Equilibrium overshoot

Another measure of the asymmetric kinetic properties of the two bases in the alanine racemase mechanism is the qualitative behavior of the equilibrium overshoots observed. Overshoots are often observed in reaction progress curves run in deuterium oxide that are initiated with a single stereoisomer that is protiated at the Ca position (Fig. 7.3). The optical activity is monitored by polarimetry or circular dichroism (CD). At equilibrium, the signal is zero, since the product is a racemic mixture of d- and L-isomers. However, when there is a significant substrate-derived KIE on the reverse direction (product being fully deuterated in a two-base mecha-... 

In routine analysis, often a one-dimensional so-called end-point titration can be automatically carried out up to a pre-set pH or potential value and with a previously chosen overall titration velocity in order to avoid overshoot, the inflection point should be sufficiently sharp and the titrant delivery must automatically diminish on the approach to that point in order to maintain equilibrium, and stop in time at the pre-set value. For instance, the Metrohm 526 end-point titrator changes both the dosing pulse length and its velocity by means of a pulse regulator in accordance with the course of the titration curve in fact, the instrument follows the titration two-dimensionally, but finally reports only a one-dimensional result. The Radiometer ETS 822 end-point titration system offers similar possibilities. However, automated titrations mostly represent examples of a two-dimensional so-called eqilibrium titration, where the titration velocity is inversely proportional to the steepness of the potentiometric titration curve hence the first derivative of the curve can usually also be recorded as a more accurate means of determining the inflection... 

A chemical reaction can be designated as oscillatory, if repeated maxima and minima in the concentration of the intermediates can occur with respect to time (temporal oscillation) or space (spatial oscillation). A chemical system at constant temperature and pressure will approach equilibrium monotonically without overshooting and coming back. In such a chemical system the concentrations of intermediate must either pass through a single maximum or minimum rapidly to reach some steady state value during the course of reaction and oscillations about a final equilibrium state will not be observed. However, if mechanism is sufficiently complex and system is far from equilibrium, repeated maxima and minima in concentrations of intermediate can occur and chemical oscillations may become possible. 

Equally important is the fact that Fig. 8.2 reveals large overshoots within the reaction zone. If these occur within the reaction zone, the O atom concentration could be orders of magnitude greater than its equilibrium value, in which case this condition could lead to the prompt NO found in flames. The mechanism analyzed to obtain the results depicted in Fig. 8.2 was essentially that given in Chapter 3 Section G2 with the Zeldovich reactions. Thus it was thought possible that the Zeldovich mechanism could account for the prompt NO. 

From other more recent studies of NO formation in the combustion of lean and slightly rich methane-oxygen-nitrogen mixtures as well as lean and very rich hydrocarbon-oxygen-nitrogen mixtures, it must be concluded that some of the prompt NO is due to the overshoot of O and OH radicals above their equilibrium values, as the Bowman and Seery results suggested. But even though O radical overshoot is found on the fuel-rich side of stoichiometric, this overshoot cannot explain the prompt NO formation in fuel-rich systems. It would appear that both the Zeldovich and Fenimore mechanisms are feasible. 

Figure 14.2 Adsorbate pressure before and after dosing, showing pressure overshoot before equilibrium is attained.

The consequences of this type of activated physical adsorption is not only that the quantity adsorbed can lie off the isotherm but also that the measured quantity of adsorption is far less than the equilibrium value. No experiments have been conducted to illustrate whether or not the quantity adsorbed lies within the hysteresis loop. The occasional failure of the vacuum volumetric method to agree with the dynamic method, which is not subject to any pressure overshoot, may in part be attributed to this phenomenon. 

Equilibrium constants for the binding between substrates and micelles — Reaction (G) — generally range from 103 to 106 for hydrophobic organic substrates. Furthermore, they are expected to increase as the hydrophobic character of the substrate increases. Figure 8.10b shows that this effect sometimes overshoots optimum solubilization. The figure shows, on a... 

Stratton and Butcher have studied the effect of interrupted flow on response (376). If a steady flow is stopped and then restarted quickly, the overshoot is missing. For longer periods of rest the overshoot gradually reappears, showing that during rest the equilibrium structure of the system is slowly re-established. 

It should be noted that not all flames have the behaviors discussed above. For example, the equilibrium species distribution in some H2-N20-Ar flames has essentially the same mole number as the reactants. As a result the adiabatic flame temperature is achieved directly in the flame front with no long recombination tail. Ammonia-oxygen flames exhibit a slow approach to chemical equilibrium, albeit with a long dissociation, not recombination, tail [279], Here the temperature in the flame front overshoots the adiabatic flame temperature, with the equilibrium temperature being approached from above as the dissociation reactions proceed. In certain highly strained, rich, hydrocarbon flames (e.g., C2H2-H2-O2), such as those used for flame-based diamond growth, the temperature can also overshoot the adiabatic flame temperature in the flame front. Here the overshoot is caused by the relatively slow dissociation of the excess acetylene [270]. 

Stars in the location of LBV (luminous blue variable), i.e. blue supergiants with M q -IO, are predicted to exhibit CNO equilibrium abundances (cf. Fig. 1 and 2), whether or not overshooting is present. The observations (22) for n Carinae and the models agree, which confirms the evolutionary status of this intriguing object as a post-MS supergiant. 

Figures 6 and 7 illustrate calculations which include the putative fast component. With kj/ks = 2 and appropriate rate constants for the formation (ks) and reversion to X (k7) of the fast component, this component would increase to nearly its equilibrium level in 3 minutes, overshoot, then slowly decline to equilibrium. The optical rotation curve computed on this basis (Figure 7) follows the experimental one very closely for the first 20 minutes.

Explosive silicon burning occurs in supernova explosions when the silicon is suddenly heated to temperatures well in excess of its quiescent burning temperature and therefore burns quite rapidly (in seconds). In Type la supernovae this happens when a runaway nuclear burning causes the temperature to overshoot stable burning, leading to a quasiequilibrium that is quite close to thermal equilibrium in Type II supernovae it occurs when the rebounding shock wave blasts the silicon shell of the presupernova star and heats it suddenly, so that the silicon undergoes rapid photodestruction and quasiequilibrium transmutation. 

As mentioned above, it is far more difficult to measure extensional viscosity than shear viscosity, in particular of mobile liquids. The problem is not only to achieve a constant stretch rate, but also to maintain it for a sufficient time. As shown before, in many cases Hencky strains, e = qet, of at least 7 are needed to reach the equilibrium values of the extensional viscosity and even that is questionable, because it seems that a stress overshoot is reached at those high Hencky strains. Moreover, if one realises that that for a Hencky strain of 7 the length of the original sample has increased 1100 times, whereas the diameter of the sample of 1 mm has decreased at the same time to 33 pm, then it will be clear that the forces involved with those high Hencky strains become extremely small during the experiment. 

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