Zero-Order Kinetic

The demonstration that the rate of formation of a nucleophile adduct R-Nu is kinetically zero-order in the concentration of the nucleophilic reagent Nu. ... 

The fact that a plot of H2 volumes initially generated vs. time gave a straight line is indicative of pseudo zero order kinetics. For borohydride hydrolysis, Kaufman and Sen3 and Holbrook and Twist4 also found zero order kinetics. Zero order kinetics for Reaction [1] imply that hydrolysis is independent of the concentrations of the reacting chemical species. This can be explained by assuming that the initial reaction step probably involves a surface catalyzed reaction, most likely BH" adsorption on the catalyst. Since the number... 

All investigators concur that autoreduction of Am(vi) is kinetically zero order with respect to the AmO ion and first order with respect to total americium concentration ... 

Kinetic Zero Order First Order Intermediate Order... 

Interestingly, at very low concentrations of micellised Qi(DS)2, the rate of the reaction of 5.1a with 5.2 was observed to be zero-order in 5.1 a and only depending on the concentration of Cu(DS)2 and 5.2. This is akin to the turn-over and saturation kinetics exhibited by enzymes. The acceleration relative to the reaction in organic media in the absence of catalyst, also approaches enzyme-like magnitudes compared to the process in acetonitrile (Chapter 2), Cu(DS)2 micelles accelerate the Diels-Alder reaction between 5.1a and 5.2 by a factor of 1.8710 . This extremely high catalytic efficiency shows how a combination of a beneficial aqueous solvent effect, Lewis-acid catalysis and micellar catalysis can lead to tremendous accelerations. 

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... 

The first detailed investigation of the reaction kinetics was reported in 1984 (68). The reaction of bis(pentachlorophenyl) oxalate [1173-75-7] (PCPO) and hydrogen peroxide cataly2ed by sodium saUcylate in chlorobenzene produced chemiluminescence from diphenylamine (DPA) as a simple time—intensity profile from which a chemiluminescence decay rate constant could be determined. These studies demonstrated a first-order dependence for both PCPO and hydrogen peroxide and a zero-order dependence on the fluorescer in accord with an earher study (9). Furthermore, the chemiluminescence quantum efficiencies Qc) are dependent on the ease of oxidation of the fluorescer, an unstable, short-hved intermediate (r = 0.5 /is) serves as the chemical activator, and such a short-hved species "is not consistent with attempts to identify a relatively stable dioxetane as the intermediate" (68). 

Reaction rate limited (zero-order kinetics). In this case, the biofilm concentration has no effect on reaction rate, and the biodegradation breakthrough curve is linear. 

The first observation of sensitivity-stability was reported by Liljenroth (1918) in connection with the autothermal operation of ammonia oxidation reactors. Papers of Damkdhler (1937) and Wagner (1945) went unnoticed. At Union Carbide Corp. Perkins (1938) used zero order kinetics to define a safe range for ethylene oxidation in an unpublished report. His result,... 

Saturation kinetics are also called zero-order kinetics or Michaelis-Menten kinetics. The Michaelis-Menten equation is mainly used to characterize the interactions of enzymes and substrates, but it is also widely applied to characterize the elimination of chemical compounds from the body. The substrate concentration that produces half-maximal velocity of an enzymatic reaction, termed value or Michaelis constant, can be determined experimentally by graphing r/, as a function of substrate concentration, [S]. 

Figure 2-2. Plot of Eq. (2-3) with simulated kinetic data. Evidently the reaction is not zero-order.

The rate equation is first-order in acetone, first-order in hydroxide, but it is independent of (i.e., zero order in) the halogen X2. Moreover, the rate is the same whether X2 is chlorine, bromine, or iodine. These results can only mean that the transition state of the rds contains the elements of acetone and hydroxide, but not of the halogen, which must enter the product in a fast reaction following the rds. Scheme VI satisfies these kinetic requirements. 

FIGURE 14.7 Substrate saturation curve for au euzyme-catalyzed reaction. The amount of enzyme is constant, and the velocity of the reaction is determined at various substrate concentrations. The reaction rate, v, as a function of [S] is described by a rectangular hyperbola. At very high [S], v= Fnax- That is, the velocity is limited only by conditions (temperature, pH, ionic strength) and by the amount of enzyme present becomes independent of [S]. Such a condition is termed zero-order kinetics. Under zero-order conditions, velocity is directly dependent on [enzyme]. The H9O molecule provides a rough guide to scale. The substrate is bound at the active site of the enzyme. 

On the other hand, for an enzyme that obeys Michaelis-Menten kinetics, the reaction is viewed as being first-order in S at low S and zero-order in S at high S. (See Chapter 14, where this distinction is discussed.)... 

Case 1 When [S] is large compared to K , the enzyme is saturated with S and the kinetics are zero-order in S. 

The most widely accepted mechanism of reaction is shown in the catalytic cycle (Scheme 1.4.3). The overall reaction can be broken down into three elementary steps the oxidation step (Step A), the first C-O bond forming step (Step B), and the second C-O bond forming step (Step C). Step A is the rate-determining step kinetic studies show that the reaction is first order in both catalyst and oxidant, and zero order in olefin. The rate of reaction is directly affected by choice of oxidant, catalyst loadings, and the presence of additives such as A -oxides. Under certain conditions, A -oxides have been shown to increase the rate of reaction by acting as phase transfer catalysts. ... 

Detailed investigations indicated an interesting mechanism for azide openings catalyzed by 2 [6]. Chloride-epoxide addition products were observed in the initial stages of the ARO reaction with 2 in amounts commensurate with the catalyst loading. Azide complex 3, characterized as the TH F adduct, was isolated from the reaction mixture and proved to be an active and recyclable catalyst for the ARO, pointing to the role of 2 as that of a precatalyst. Kinetic experiments revealed a second-order dependence on the concentration of 3, a zero-order dependence on azide source, and inverse-order dependence on epoxide concentration. The sue-... 

Kinetic observations of the homogeneous part of the reaction in water12,13 do not provide any substantially new element to the knowledge of this system. The obvious observations that the rate of resinification increases with increasing temperature and decreasing pH of the mixture only provide technically useful correlation parameters and the zero-order of reactions carried out to small conversion of 2-furfuryl alcohol13 does not indicate anything except an elementary kinetic approximation (the use of colour build-up as a criterion for the extent of alcohol consumed is also questionable since no firm relationship has ever been established between these two quantities). 

Schlatter et al. found that their data with copper chromite agrees better with 0.7 order for CO concentrations (53). For crystals of nickel oxide and chromium oxide, Yu Yao and Kummer have found that the kinetics depend on CO or hydrocarbon around 0.55 order and depend on oxygen around 0.45 order (79). Hertl and Farrauto found evidence that CO adsorbs on copper as a carbonyl group, and adsorbs on chromium oxide as a unidentate carbonate. They found that the kinetics depends on CO to the first order, and depends on oxygen to the zero order (80). 

The NO reduction over Cu-Ni-Fe alloys has been studied recently by Lamb and Tollefson. They tested copper wires, stainless steel turnings, and metal alloys from 378 to 500°C, at space velocities of 42,000-54,000 hr-1. The kinetics is found to be first order with respect to hydrogen between 400 and 55,000 ppm, and zero order with respect to NO between 600 and 6800 ppm 104). The activation energies of these reactions are found to be 12.0-18.2 kcal/mole. Hydrogen will reduce both oxygen and NO when they are simultaneously present. CO reduction kinetics were also studied over monel metals by Lunt et al. 43) and by Fedor et al. 105). Lunt speculated that the mechanism begins by oxidant attack on the metal surface... 

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