have already been arranged. For the first (AS = —161 AS° = —136 JK-1 mol-1) as well as for the second propagation... 

Quite similar equations can be formulated for AG and AH by use of the partition function f of the activated complex. It follows from equations (6) and (7) that AEp can only be evaluated if the partition functions and AEz are available from spectroscopic data or heat capacity measurements. However, if AG = AH, the entropy change AS equals zero, and if AEz also equal to zero, either AG or AH can then be identified with the potential energy change. If... 

Of course, the converse situation, in which the entropy of the transition state is lower than that of the ground state of the reactant, can also occur (Fig. 3.11). In this case, one speaks of a tight transition state tight, because rotations, vibration or motion of the activated complex are more restricted than in the ground state of the reactant. The dissociation of molecules on a surface provides an example that we shall discuss in the next section. 

St complex is the formal ionic entropy of the activated complex St p, =ASt +2rS acianis Some values used for S°reaciani are estimated ones. 

The redox reactions of the actinide elements have been the subject of a recent and authoritative review by Newton and Baker . The net activation process concept is used to interpret the experimental data. Empirical correlations shown to exist include those between the entropies of the activated complexes and their charges, and, for a set of similar reactions, between AG and AG , and and A/f . The present state of the evidence for binuclear species is discussed. 

In the formation of activated complex, if AG, AH and AS are change in free energy, enthalpy and entropy, respectively, for one gram mole of the substance, then equilibrium constant... 

Thus, the steric factor may be explained with the help of entropy change. When two molecules come together to produce the activated complex, the total translational degrees of freedom are reduced (from 6 to 3) and rotational degrees of freedom also diminish. This is compensated by an increase in vibrational degrees of freedom. But the definite orientation in forming the activated complex necessarily reduced the entropy, i.e. AS is negative. This decrease in entropy is small when reaction takes place between simple atoms. The calculated value of kbT/h corresponds to collision frequency... 

On the other hand, when reacting ions are of opposite charge, there will be a loss of charge on activated complex. Consiquently, there is a decrease in electrostriction and an increase in the entropy. This is shown schematically in Fig. 8.2. 

Furthermore, antibodies should be capable of efficiently catalyze reactions with unfavorable entropies of activation by acting as entropy traps the binding energy of the antibody being used to freeze out the rotational and translational degrees of freedom necessary to form the activated complex. This principle has been applied to the design of antibodies that catalyze both unimolecular and bimolecular reactions (see below). 

The general equation for L is Eq. (10), and the expressions to be used for C in that equation are listed in Table 1 in terms of partition functions. But the entropies of both the activated complex and the reactants, and therefore AS, can also be expressed in terms of partition functions. Therefore, C can be expressed in terms of the entropies of the activated complex and the reactants. As we shall see, it is possible to eliminate partition functions entirely. Also, in all but one case. Step 11, the entropy factor in C can be determined if one knows only the entropy of activation in those cases the entropy of a reactant or the activated complex is not needed. 

For Step 1, the adsorption of a gas to form an activated complex, the entropy of activation is... 

Is it possible that low site densities are obtained in some desorption reactions because an incorrect assumption is made about the entropy of activation For Step 5 we have assumed that AS = 0. Were we to modify this step to obtain a larger log L, we would have to postulate that the adsorbed molecule loses more entropy as the activated complex forms (4.6 e.u. per unit change in log L) than it does in Step 5 as we have described it. Such a sequence of events is not impossible for a surface reaction. But if the adsorbed molecule is immobile, it is difficult to imagine such a species losing... 

The entropy change between reactant and activated complex might not be zero. Thus, if the reactant had some rotational and/or translational... 

For the moment, we can consider the activated complex as a type of intermediate (although not isolatable) reached by the reactants as the highest energy point of the most favorable reaction path. The activated complex is in equilibrium with the reactants and is commonly regarded as an ordinary molecule, except that movement along the reaction coordinate will lead to decomposition. The activated complex can be assumed to have the associated properties of molecules, such as volume, heat content, acid-base behavior, entropy, and so forth. Indeed, formal calculations of equilibrium constants involving reactions of the activated complex to form another activated complex can be carried out (Sec. 5.6 (b)). ... 

The standard enthalpy difference between reactant(s) of a reaction and the activated complex in the transition state at the same temperature and pressure. It is symbolized by AH and is equal to (E - RT), where E is the energy of activation, R is the molar gas constant, and T is the absolute temperature (provided that all non-first-order rate constants are expressed in temperature-independent concentration units, such as molarity, and are measured at a fixed temperature and pressure). Formally, this quantity is the enthalpy of activation at constant pressure. See Transition-State Theory (Thermodynamics) Transition-State Theory Gibbs Free Energy of Activation Entropy of Activation Volume of Activation... 

These parameters (AG, A//, and A5 ) differ slightly from normal standard parameters in that the contribution of motion along the reaction coordinate toward the transition state is not included. The values are the difference in free energy, enthalpy, and entropy between 1 mole of activated complex and 1 mole of each reactant, all substances being at their standard-state concentrations (usually 1 M). 

---