Pseudo zero-order

Zero-order, pseudo, 23 Zero-order approximation, 450... 

Since the zero order pseudo wave functions are plane waves, each one of these zero order terms contains a uniform contribution I/O to the density. This gives a uniform distribution outside the core region ... 

It may even be possible to adjust conditions such that measurements are made under pseudo-zero-order conditions where... 

The data shown in the following table were collected for a reaction known to follow pseudo-zero-order kinetics during the time in which the reaction was monitored. 

Eor a pseudo-zero-order reaction a plot of [A]( versus time should be linear with a slope of -k, and a y-intercept of [A]o (equation 13.8). A plot of the kinetic data is shown in figure 13.7. Linear regression gives an equation of... 

Since the reaction is carried out under conditions in which it is pseudo-zero-order in creatinine and OH , the rate constant, k, is... 

A third method, or phenomenon, capable of generating a pseudo reaction order is exemplified by a first-order solution reaction of a substance in the presence of its solid phase. Then if the dissolution rate of the solid is greater than the reaction rate of the dissolved solute, the solute concentration is maintained constant by the solubility equilibrium and the first-order reaction becomes a pseudo-zero-order reaction. 

We can reach two useful conclusions from the forms of these equations First, the plots of these integrated equations can be made with data on concentration ratios rather than absolute concentrations second, a first-order (or pseudo-first-order) rate constant can be evaluated without knowing any absolute concentration, whereas zero-order and second-order rate constants require for their evaluation knowledge of an absolute concentration at some point in the data treatment process. This second conclusion is obviously related to the units of the rate constants of the several orders. 

The rate of the reaction with most reagents is proportional to the concentration of NO2, not to that of other species. When the reagent produces this ion in small amounts, the attack is slow and only active substrates can be nitrated. In concentrated and aqueous mineral acids the kinetics are second order first order each in aromatic substrate and in nitric acid (unless pure nitric acid is used in which case there are pseudo-first-order kinetics). But in organic solvents, such as nitromethane, acetic acid, and CCI4, the kinetics are first order in nitric acid alone and zero order in aromatic substrate, because the rate-determining step is formation of NOj and the substrate does not take part in this. 

A full development of the rate law for the bimolecular reaction of MDI to yield carbodiimide and CO indicates that the reaction should truly be 2nd-order in MDI. This would be observed experimentally under conditions in which MDI is at limiting concentrations. This is not the case for these experimements MDI is present in considerable excess (usually 5.5-6 g of MDI (4.7-5.1 ml) are used in an 8.8 ml vessel). So at least at the early stages of reaction, the carbon dioxide evolution would be expected to display pseudo-zero order kinetics. As the amount of MDI is depleted, then 2nd-order kinetics should be observed. In fact, the asymptotic portion of the 225 C Isotherm can be fitted to a 2nd-order rate law. This kinetic analysis is consistent with a more detailed mechanism for the decomposition, in which 2 molecules of MDI form a cyclic intermediate through a thermally allowed [2+2] cycloaddition, which is formed at steady state concentrations and may then decompose to carbodiimide and carbon dioxide. Isocyanates and other related compounds have been reported to participate in [2 + 2] and [4 + 2] cycloaddition reactions (8.91. 

Finally, although rare, we mention the occurrence of zero-order reactions. The special case of a pseudo-zero order reaction arises if a reactant is present in large excess, and the reaction does not noticeably change the concentration of the reactant. The differential and integral rate equations for a zero-order reaction R —> P are... 

GL 16] [R 12] [P 15] As excess of cyclohexene was used, the kinetics were zero order for this species concentration and first order with respect to hydrogen [11]. For this pseudo-first-order reaction, a volumetric rate constant of 16 s was determined, considering the catalyst surface area of 0.57 m g and the catalyst loading density of1g cm. ... 

The adiabatic induction time can be approximately evaluated from graphs in Fig. 5.4-68. They are plotted for the condition qR qp, which is nearly equivalent to adiabatic operation if the initial temperature is greater than Tr.i- Eqn. (5.4-214) is the basis of the graph in Fig. 5.4-68. From both graphs in Fig. 5.4-68 the apparent activation energies (E/Rf.) for pseudo-zero order reactions can be determined. 

