Reverse activation energies

A detailed analysis shows that the activation energy (reverse) differs from E (forward) by the difference in enthalpy of the reactants and the products. For the reactions Hg + I2 2HI this enthalpy difference is 10 kJ mole" (Table VI-10) hence, with the result from Example 10-5, we can state that the value of E (reverse) for the reaction 2HI —> Hg -b I2 is 180 -t- 10 = 190 kJ mole". ... 

As tire reaction leading to tire complex involves electron transfer it is clear that tire activation energy AG" for complex fonnation can be lowered or raised by an applied potential (A). Of course, botlr tire forward (oxidation) and well as tire reverse (reduction) reaction are influenced by A4>. If one expresses tire reaction rate as a current flow (/ ), tire above equation C2.8.11 can be expressed in tenns of tire Butler-Volmer equation (for a more detailed... 

Below a critical size the particle becomes superparamagnetic in other words the thermal activation energy kTexceeds the particle anisotropy energy barrier. A typical length of such a particle is smaller than 10 nm and is of course strongly dependent on the material and its shape. The reversal of the magnetization in this type of particle is the result of thermal motion. 

Endotliermic Decompositions These decompositions are mostly reversible. The most investigated substances have been hydrates and hydroxides, which give off water, and carbonates, which give off CO9. Dehydration is analogous to evaporation, and its rate depends on the moisture content of the gas. Activation energies are nearly the same as reaction enthalpies. As the reaction proceeds in the particle, the rate of reaction is impeded hy resistance to diffusion of the water through the already formed product. A particular substance may have sever hydrates. Which one is present will depend on the... 

The reverse reaction, closure of butadiene to cyclobutene, has also been explored computationally, using CAS-SCF calculations. The distrotatory pathway is found to be favored, although the interpretation is somewhat more complex than the simplest Woodward-Hoffinann formulation. It is found that as disrotatory motion occurs, the singly excited state crosses the doubly excited state, which eventually leads to the ground state via a conical intersection. A conrotatory pathway also exists, but it requires an activation energy. 

It may be unsafe to carry this discussion further until more data are available. Knowledge of the activation parameters would be especially desirable in several respects. Reactivity orders involving different reagents or substrates may be markedly dependent on temperature. Thus, in Table IV both 2- and 4-chloroquinolines appear to be about equally reactive toward sodium methoxide at 86,5°. However, the activation energies differ by 3 kcal/mole (see Section VII), and the relative rates are reversed below and above that temperature. Clearly, such relative rates affect the rs-/ ro- ratios. 

In view of the enthalpy and activation energy (see Section II, B, 1) of the decomposition of arylpentazoles the activation energy for the reversal of the decomposition, the 1,3-addition of elementary nitrogen to arylazides, can be estimated to be 25-30 kcal/mole, an amount which does not exclude the reaction. To ascertain whether the decomposition of arylpentazoles is a reversible reaction, p-ethoxyphenylazide-[j8-N ] (see Section II, B, 3) adsorbed on charcoal was exposed to unlabeled nitrogen (45-50°, 380 atm, 100 hr), but the anticipated exchange of between the reactants was not detected. ... 

Kinetic studies on 2-, 3-, and 4-chloro-l-methylpyridinium salts showed a 30 10 ratio of the reaction rates at 50° with 4-nitro-phenoxide ion in methanol. The activation energy for reaction at the 4-position is one kilocalorie lower ( 8-fold higher rate) than for reaction at the 2-position. The reversal in rates relative to the corresponding halopyridines is the result of a much higher entropy of activation for the 2-chloro compound. The 3-chloro compound has a favorable entropy of activation also, but the energy of activation is about 13 kcal higher than that of the isomers (cf. Table II and Section III, A, 2). 

The general principle that activation of para substitution is greater than of ortho substitution holds true also for an azinium moiety in the one instance studied. Thus, the activation energy for the 4-chloropyridine quaternary salt 280 (Table II, line 9) is 1 kcal lower than that for the 2-isomer (line 5). The rate relation (2- > 4-isomer) is controlled by the entropies of activation in this reaction due to electrostatic attraction in the transition state (281). The reverse rate relation (4- > 2-position) is predicted for aminations of such quaternary compounds due to electrostatic repulsion (282) plus the difference in E. A kinetic study of the 2- and 4-pyridine quaternary salts... 

Table XIV, line 3). The rates are equal (only at 20°) due to a large, compensating difference between the entropies of activation. In piperidino-dechlorination, 4-chloroquinoline (Table XI, line 3) has a higher and a lower rate (by about 200-fold at 20°) than 1-chloroisoquinoline (Table XIV, line 1). This reversal of reactivity and of the relationship of the activation energies is attributed to the factors in amination reactions mentioned above. The relative reactivity of the chloro groups in 2,4-dichloroquinoline with methanolic methoxide is given as a 2 1 rate ratio of 4- to 2-displacement. 

This is the general expression for film growth under an electric field. The same basic relationship can be derived if the forward and reverse rate constants, k, are regarded as different, and the forward and reverse activation energies, AG are correspondingly different these parameters are equilibrium parameters, and are both incorporated into the constant A. The parameters A and B are constants for a particular oxide A has units of current density (Am" ) and B has units of reciprocal electric field (mV ). Equation 1.114 has two limiting approximations. 

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 ... 

The relationship between activation energies for the forward and reverse reactions can be expressed mathematically. The activation energy is denoted by the symbol A// (read delta-//-cross ) and the heat of the reaction by AH. Hence we may write ... 

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. 

Catalysts increase the rate of reactions. It is found experimentally that addition of a catalyst to a system at equilibrium does not alter the equilibrium state. Hence it must be true that any catalyst has the same effect on the rates of the forward and reverse reactions. You will recall that the effect of a catalyst on reaction rates can be discussed in terms of lowering the activation energy. This lowering is effective in increasing the rate in both directions, forward and reverse. Thus, a catalyst produces no net change in the equilibrium concentrations even though the system may reach equilibrium much more rapidly than it did without the catalyst. 

Furthermore, we have to keep in mind that differences in thermodynamic stability of reagent(s) and product(s) do not include a kinetic parameter, the activation energy. The assumption made by Vincent and Radom, as well as by Brint et al., that the addition of N2 to the phenyl cation is a reaction with zero activation energy may be correct for the gas phase, but perhaps not for reaction in solution. One must therefore add an activation energy barrier to the calculated thermodynamic stability mentioned above for the reverse reaction (C6HJ + N2 — C6H5NJ). 

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. 

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)]. 

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