Quasi-equilibrium ratio

To show that a quasi-equilibrium ratio [N2(e)/Np(e)]ss is established very quickly, Eq. (5) is solved for a step function laser pulse (laser power Pp, = 0, t < 0 PL = constant, t > 0),... 

Thermodynamic control (Figure 1, right) is based on adsorption of substances until quasi-equilibrium stage. In this case, the surface ratio of the adsorbed species is defined by the ratio of products of their concentration and binding constant. This deposition is much less influenced by poorly controllable fluctuations of external conditions and provides much better reproducibility. The total coverage can be almost 100%. Because of these reasons, the thermodynamic control is advantageous for preparation of mixed nanostructured monolayers for electrochemical applications including a formation of spreader-bar structures for their application as molecular templates for synthesis of nanoparticles. 

Under ordinary mass spcctrometric conditions only unimolecular reactions of excited ions occur, but at higher ionization chamber pressures bimolecular ion molecule reactions are observed in which both the parent ions and their unimolecular dissociation product ions are reactants. Since it requires a time of 10 5 sec. to analyze and collect the ions after their formation all of the ions in the complete mass spectrum of the parent molecule are possible reactants. However, in radiation chemistry we are concerned with the ion distribution at the time between molecular collisions which is much shorter than 10 5 sec. For example, in the gas phase at 1 atm. the time between collisions is 10 10 sec. and in considering the ion molecule reactions that can occur one must know the amount of unimolecular decomposition within that time. By utilizing the quasi-equilibrium theory of mass spectra6 it is possible to calculate the ion distribution at any time. This has been done for propane at a time of 10 10 sec.,24 and although the parent ion is increased by a factor of 2 the relative ratios of the other ions are about the same as in the mass spectrum observed in 10 r> sec. Thus for gas phase radiolysis the observed mass spectrum is a fair first approximation to the ion distribution. In... 

The quasi-equilibrium character of expansion ratio distribution along foam column height is also confirmed by the study of the pressure profile (Fig. 5.16). At levels higher than... 

Does not include equations that can be replaced by stoichiometric constraints or yield ratios. If quasi-equilibrium ole + cat — X, can be assumed as in network 6.9, kh is negligible and only seven coefficients are needed. 

Strictly true for the quasi-equilibrium CO response of Fig. 1, but for the CH4 response the curve produced is not fitted by a simple exponential. It can perhaps be modeled by two or more pools in par lel of different size and reactivity each pool has a t that can be estimated from fitting the observed response, but we can measure neither the capacity ( ) nor the rate for an individual pool but only their ratio. 

On Figure 34 we note a sharp drop from the interpolated NO-level between 0730 and 0740 hours. This reflects the previously noted failure of the data to approach quasi-equilibrium between NO, NO2, O3, and sunlight intensity under high-oxidant conditions. The NO-conversion seems to proceed at roughly the observed rate after the transient is absorbed in the system however, the level ends up closer to Azusa values than to El Monte values. If we were to use 0830 El Monte concentrations as initial values, we would have a lower HC/NO-ratio and could expect still slower nitric oxide conversion rates. Thus, nitric oxide and hydrocarbon decay more like the Azusa data than the El Monte data. 

A steady state implies that the activity of the daughter and its precursor are equal and do not change in time. However, it is easy to see that in a finite time interval such a state of so-called secular equilibrium can only be approached and never be reached due to the fact that the primordial nucleus can never have a steady state. As a result its daughter product can never reach a steady state, etc. On the other hand, when X/A,, 1 a state of quasi equilibrium may be reached where the activity ratio of mother and daughter nuclei is given by... 

The work described in the foregoing sections is of a preliminary nature. Nevertheless, it offers hope that experimental scales of free hydrogen ion concentration (pcn or pmn) in seawater may be feasible. One need not know pmn or pan to derive meaningful equilibrium data, such as acid-base ratios and solubilities, provided that suitable apparent equilibrium constants are chosen (7). In these cases, the unit selected for the acidity scale disappears by cancellation. Nevertheless, the acidity of seawater is a parameter of broader impact. It plays a role, for example, in the kinetics of organic oxidation-reduction reactions and in a variety of quasi-equilibrium processes of a biological nature. The concentration of free hydrogen ions is clearly understood, and its role in these complex interactions is more clearly defined than that of a quantity whose unit purports to involve the concept of a single-ion activity. 

Organic Surface ratio of different types of molecules in mixed self-assembled monolayers formed in quasi-equilibrium conditions 118... 

In most of the simulated curves in Fig. 4 two linear regions in both the cathodic and anodic branches can be clearly seen that have slopes of 1391 and 11181 mV dec (at 298 K), whereas the quasi-equilibrium treatment would have predicted only a single linear Tafel region of slope 1391 mV dec for this mechanism. When the 1 2 ratio increases, varying from 10 (solid line) to... 

One can show that the abundance ratio of deuterium to hydrogen in a quasi-equilibrium has an extremely small value, signifying that deuterium is destroyed in thermonuclear burning. The time dependence of deuterium... 

Such a distribution is shown in Figure 3 for both hexanes. The figures give the approximate G-values for a particular bond, when the disproportionation is neglected. Under the condition that the dispropor-tionation/combination ratio does not change on deuteration, they can be compared for a possible isotope effect of the fragmentation yielding radicals. The probability is the same for the split of a C-H bond—e.g., 0.8 for the sum of the four C-H bonds in position 2 of hexane—but a small inverse isotope effect is observed for C-C scission. Because of the above mentioned assumptions we are unable to decide if this corresponds to reality, however such an effect would be predicted on the basis of quasi-equilibrium theory. 

In the original derivation of Michaelis and Menten it was assumed that the first step is rapid and reversible, thus this step can be considered as a quasi-equilibrium with a constant Kcq. Note that it is defined as the ratio of constant in the reverse direction to the constant in the forward one (or the ratio of reactants to products) following a special bio logic. 

Eq. (6.36) can also be derived from the general equation for the three-step sequence. In the treatment above, the quasi-equilibrium steps were defined as the ratio of reactants to the ratio of products following the bio logic to have an analogy with the Michaelis Menten constant. In the Lineweaver-Burk coordinates, eq. (6.36) becomes... 

Arthur M. Squires Since the paper by Forney et al. reports product-gas methane concentrations which are rounded off to the nearest integer, it was a surprise to discover that methane equilibrium ratios calculated from the data are consistent with the hypothesis that methane production was governed by a quasi-equilibrium. 

The temperatiue difference between electrons and heavy neutral particles due to Joule heating in the collisional weakly ionized plasma is conventionally proportional to the sqirare of the ratio of the electric field ( ) to the pressure p). Only in the case of small values of E/p do the temperatiues of electrons and heavy particles approach each other. Thus, this is a basic requirement for local thermodynamic equilibrium (LTE) in plasma. Additionally, LTE conditions require chemical equilibrium as well as restrictions on the gradients. The LTE plasma follows the maj or laws of equilibrium thermodynamics and canbe characterized by a single temperature at each point of space. Ionization and chemical processes in such plasmas are determined by temperature (and only indirectly by the electric fields through Joule heating). The quasi-equilibrium plasma of this kind is usually called thermal plasma. Thermal plasmas in nature canbe represented by solar plasma (Fig. 1-4). 

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