Microscopic reversibility, definition

The mechanism is in complete agreement with results from recent tryptophan fluorescence experiments (which, due to the inviolability of microscopic reversibility, also hold in the synthesis mode) that establish definitively that (i) P, cannot simply bind spontaneously, (ii) an enzyme species with all three catalytic sites occupied is the only catalytically competent species, and (iii) release of product and binding of substrate caimot be simultaneous, rather product release must precede substrate binding [38]. 

Marcus and Rice6 made a more detailed analysis of the recombination from the point of view of the reverse reaction, the unimolecular decomposition of ethane, C2Ha - 2CH3. By the principle of microscopic reversibility the transition states must be the same for forward and reverse paths. Although they reached no definite conclusion they pointed out that a very efficient recombination of CH3 radicals would imply a very high Arrhenius A factor for the unimolecular rate constant of the C2H6 decomposition which in turn would be compatible only with a very "loose transition state. Conversely, a very low recombination efficiency would imply a very tight structure for the transition state and a low A factor for the unimolecular decomposition. 

Definition of Critical and Rate-Limiting Bottlenecks" The hypothesis of local equilibrium within the reservoirs means that the set of transitions from reservoir to reservoir can be described as a Markov process without memory, with the transition probabilities given by eq. 4. Assuming the canonical ensemble and microscopic reversibility, the rate constant Wji, for transitions from reservoir i to reservoir j can be written... 

By definition, the transition state cannot engage in chemical reactions with other species. It can either pass on to the product state or revert to the reactants, that is, to the products of the reverse reaction. (According to the principle of microscopic reversibility, the forward and reverse of the same reaction must proceed through the same transition state.)... 

Both Newton s equation of motion for a classical system and Schrodinger s equation for a quantum system are unchanged by time reversal, i.e., when the sign of the time is changed. Due to this symmetry under time reversal, the transition probability for a forward and the reverse reaction is the same, and consequently a definite relationship exists between the cross-sections for forward and reverse reactions. This relationship, based on the reversibility of the equations of motion, is known as the principle of microscopic reversibility, sometimes also referred to as the reciprocity theorem. The statistical relationship between rate constants for forward and reverse reactions at equilibrium is known as the principle of detailed balance, and we will show that this principle is a consequence of microscopic reversibility. These relations are very useful for obtaining information about reverse reactions once the forward rate constants or cross-sections are known. Let us begin with a discussion of microscopic reversibility. 

The assumption of a definite location for the negative charge on the j8-carbon requires that 59a and 60a both be on the lowest energy path for substitution and isomerization. That this location should be formed anti derives from orbital symmetry, i.e. microscopic reversibility suggests that anti entry of one halide and syw-departure of the other are improbable. We deduce, therefore, that the substitutions in (142) require at least three elementary steps, e.g. cis-1 - 59a -> 60b -v cis-2 isomerizations with exchange require at least three steps, e.g. cis-l 59a —> 59b - trans-2 isomeriza-... 

Until recently, it had not been established whether the association of O atoms with CO was bi- or term olecular. Althou Dixon-Lewis and Linnett [30] and Buckler and Norrish [368] considered their results to be> more consistent with a bimolecular association, Baldwin et al. [395] have pointed out that their interpretation was based on too simple a mechanism for data obtained with KCl coated vessels (see Sect. 10.1.3(6)(iii) and Fig. 68). Shock tube studies definitely indicate that the dissociation is second order at lower pressures, and this implies by microscopic reversibility that the reverse association reaction is termolecular. Kondratiev and Intezarova... 

Magnetic moment, 153, 155, 160 Magnetic quantum number, 153 Magnetization, 160 Magnetogyric ratio, 153, 160 Main reaction, 237 Marcus equation, 227, 238, 314 Marcus plot, slope of, 227, 354 Marcus theory, applicability of, 358 reactivity-selectivity principle and, 375 Mass, reduced, 189, 294 Mass action law, 11, 60, 125, 428 Mass balance relationships, 19, 21, 34, 60, 64, 67, 89, 103, 140, 147 Maximum velocity, enzyme-catalyzed, 103 Mean, harmonic, 370 Mechanism classification of. 8 definition of, 3 study of, 6, 115 Medium effects, 385, 418, 420 physical theories of, 405 Meisenheimer eomplex, 129 Menschutkin reaction, 404, 407, 422 Mesomerism, 323 Method of residuals, 73 Michaelis constant, 103 Michaelis—Menten equation, 103 Microscopic reversibility, 125... 

A dtserepancy between SCK and Noyes theories led Natjvi rial, to reformulate holh[l94. litis was not necessary. The discrepancy results limn a violation of the Principle of Microscopic Reversibility in Noves original treatment 09. I he present definition ol hit) avoids that iolation. 

A tliscrepnncy bclucon SCK and Noyes ihoo-l ies led Naqvi ri til. U) rerormulalc h()lh l94. This was iiol necessary. The discrepancy residis Ironi a v iolalion of the Principle of Microscopic Reversibility in Noyes original irealincnt 69. The present definition at li(l) avoids that violation. 

It is difficult to experimentally detect simultaneously reactants and products in definite quantum states. Either the quantum state of products or the quantum state of reactants is usually detected. In the first case, we have to speak about the eneigy distribution in the reaction products, and in the second case, about the reaction of excited molecules. These approaches are equivalent because the corresponding rate constants are related by the principle of microscopic reversibility. 

What is the physical nature of the Gibbs free energy, and what is free about it We can consider this question first from the viewpoint of fundamental thermodynamic definitions, with no microscopic molecular connotations. For a reversible change of state carried out under conditions of constant T and P, we can write... 

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