Activated complex activation energy

In many instances tire adiabatic ET rate expression overestimates tire rate by a considerable amount. In some circumstances simply fonning tire tire activated state geometry in tire encounter complex does not lead to ET. This situation arises when tire donor and acceptor groups are very weakly coupled electronically, and tire reaction is said to be nonadiabatic. As tire geometry of tire system fluctuates, tire species do not move on tire lowest potential energy surface from reactants to products. That is, fluctuations into activated complex geometries can occur millions of times prior to a productive electron transfer event. 

In summary, it seems that for most Diels-Alder reactions secondary orbital interactions afford a satisfactory rationalisation of the endo-exo selectivity. However, since the endo-exo ratio is determined by small differences in transition state energies, the influence of other interactions, most often steric in origin and different for each particular reaction, is likely to be felt. The compact character of the Diels-Alder activated complex (the activation volume of the retro Diels-Alder reaction is negative) will attenuate these eflfects. The ideas of Sustmann" and Mattay ° provide an attractive alternative explanation, but, at the moment, lack the proper experimental foundation. 

Table 2.10 shows the effect of substituents on the endo-exo ratio. Under homogeneous conditions there is hardly any substituent effect on the selectivity. Consequently the substituents must have equal effects on the Gibbs energies of the endo and the exo activated complex. 

Activation Parameters. Thermal processes are commonly used to break labile initiator bonds in order to form radicals. The amount of thermal energy necessary varies with the environment, but absolute temperature, T, is usually the dominant factor. The energy barrier, the minimum amount of energy that must be suppHed, is called the activation energy, E. A third important factor, known as the frequency factor, is a measure of bond motion freedom (translational, rotational, and vibrational) in the activated complex or transition state. The relationships of yi, E and T to the initiator decomposition rate (kJ) are expressed by the Arrhenius first-order rate equation (eq. 16) where R is the gas constant, and and E are known as the activation parameters. 

The position of this equilibrium is related to the free energy required for attainment of the transition state. The double-dagger superscript ( ) is used to specify that the process under consideration involves a transition state or activated complex ... 

The transition state represents the highcsl-energy structure involved in this step of the reaction. It is unstable and can t be isolated, but we can nevertheless imagine it to be an activated complex of the two reactants in which both the C=C tt bond and H-Br bond are partially broken and the new C-H bond is partially formed (Figure 5.5). 

We call the carbocation, which exists only transiently during the course of the multistep reaction, a reaction intermediate. As soon as the intermediate is formed in the first step by reaction of ethylene with H+, it reacts further with Br in a second step to give the final product, bromoethane. This second step has its own activation energy (AG ), its own transition state, and its own energy change (AG°). We can picture the second transition state as an activated complex between the electrophilic carbocation intermediate and the nucleophilic bromide anion, in which Br- donates a pair of electrons to the positively charged carbon atom as the new C-Br bond starts to form. 

An explanation of the relationship between reaction rate and intermediate stability was first advanced in 1955. Known as the Hammond postulate, the argument goes like this transition states represent energy maxima. They are high-energy activated complexes that occur transiently during the course of a reaction and immediately go on to a more stable species. Although we can t... 

Transition state (Section 5.9) An activated complex between reactants, representing the highest energy point on a reaction curve. Transition states are unstable complexes that can t be isolated. 

Forming the activated complex shown in Figure 11.8 requires the absorption of relatively little energy, because it requires only the weakening of reactant bonds rather than their rupture. 

For a certain reaction, a is 135 kj and AH = 45 kj. In the presence of a catalyst, the activation energy is 39% of that for the uncatalyzed reaction. Draw a diagram similar to Figure 11.11 but instead of showing two activated complexes (two humps) show only one activated complex (i.e., only one hump) for the reaction. What is the activation energy of the uncatalyzed reverse reaction ... 

Figure 8-8 shows the analogous situation for a chemical reaction. The solid curve shows the activation energy barrier which must be surmounted for reaction to take place. When a catalyst is added, a new reaction path is provided with a different activation energy barrier, as suggested by the dashed curve. This new reaction path corresponds to a new reaction mechanism that permits the reaction to occur via a different activated complex. Hence, more particles can get over the new, lower energy barrier and the rate of the reaction is increased. Note that the activation energy for the reverse reaction is lowered exactly the same amount as for the forward reaction. This accounts for the experimental fact that a catalyst for a reaction has an equal effect on the reverse reaction that is, both reactions are speeded up by the same factor. If a catalyst doubles the rate in one direction, it also doubles the rate in the reverse direction. 

Sketch a potential energy diagram which might represent an endothermic reaction. (Label parts of curve representing activated complex, activation energy, net energy absorbed.)... 

The last factor is, again, the rate that molecules can pass over the energy barrier—the activated complex for precipitation. Again there is a rate constant, kp, that is determined by temperature and the height of the energy barrier to precipitation. 

The slope of the Arrhenius plot has units (temperature) 1 but activation energies are usually expressed as an energy (kJ mol 1), since the measured slope is divided by the gas constant. There is a difficulty, however, in assigning a meaning to the term mole in solid state reactions. In certain reversible reactions, the enthalpy (AH) = E, since E for the reverse reaction is small or approaching zero. Therefore, if an independently measured AH value is available (from DSC or DTA data), and is referred to a mole of reactant, an estimation of the mole of activated complex can be made. 

The following assumptions are made (i) the activated complexes are in equilibrium with the reactants, (ii) the energy of a molecule is not altered when an activated complex is substituted for a nearest neighbour, and (iii) the products do not affect the course of reaction, except to define a boundary in surface processes. The various cases can be recognized from the magnitude of the pre-exponential term and calculated values [515] are summarized in Table 7. Low values of A indicate a tight surface complex whereas higher values are associated with a looser or mobile complex. 

Activation energy values for the recombination of the products of carbonate decompositions are generally low and so it is expected that values of E will be close to the dissociation enthalpy. Such correlations are not always readily discerned, however, since there is ambiguity in what is to be regarded as a mole of activated complex . If the reaction is shown experimentally to be readily reversible, the assumption may be made that Et = ntAH and the value of nt may be an indication of the number of reactant molecules participating in activated complex formation. Kinetic parameters for dissociation reactions of a number of carbonates have been shown to be consistent with the predictions of the Polanyi—Wigner equation [eqn. (19)]. 

Use die activated complex theory for explaining clearly how the applied potential affects the rate constant of an electron-transfer reaction. Draw free energy curves and use proper equations for your explanation. 

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