Steady state concentration, of intermediates

Of course it is also possible for a reaction system not to belong to any of these classes of approximate description.) Only in class III can equilibrium be said to be a special case of the steady-state treatment. Note that, for class III systems, the steady-state concentration of intermediate is very large,whereas for class I it is very small. Zuman and Patel have discussed the equilibrium and steady-state approximations in terms similar to the present treatment. 

Sometimes instead of a steady state concentration of intermediates there is an explosive build-up. 

A traditional kinetic model of steady-state catalytic reaction assumes quasi-steady-state concentrations of intermediate species on the catalyst surface. This assumption is often invalid for unsteady-state conditions characterized by continuous changes in a fluid phase composition and temperature above the catalyst surface. Additionally, the catalyst itself can interact with the reaction mixture and can undergo significant changes, influenced by changing conditions in the gas phase. Such a modification of the catalyst can be con-... 

The technique of transient isotope-switching can provide fundamental information about the kinetics of catalytic reactions that is difficult or impossible to obtain with other methods. Following a gas-phase isotope switch at steady state, transients of products labeled with the original isotope result from reactions of intermediates that have been left behind on/in the catalyst after the gas-phase switch. The area under the transients provides a direct measure of the steady-state concentrations of intermediates on/in the catalyst at the time of the switch. The temporal shape of the transients provides information on the reaction kinetics of the intermediates. In the present study, we compliment the transient techniques with steady-state measurements to obtain information on the rates of the various... 

Calculate steady state concentrations of intermediates in linear pathways. 

However, if the concentration of species A is much larger than that of species B, we shall have at the beginning the steady state dehned by the reactions (8.8a) and (8.8b), whereas later, when the concentration of reactant B will be close to zero, the steady state defined by the reactions (8.8a) and (8.8c). In that case, the net stoichiometric equation will also change from A -F B Pi to A P2. The pseudo-steady-state concentration of intermediate X change from the initial value of about fci[A]/fc2[B] to the end value of about ki[K jkj,. 

It is important to emphasize that direet studies sueh as those earned out on the eyelopropylmethyl radieal ean be done with low steady-state eoneentrations of the radical. In the case of the study of the eyelopropylmethyl radical, removal of the source of irradiation leads to rapid disappearance of the EPR spectrum, because the radicals react rapidly and are not replaced by continuing radical formation. Under many conditions, the steady-state concentration of a radical intermediate may be too low to permit direct detection. Failure to observe an EPR signal, therefore, cannot be taken as conclusive evidence against a radical intermediate. 

FIGURE 18.12 The use of inhibitors to reveal the sequence of reactions in a metabolic pathway, (a) Control Under normal conditions, the steady-state concentrations of a series of intermediates will be determined by the relative activities of the enzymes in the pathway, (b) Plus inhibitor In the presence of an inhibitor (in this case, an inhibitor of enzyme 4), intermediates upstream of the metabolic block (B, C, and D) accumulate, revealing themselves as intermediates in the pathway. The concentration of intermediates lying downstream (E and F) will fall. 

Reaction of purified Ca " -ATPase with 0.3 mM NBD-Cl in the presence of 1 mM AMP-PNP and 1 mM CaCl2 caused inhibition of ATPase activity with the incorporation of 2= 15 nmol NBD-Cl per mg protein [335]. The inhibition was attributed to the binding of 7-8 nmol NBD-Cl/mg enzyme protein, corresponding to = 1 mol NBD-Cl per mol ATPase. The NBD-labeled enzyme was digested with pepsin and several NBD-labeled peptides were isolated [335]. All peptides contained the Gly-X (Cys) sequence that occurs only in one place in the Ca -ATPase, i.e., at Gly343-Cys344. Therefore NBD-Cl reacts with the same cysteine 344 residue that is also modified by maleimide derivatives [319]. The NBD modified enzyme had only 5-10% of the ATPase activity of the control ATPase, but the steady state concentration of the phosphoenzyme intermediate was only slightly reduced [335]. The Ca ... 

Substitution of the steady-state concentrations of the two intermediates into the equation for the rate of disappearance of ozone gives... 

Phenols are rather common antimicrobial components of metalworking fluids however, their use in recent years has been declining (36). The inhibition of nitrosation by phenols has recently been reviewed (35). In general, phenolic compounds inhibit nitrosation by reacting with nitrite (phenol reacts with nitrite 10,0 0 0 times faster than with dimethylamine), but the intermediate nitrosophenolis unstable and enhances nitrosation. "The overall effect is dependent on the steady state concentration of the nitrosophenol and the relative degrees of retardation and enhancement exerted by the phenol and the nitrosophenol, respectively ( 35)". 

The addition of water to a free carbocation intermediate of solvolysis can be distinguished from addition to an ion-pair intermediate by an examination of common ion inhibition of solvolysis. Common leaving group inhibition of solvolysis is observed when the leaving group ion (X ) acts, by mass action, to convert the free carbocation (R , Scheme 5A) to substrate (R-X). This results in a decrease in the steady-state concentration of R that leads directly to a decrease in the velocity of solvolysis. Some fraction of the solvolysis reaction products form by direct addition of solvent to the carbocation-anion pair intermediate. The external... 

