Formation and disappearance

The type of catalyst influences the rate and reaction mechanism. Reactions catalyzed with both monovalent and divalent metal hydroxides, KOH, NaOH, LiOH and Ba(OH)2, Ca(OH)2, and Mg(OH)2, showed that both valence and ionic radius of hydrated cations affect the formation rate and final concentrations of various reaction intermediates and products.61 For the same valence, a linear relationship was observed between the formaldehyde disappearance rate and ionic radius of hydrated cations where larger cation radii gave rise to higher rate constants. In addition, irrespective of the ionic radii, divalent cations lead to faster formaldehyde disappearance rates titan monovalent cations. For the proposed mechanism where an intermediate chelate participates in the reaction (Fig. 7.30), an increase in positive charge density in smaller cations was suggested to improve the stability of the chelate complex and, therefore, decrease the rate of the reaction. The radii and valence also affect the formation and disappearance of various hydrox-ymethylated phenolic compounds which dictate the composition of final products. 

Both terms must be included because A is being formed by the reverse reaction as well as being used up by the forward reaction. This equation is of very little help as it stands since we cannot measure the concentration of the intermediate. However, the combined rate law for the formation and disappearance of I is... 

Chemical reactions in the system are irreversible processes, affecting transport processes, as they result in the formation and disappearance of components of the system and in the release or consumption of thermal energy. 

FIGURE 1—1 Formation and disappearance of methemoglobin from blood of rats exposed at 100 ppm for 8 or 12 h. Source Modified from Kim and Carlson 1986. 

The kinetics of the formation and disappearance of the ions and the kinetics of the polymerisation are both complicated, and so the interpretation of the kp+A is far from clear. We have at least two complications to contend with. One is the extent to which a pseudocationic polymerisation contributes to the rate, the other is the relative importance of unpaired and paired cations. Neither of these questions is addressed by the authors, but we can attempt to resolve them in the light of what we discovered by analysing Kunitake and Takarabe s results obtained with what was ostensibly the same system. 

Figure 4. ReactIR trends of intermediate formation and disappearance.

Ordinarily, however, the population of the triplet state is achieved through excitation into the singlet manifold which is followed by intersystem crossing to the excited triplet state. Therefore, in considering the yield of phosphorescence we must consider the processes involved in formation and disappearance of both the singlet and triplet states. 

Writing these two equations equal to zero does not imply that equilibrium conditions exist, as was the case for Eq. (2.28). It is also important to realize that the steady-state approximation does not imply that the rate of change of the radical concentration is necessarily zero, but rather that the rate terms for the expressions of radical formation and disappearance are much greater than the radical concentration rate term. That is, the sum of the positive terms and the sum of the negative terms on the right-hand side of the equality in Eqs. (2.33) and (2.34) are, in absolute magnitude, very much greater than the term on the left of these equalities [3],... 

An intense purple-blue species forms within a few seconds when Cr +, in excess, is added to 4,4 -bipyridinium ion, bpyH. The color fades slowly over many minutes. The formation and disappearance of the intermediate, kf and respectively, are assigned to k2 and Atj respectively from considerations of the assessed spectrum of the intermediate. The reactions involved are... 

The growth of the separate species has been followed, as well as the formation and disappearance of sulfide. The harvested microbes were analysed for protein content. 

Given the reaction 2NO2 + 02 = N2O5, what is the relation between the rates of formation and disappearance of the three reaction components ... 

The disappearance of A is given by the complicated Eq. 10, and the formation and disappearance of R is given by an even more complicated equation. Developing the product distribution relationship, solving numerically, and comparing the results with those for plug flow and for mixed flow gives Fig. 15.11 see Johnson (1970) and Levien and Levenspiel (1998). 

Figure 4 TiO2 photocatalysis of DMMP and the formation and disappearance of phosphorus-containing products as a function of irradiation time. 

When the exciting light is cut off, i.e., when the delayed fluorescence is measured, the population of excited states (P, Pi ) is maintained only by triplet-triplet quenching. Considering then the formation and disappearance of P, ... 

