Marcus equilibrium-rate theory, reaction

The rationalization of PER by Marcus is based on a simple model of the reaction profile, that of two intersecting parabolas (Pigure 5.10) [35]. In most applications of the Marcus equilibrium-rate theory, the reaction coordinate is a normalized quantity between 0 and 1, measuring in a generalized way the progress of reaction it is usually poorly defined from a geometrical, structural point of view. Indeed, when the word structure is used in works on PER, it refers mainly to the connectivity... 

A b is the Boltzmann constant, a transmission coefficient of unity is assumed). The second concept is the equilibrium-rate theory of Marcus [32], which may be considered as an interpretation of the empirical relationships between (thermodynamic) free energy of reaction and (kinetic) energy of activation [33], the so-called free-energy relationships (PER). This theory states that... 

In the o.s. reaction, the ion pair A+ - B is formed in a first step. The corresponding equilibrium constant can usually be obtained from simple electrostatic models. In this "ideal" case specific chemical interactions can be neglected and the rate constant of the E.T. step follows the theory of R.A. Marcus (see for example Marcus, 1975, or Cannon, 1980). In the i.s. reaction each of the three steps in reaction (9.2) may determine the reaction rates. The lability of the coordinated ligands at the... 

Rate and equilibrium constants have been measured for representative intramolecular aldol condensations of dicarbonyls.60a For the four substrates studied (32 n = 2, R = Me n = 3, R = H/Me/Ph), results have been obtained for both the aldol addition to give ketol (33), and the elimination to the enone (34). A rate-equilibrium mismatch for the overall process is examined in the context of Baldwin s rales. The data are also compared with Richard and co-workers study of 2-(2-oxopropyl)benzaldehyde (35), for which the enone condensation product tautomerizes to the dienol60b (i.e. /(-naphthol). In all cases, Marcus theory can be applied to these intramolecular aldol reactions, and it predicts essentially the same intrinsic barrier as for their intermolecular counterparts. 

Detailed analysis of the rate and equilibrium constants determined for both phases of intramolecular aldol condensation reactions (13 —>15, 16—>18, and 19—>21) in terns of Marcus theory, has established that the intrinsic barriers for die intramolecular reactions are the same as those determined previously for the intermolecular counterparts.31 Consequently, rate constants for intramolecular aldol reactions are predictable from the energetics of the reactions and the effective molarity can be calculated. An associated discussion of Baldwin s rales suggests that they are a consequence of the need to achieve a conformation from which reaction can take place... 

In order to calculate values of G from equation (29) we have to know not only the kinetic parameters but also the thermodynamic driving force for the SN2 reaction. We are grateful for Dr Abraham s advice and help in calculating these values. His values for the reactants and products are collected together in Table 1 (Abraham and McLennan, 1977). The results for the calculation of G are displayed in Table 2 which has been arranged like a football league table. Only half the table needs to be filled in, since, as shown in (31), the Marcus theory does obey the proper thermodynamic constraint that the ratio of the rates of the forward and backward reactions is given by the equilibrium... 

As a first step toward reducing the amount of empirical information needed to go from equilibrium to rate constant, we developed multidimensional Marcus theory (MMT)8 as a way of treating concerted reactions that could... 

Bronsted plots for other carbon acids may be curves but this is not detected because of the limited range of reactivity over which the reactions can be studied and the Bronsted relation is therefore a sufficiently good approximation. The demonstration of a sharply curved Bronsted plot for diazoacetate ion came shortly after a new rate-equilibrium equation for proton transfer reactions had been proposed by Marcus. This will be discussed fully in Sect. 5.2 but it should be noted here that with this new theory, Bronsted plot curvature is easily accounted for. 

Recently a new method has been developed for analysing rate-equilibrium data for proton transfer reactions (Marcus Theory) [200], Although the theory has not been tested extensively, it seems to have received fairly wide acceptance. This new treatment leads to various parameters which are useful in understanding results for carbon acids and offers an explanation for some anomalies in Bronsted plots such as curvature and Bronsted exponents outside the range 0 < a or j3 < 1. 

The radiation chemistry of 2-propanol is analogous to that of methanol, that is, the main reactive species are Cs and (CH3)2 COH. In alkaline solution, (CH3)2 COH deprotonates to (CH3)2CO . In the presence of N2O or acetone, es is converted to (CH3)2 C0H/(CH3)2C0 by the reactions in Eqs. 30 and 18, or the reaction of Eq. 20, respectively. The solvated electron in 2-propanol has been utilized to study electron-transfer reactions between aromatic radical anions (donor) and aromatic molecules (acceptor) [16]. The donor-acceptor pairs studied were pyrene-anthracene, pyrene-9,10-dimethylanthracene and w-terphenyl-/ -terphenyl. In the first two cases an equilibrium was established and the parameters forward and kback were measured this was the first example of the measurement of an equilibrium constant by use of pulse radiolysis. The rate constants for the electron-transfer reactions were examined in terms of the Marcus theory [17]. 

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