The 40s conversion of the 600nm intermediate to RbOgray (Scheme 10.1) might seem too low to compete with spontaneous disproportionation of superoxide, which occurs with a second-order rate constant of 5 x lO M s at pH 7 (Bielski and Cabelli 1991). However, in aerobic bacterial cells such as E. coli, the steady-state concentration of superoxide is esti-... 

The first intermediate to be generated from a conjugated system by electron transfer is the radical-cation by oxidation or the radical-anion by reduction. Spectroscopic techniques have been extensively employed to demonstrate the existance of these often short-lived intermediates. The life-times of these intermediates are longer in aprotic solvents and in the absence of nucleophiles and electrophiles. Electron spin resonance spectroscopy is useful for characterization of the free electron distribution in the radical-ion [53]. The electrochemical cell is placed within the resonance cavity of an esr spectrometer. This cell must be thin in order to decrease the loss of power due to absorption by the solvent and electrolyte. A steady state concentration of the radical-ion species is generated by application of a suitable working electrode potential so that this unpaired electron species can be characterised. The properties of radical-ions derived from different classes of conjugated substrates are discussed in appropriate chapters. 

Fig. 8.5. In electrochemical reactions involving one or more adsorbed reaction intermediates (sometimes involved in the rate-determining step), the steady-state concentration of the intermediate changes with the potential. However, each intermediate has a time constant to reach the surface coverage corresponding to a given overpotential. The downside of too low a pulse time, or too fast a sweep rate, is that the intermediate concentration does not relax to its appropriate concentration in time. The Tafel slope (sometimes a significant mechanism indicator) may then differ from that calculated for the assumed path and rate-determining step.

Co(II) acetate in acetic acid with acetaldehyde also gives good selectivity in the formation of adipic acid (73% at 88% conversion at 90oC).200 The role of acetaldehyde is to promote oxidation of Co(II) to Co(III) and maintain a steady-state concentration of Co(III). Later during the reaction, however, cyclohexanone formed as an intermediate in oxidation serves as promoter. Zirconium ions also exhibit a significant promoter effect.201... 

The assumption of a steady-state ozone concentration for the direct reaction is based on the relatively large concentration of ozone compared to the micropollutants, which means the change in the ozone concentration over time is negligible. Several authors have shown that the indirect reaction of OH° with organic compounds is pseudo-first order due to the steady-state concentration of the hydroxyl radicals (e. g. Yao and Haag, 1992 von Gunten et al., 1995). Further assumptions are that the concentrations of the intermediates, e. g. 02°, 0,°-, H0,° and organic radicals, are also at steady-state (Peyton, 1992). 

The numerator contains all hydroxyl radical forming reactions and all initiating reactions are summarized (Sk c(/()). The denominator contains all hydroxyl radical consuming reactions. The second term includes all reactions with intermediates (EkPi c(P,)), the third the reactions with scavengers(Lksi c(S,)). Similarly, the steady-state concentrations of ozone and hydrogen peroxide can be calculated from the liquid phase mass balances. 

Addition of some arylboranes to solutions containing HNi[P(0-o-tolyl)3]3CN affects the course of the reaction of 4PN similarly the steady state concentration of alkyl intermediates is reduced, the rate of product formation is reduced, and the product distribution is shifted in favor of linear product, as shown in Table X. 

Figure 7. IR spectra in the combination/overtone region showing the photochemical reaction of Cr(CO)6 in scC2H4 at ambient temperature. The first spectrum shown in the Figure was recorded just before the UV lamp was switched on, and subsequent spectra were taken at ca. 10 min intervals. The bands labelled are those of Cr(CO)6 and those labelled A show the growth of the final photoproduct Cr(CO)4(C2H4)2. The steady state concentration of the intermediate species Cr(CO)5(C2H4) is relatively low, hence the overtone/combination bands of this species are not observed in this experiment.

Because of the high reactivity of hydroxyl radicals, activated complex, and chlorinated intermediates, their concentrations are extremely low at the steady state therefore, a pseudo first-order steady state can be assumed for the kinetic modeling. As a result, the steady-state concentration of the activated complex can be obtained by setting the change of its concentration to zero ... 

The pKa values of Thy and Ura are close to 9.5. Thus, near neutrality they are deprotonated by OH formed in the pulse. Due to the low pfCa values, the reprotonation of the anions by water is sufficiently slow ( 3 x 105 s 1) to allow the anions to build-up to higher than steady-state concentrations. Of the two anions that are formed upon deprotonation [e.g., reaction (1)] only the one deprotonated at N( ) absorbs at longer wavelengths than the neutral molecules (Morita et al. 1981). This explains, why with the nucleosides which have the same pfCa values as the nucleobases no such intermediates are formed, although deprotonation by OH occurs as well. 

For given mechanisms, it is possible to predict expressions for the steady state concentrations of the intermediates in terms of rate constants and reactant concentrations. 

Although free radical reactions are found less often in solution than in the gas phase, they do occur, and are generally handled by steady state methods. There are also organic and inorganic reactions that involve non-radical intermediates in steady state concentrations. These intermediates are often produced by an initial reversible reaction, or a set of reversible reactions. This can be compared with the pre-equilibria discussed in Section 8.4, where the intermediates are in equilibrium concentrations. The steady state treatment is also used extensively in acid-base catalysis and in enzyme kinetics. 

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