In many studies precise quantitative data are not needed to clarify the chemistry under study. Especially in a series of related samples, low voltage mass spectrometry can quickly and easily furnish data that parallel changes in concentration and are entirely adequate for the purpose of the study. This analytical tool has enabled us to follow readily the formation and disappearance of products, instead of being limited to observing the rate of oxygen absorption we expect it to be at least equally useful in determining rates and analyzing products of co-oxidations now under way. 

To a stirred soln of Z-(aTfm)Xaa-OH (2 mmol) in CH2C12 (10 mL) were added DIC 109 (or DCC, 115 2.2 mmol) and the N-deprotected peptide or amino acid derivative (2 mmol). The mixture was stirred at rt for 12 h [the progress of the reaction, indicated by the formation and disappearance of the oxazol-5(4H)-one, can be monitored by TLC]. 115 The precipitate was separated by filtration, the mother liquor was concentrated to dryness, and the residue was purified by flash chromatography. 

If the concentration of ES is virtually constant during the steady state, the rates of formation and disappearance of ES must be nearly equal, vf = vd. We therefore can describe the situation in the steady state by combining equations (20) and (21). 

The heart of the apparatus consists of a sight glass (typically 300 cm3) for visual confirmation of hydrate formation and disappearance. Normally only 20-150 cm3 of the cell volume contains water, with the remainder being gas and hydrate. 

As in the previous sections, Eq. (88) is obtained by multiplying by [K2Yj all possible terms that can be written down for formation, and disappearance, of an /, -mer followed by summing up the result over all i and . 

The steady-state approach treats such intermediates by making a not entirely correct assumption that equates the rates of formation and disappearance of the intermediate. The treatment has proved successful in a large number of cases but it is, after all, an approximation that sometimes needs to be improved or replaced by more rigorous equations. 

The kinetics and mechanisms of radical reactions important in combustion chemistry are best studied under conditions in which single reactions can be isolated rather than in flames where there are multiple pathways for formation and disappearance of the radicals. Reactions of C2 are of particular importance since recent laser saturation measurements in our laboratory (1) have shown that C2 a3IIu is present in oxyacetylene flames at concentrations on the order of 1016 molecules/cm3 (approximately 0.1 torr). Although concentrations of ground state C2 in flames are unknown and cannot be measured by the same technique due to spectroscopic constraints, we expect that C2 X3 g populations are at least comparable. Because of these relatively large concentrations the reactions of both species are of considerable importance in combustion chemistry. However, until recently very little was known about these reactions due to the difficulty of producing a clean source of C2 radicals. 

The chromophoric pyridoxal phosphate coenzyme provides a useful spectrophotometric probe of catalytic events and of conformational changes that occur at the pyridoxal phosphate site of the P subunit and of the aiPi complex. Tryptophan synthase belongs to a class of pyridoxal phosphate enzymes that catalyze /3-replacement and / -elimination reactions.3 The reactions proceed through a series of pyridoxal phosphate-substrate intermediates (Fig. 7.6) that have characteristic spectral properties. Steady-state and rapid kinetic studies of the P subunit and of the aiPi complex in solution have demonstrated the formation and disappearance of these intermediates.73-90 Fig. 7.7 illustrates the use of rapid-scanning stopped-flow UV-visible spectroscopy to investigate the effects of single amino acid substitutions in the a subunit on the rate of reactions of L-serine at the active site of the P subunit.89 Formation of enzyme-substrate intermediates has also been observed with the 012P2 complex in the crystalline state.91 ... 

The authors pointed out the similarity of the conductivity curves (Fig. 4) and viscosity curves (Fig. 14) which they observed. The shapes of both curves may be explained in the same way, namely by the formation and disappearance of... 

Photostationary state A steady state reached by a reacting chemical system when light has been absorbed by at least one of the components. At this state the rates of formation and disappearance are equal for each of the transient molecular entities formed. 

It is supposed that any unit of the chain may form a contact with any unit of another chain. Variations of parameters allow the kinetics of dissociation and association in the system to be controlled. Rate constants of formation and disappearance of one contact were estimated122. It is seen on the computer display screen that a strongly defect structures are formed first. In time, these structures go over to completely stretched ones. A completely stretched ladder form of the complex was found to be the most advantageous from the energetic point of view. 

For the overall series-parallel reaction scheme, a set of differential equations can be developed to describe the rates of formation and disappearance of phenol and all its aromatic and carboxylic intermediates. It is well known... 

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