Thermodynamically symmetric reaction

In Fig. 7 we have taken a symmetrical reaction where, apart from the isotopic mixing, AG ° = 0. One of the first successes of the Marcus theory was the correlation of rates for such homogeneous reactions with the rates found for the same electron transfer taking place on an electrode (Marcus, 1963). The theory then went on to predict the rates of cross reactions between two different redox couples in terms of the kinetic and thermodynamic properties of the two redox couples. The free energy profile for an unsymmetrical cross reaction such as (17) is shown in Fig. 8. The free energy of activation depends... 

The free energies in (18) are illustrated in Fig. 10. It can be seen that GA is that part of AG ° available for driving the actual reaction. The importance of this relation is that it allows AGXX Y to be calculated from the properties of the X and Y systems. In thermodynamics, from a list of n standard electrode potentials for half cells, one can calculate j (m — 1) different equilibrium constants. Equation (18) allows one to do the same for the %n(n— 1) rate constants for the cross reactions, providing that the thermodynamics and the free energies of activation for the symmetrical reactions are known. Using the... 

Fig. 9 Test of the Marcus theory of electron transfer where fcca,c for the cross-reaction O, + R - R, + On is calculated from the thermodynamic free energies and the free energies of activation of the symmetrical reactions. The symbols are as follows O, Ce(IV), x IrCl -, + Mo(CN)j-, Fe(CN) ", R O, Fe(CN)J , A Mo(CN)f, W(CN)<-...

The idea of kinetic versus thermodynamic control can be illustrated by discussing briefly the case of formation of enolate anions from unsymmetrical ketones. This is a very important matter for synthesis and will be discussed more fully in Chapter 1 of Part B. Most ketones, highly symmetric ones being the exception, can give rise to more than one enolate. Many studies have shown tiiat the ratio among the possible enolates that are formed depends on the reaction conditions. This can be illustrated for the case of 3-methyl-2-butanone. If the base chosen is a strong, sterically hindered one and the solvent is aptotic, the major enolate formed is 3. If a protic solvent is used or if a weaker base (one comparable in basicity to the ketone enolate) is used, the dominant enolate is 2. Enolate 3 is the kinetic enolate whereas 2 is the thermodynamically favored enolate. 

Actually the assumptions can be made even more general. The energy as a function of the reaction coordinate can always be decomposed into an intrinsic term, which is symmetric with respect to jc = 1 /2, and a thermodynamic contribution, which is antisymmetric. Denoting these two energy functions h2 and /zi, it can be shown that the Marcus equation can be derived from the square condition, /z2 = h. The intrinsic and thermodynamic parts do not have to be parabolas and linear functions, as in Figure 15.28 they can be any type of function. As long as the intrinsic part is the square of the thermodynamic part, the Marcus equation is recovered. The idea can be taken one step further. The /i2 function can always be expanded in a power series of even powers of hi, i.e. /z2 = C2h + C4/z. The exact values of the c-coefficients only influence the... 

In most cases, more 1,4- than 1,2-addition product is obtained. This may be a consequence of thermodynamic control of products, as against kinetic. In most cases, under the reaction conditions, 15 is converted to a mixture of 15 and 16, which is richer in 16. That is, either isomer gives the same mixture of both, which contains more 16. It was found that at low temperatures, butadiene and HCl gave only 20-25% 1,4 adduct, while at high temperatures, where attainment of equilibrium is more likely, the mixture contained 75% 1,4 product. 1,2 Addition predominated over 1,4 in the reaction between DCl and 1,3-pentadiene, where the intermediate was the symmetrical (except for the D label) HjCHC—CH—CHCH2D. Ion pairs were invoked to explain this result, since a free ion would be expected to be attacked by Cl equally well at both positions, except for the very small isotope effect. 

Many researchers have considered models for possible intermediates in the nitrogenase reaction. Two possible dinitrogen attachments to the FeMoco factor of MoFe-protein have been put forward. Symmetric, edge- or side-on modes discussed by Dance48 would lead to a reaction sequence such as is shown in reaction 6.11. In contrast, the asymmetric end-on terminal mode discussed in the work of Nicolai Lehnert50 may be favored thermodynamically and by molecular orbital calculations. Reaction sequence 6.13 below illustrates one scenario for the asymmetric model. 

Reaction of the unsymmetrical substituted acetylene Me3SiC=CPy with 1 yields, after substitution of the alkyne, the kinetically favored unsymmetrical substituted complex 55a as well as the symmetrically substituted, thermodynamically more stable product 55b [38]. 

The latter results have been explained on the basis of the following reaction scheme. The 1,2-regioisomers derived from butadiene are obtained through a non-symmetrical iodonium ion intermediate. The subsequent nucleophilic attack on the allylic position gives, under kinetic control, 1,2-derivatives. Nevertheless, when poorer nucleophiles such as benzene or acetonitrile are employed, the conversion of the initially formed iodonium ion into the allylic cation has been suggested to give 1,4-products, under thermodynamic control. However, other alternatives like nucleophilic attack involving allylic participation have not been excluded for the formation of 1,4-derivatives. 

With respect to the formal potential of the surface electrode reaction, Figs. 2.45c and 2.46 show that the split peaks are symmetrically located around the formal potential, which enables precise determination of this important thermodynamic parameter. 

Carbon dioxide is a symmetrical, linear triatomic molecule (0 = C=0) with a zero dipole moment. The carbon-to-hydrogen bond distances are about 1.16A, which is about 0.06A shorter than typical carbonyl double bonds. This shorter bond length was interpreted by Pauling to indicate that greater resonance stabilization occurs with CO2 than with aldehydes, ketones, or amides. When combined with water, carbonic acid (H2CO3) forms, and depending on the pH of the solution, carbonic acid loses one or two protons to form bicarbonate and carbonate, respectively. The various thermodynamic parameters of these reactions are shown in Table I. 

The slope of the plot is a function of the reaction stoichiometry although the functional dependence is complicated. In addition, the thermodynamic point, i.e., the point which corresponds to Keq (which is at 1 X 10"5 for all curves given here) does not correspond to the point of inflection, and even for the simplest case, dimerization, the point of inflection does not correspond to the midpoint. In addition, the curves are not symmetrical about the midpoint. Thus, no simple analysis of curve shape based on midpoint value or inflection point can give the thermodynamic or stoichiometric numbers. 

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