Reversibility requirements

The principle of microscopic reversibility requires that the reverse process, ring closure of a butadiene to a cyclobutene, must also be a coiuotatory process. Usually, this is thermodynamically unfavorable, but a case in which the ring closure is energetically favorable is conversion of tra s,cis-2,4-cyclooctadiene (1) to bicyclo[4.2.0]oct-7-ene (2). The ring closure is favorable in this case because of the strain associated with the trans double bond. The ring closure occurs by a coiuotatory process. 

Since microscopic reversibility requires that the transition states for each direction of the ET reaction be identical,... 

This interpretation was proved correct by considering the oxidation of a sample of diphenylmethane that had an isotopic purity of 97.0% a,a-dideuterio and 2.7% a-deuterio by mass spectrometry. The oxidation rate observed after the initial 15-second period (see Figure 2), during which the undeuterated and monodeuterated material were destroyed, yielded a second-order rate constant, ki = 0.0148 mole"1 per second. There is thus an appreciable isotope effect ku/kD of about 6 in the ionization of diphenylmethane by potassium ferf-butoxide in DMSO(80%)-tert-butyl alcohol (20% ) at 25°C. This compares with a value of fcH/ D of 9.5 reported for the ionization of triphenylmethane (16). The observation of primary isotope effects of this magnitude requires that the protonation of the diphenylmethide ion by tert-butyl alcohol in DMSO solution does not proceed at the diffusion rate which would, by the principle of microscopic reversibility, require the absence of an isotope effect in the deprotonation step. 

The principle of microscopic reversibility, required by the laws of thermodynamics, specifies that there must be a reverse for every microscopic process. It is therefore strictly speaking incorrect to omit reverse steps, and doing so is justified only when the omitted reverse step is occurring so slowly as to have no observable effect on the reaction during the time it will be under observation. 

Schematic stress-strain curves. Superelasticity occurs at temperatures above the Af. The deformation in shape memory occurs below the Mf temperature. Reversion requires heating above the Af. 

AS = —25 29 J/ (mol K), from which Keq = 1.5 0.1 and AH0 0 were obtained. The identical rate constant for the homolysis of C-R in the presence of TEMPO and for reversion to (Co)-R in the absence of the scavenger shows that the two processes have the same rate-limiting step, that is, cobalt-carbon bond homolysis. The principle of microscopic reversibility requires that the conversion of (Co)-R to C-R have the same transition state. Scheme 8.20 rationalizes all of the observations. 

Processes occurring entirely in the surroundings of the system are usually assumed to take place reversibly this is done so that one may set T0dS0 - dQ0 - - dQ. It is then also clear what is meant by T — T. We proceed by a different route, in which the reversibility requirement for processes in the surroundings is relaxed. This does raise the point as to what is then meant by the temperature T. In general, there is no easy answer to this dilemma. However, as will be shown in Chapter 6, when departures from equilibrium are small it is still possible to adapt the concept of an average temperature for irreversible processes this is the attitude we adopt here. In these circumstances we proceed as follows On account of the inequality... 

The principle of microscopic reversibility requires the same direction for protonation or deprotonation. Base catalysed decomposition of the sulphone in (95)... 

This effect is in agreement with the findings of Ashmore et To explain the anomalously fast rate of the decomposition of NO2, these workers postulated that parallel reaction paths were occurring, one the usual molecular path and the other by a free radical mechanism. If this is correct then the principle of microscopic reversibility requires that the oxidation of NO also proceeds by two paths ... 

The principle of microscopic reversibility requires that any reversible reaction must have identical pathways for the forward and reverse reactions, simply proceeding in opposite directions. (This principle is similar to the idea that the lowest pathway over a mountain chain must be the same regardless of the direction of travel.) If the forward reaction is carbonyl migration (Mechanism 2), the reverse reaction must proceed by loss of a CO ligand, followed by migration of CO from the acyl ligand to the empty site. Because this migration is unlikely to occur to a trans position, all the product should be... 

Ciclosporin can cause considerable prolongation of the neuromuscular paralysis induced by pancuronium (42) in one patient (and also in another given vecuronium). Reversal required both neostigmine and edrophonium. Subsequently, recurarization occurred (SEDA-14, 116). Contributing factors could have been the solvent Cremophor EL in the ciclosporin formulation (Sandimmun) and minor renal dysfunction. 

The principle of microscopic reversibility requires that hydrogen exchange proceeds only through those mechanisms whose reverse... 

Two mechanisms can be written for the pyridone-catalysed reactions, depending on whether the ring opening catalyst is the pyridone, or its minor 2-hydroxypyridine tautomer (Figure 1.20). Microscopic reversibility requires the ring closure reaction to use the opposite catalyst tautomer to the ring opening reaction. 

Figure 5.32 Canonical mechanism for a retaining glycosidase or transglycosylase Whether the substrates are pyranosidases or furanosidases, whether the leaving group is axial or equatorial and whether the protonation trajectory is syn or anti depend on the enzyme. If R = R, then the principle of microscopic reversibility requires transition states 1 and 2 to be identical. More generally, the group which acts as a general acid in the first step must act as a general base in the second.

Quick reversibility requires that the metal ion is substitutionally labile thus, Cu(II) and Ni(II) are suitable ions for translocation, and Co(III) is not. Moreover, the envisaged system should be flexible enough to bring A and B moieties at occasional contact, in order to allow the metal to be transferred from one compartment to the other. 

A useful analogy involves the removal of a large weight from a spring balance. Carrying out this process strictly reversibly requires continuous equilibrium the thermodynamic equation that always applies is... 

VV is actually very nearly a linear function of the atomic number by atomic number is understood the number expressing the position of an atom in the series order of the periodic system (1 H, 2 He, 3 Li. . . ), thus practically in the order of the atomic weights the gaps required by chemistry (e.g. that of the element 43 homologous to manganese) are to be taken into account as well as the reversals required by chemical behaviour [e.g. ] 8 A (at. wt. 39-88), and 19 K (39-10)]. 

The results in II.C.3 may indicate a conflict between selectivity and reversibility requirements. In extraction from a concentrated solution comprising a strong acid (e.g., HCl), the HA should be quite strong to provide for reversibility, i.e., back-extraction with water at concentrations approaching those in the feed. 

Figure 6.8. Inversion of n -adsorbed cyclopentane by top-side addition of a deuterium atom to a n -alkenyl intermediate Eley-Rideal step note that Microscopic Reversibility requires that the jr-alkenyl can be formed by topside removal of an atom.

The expression on the right specifically expresses what the one on the left implies. This is the fact that entropy may not be generated because this would reduce the amount of heat being supplied, falsifying the result. In the case of water formation, reversibility requires = const., and in the case of NO2 dimerization, ji = 0 ... 

The temperature, the volume of crystal, and the number of atoms are assumed to be constant. The reversibility requirement in the definition of y means that the composition in the surface region is also in thermodynamic equilibrium. The distances between atoms remain unchanged. 

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