This simple example of a non-catalytic reaction demonstrates how a reaction rate law may be comprehensively defined in two substrates by just two reaction progress experiments employing two different values of excess [e]. A classical kinetics approach using initial rate measurements would require perhaps a dozen separate initial rate or pseudo-zero-order experiments to obtain the same information. 

A linear relationship between % SiH and time suggests pseudo-zero-order kinetics, in which the rate of reaction appears to be independent of the concentrations of isoprene and siloxane. A plot of % conversion of SiH vs. concentration of catalyst at 110°C for 5 hours also gave a straight line, indicating that the rate of reaction is directly proportional to concentration of catalyst, i.e., first-order in catalyst. 

It has already been mentioned that in the absence of added water the reaction kinetics follows a pseudo zero-order rate profile the rate-controlling step under these conditions appears to involve the complexation of the crown in the organic phase with the salt in the solid phase. In contrast to this, in the presence of small quantities of water the reaction kinetics follows a pseudo first-order rate profile. Thus it appears that the water facilitates the interaction between the crown and the salt by forming an omega phase since the displacement process now becomes the rate-controlling step. The phase region where the displacement process actually takes place is not certain at this juncture. 

It is impossible to conceive of a reaction rate as being independent of the concentration of all the species involved in the reaction. The rate might, however, very easily be independent of the concentration of one of the reactants. If this species, say A, is used in deficiency, then a pseudo zero-order reaction results. The rate —d[Jk]/dt will not vary as [A] decreases, and will not depend on the initial concentration of A. 

The rate laws (8.29) and (8.30), with [Cr(II)]t ,a[ in excess, lead to oxidation by Co(C204)j and Ij" showing initially pseudo zero-order kinetics. As the concentration of the oxidant decreases however, Arjfoxid] S and some deviation from linearity for the plot occurs and eventually becomes first-order, although this may be near to the completion of reaction. With Co(edta) in deficiency, the reaction is pseudo first-order. 

In nature, the reaction rate depends on the reactant concentration. However, practically speaking, when a reactant exists at a very high concentration, it is essentially unchanged due to the reaction, and the reaction is called pseudo-zero order. 

V = V max [S]// m- A reaction of higher order is called pseudo-first-order if all but one of the reactants are high in concentration and do not change appreciably in concentration over the time course of the reaction. In such cases, these concentrations can be treated as constants. See Order of Reaction Half-Life Second-Order Reaction Zero-Order Reaction Molecularity Michaelis-Menten Equation Chemical Kinetics... 

Reactions in which the velocity (v) of the process is independent of the reactant concentration, following the rate law v = k. Thus, the rate constant k has units of M sAn example of a zero-order reaction is a Michaelis-Menten enzyme-catalyzed reaction in which the substrate concentration is much larger than the Michaelis constant. Under these conditions, if the substrate concentration is raised even further, no change in the velocity will be observed (since v = Umax)- Thus, the reaction is zero-order with respect to the substrate. However, the reaction is still first-order with respect to total enzyme concentration. When the substrate concentration is not saturating then the reaction ceases to be zero order with respect to substrate. Reactions that are zero-order in each reactant are exceedingly rare. Thus, zero-order reactions address a fundamental difference between order and molecularity. Reaction order is an empirical relationship. Hence, the term pseudo-zero order is actually redundant. All zero-order reactions cease being so when no single reactant is in excess concentration with respect to other reactants in the system. 

Figure 2. First and pseudo-zero order kinetic components of change in absorbance at 350 nm with time for kraft lignin preparation during incubation at 0.46 gL 1 in aqueous 0.10 M NaOH at 25.0 °C kx = 0.0039 h 1, v0 = 0.0000026 A35 h 1 (0.1 cm pathlength).

Figure 5. First and pseudo-zero order kinetic components of change in Mw...

At the time this work was carried out, the mechanistic basis for the conversion of acyl Meldrum s acid adducts to corresponding P-keto esters/amides such as 25 was not well understood [16] . The IR method used to determine the nature of the protonation state of 24 presented an excellent opportunity to perform kinetic studies. These studies [17] showed that the reaction of 24 with amine nucleophile 3 was pseudo zero order in the anionic form 24. The reaction kobs was almost the same in the one-pot process as when the isolated 24 was used. This was consistent with the rate-determining step being the formation of the a-oxoketene intermediate 26 (Scheme 5.15). 

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