Zero-order dependence

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 slope of the zero-order plot (when absorbance is converted into concentration) is k,M s. The value of k is found to be proportional to the concentration of Ni(POEt3 4, which is used in excess (Fig. 1.2),  

The reaction is therefore overall first-order, with a first-order rate constant Ati(s ). The zero-order situation is not often encountered (Prob. 4). A number of examples are compiled in Ref. 18 and one is shown in Fig. 8.3. 

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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). 

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-... 

The oxidation of tertiary alcohols by chromic acid is comparatively slow and shows a zero-order dependence of the rate upon oxidant concentration For 1-methylcyclohexanol the kinetics are... 

The acidity dependences are not simple. V(V) is thought to form a complex with the enol which undergoes slow oxidative breakdown. Propionaldehyde and n-butyraldehyde are, however, oxidised by Mn(III) pyrophosphate with a zero-order dependence on oxidant concentration but first-order dependences on substrate and HjO " concentrations. Here oxidation immediately follows enol formation. Ce(IV) sulphate oxidises acetaldehyde at a rate much faster than enolisation . 

Sengupta and Aditya ° find the usual reactivity sequence for Ce(IV) salts, viz. CIO4" > NOj" > S04 , but note that plots of log (Ce(lV)] versus time are linear even when equal molar concentrations of Ce(IV) and malonic acid are taken. This implies a first-order dependence on [Ce(IV)] and zero-order dependence on malonic acid concentration. Kemp , however, has found a clear first-order dependence on malonic acid concentration for the Ce(IV) sulphate oxidation, using an excess of reductant and making a four-fold variation in reductant concentration. Moreover, consumption of Ce(lV) was intermediate between first- and second-order. Further work is needed to resolve this discrepancy. 

The enoHsation may be rate-determining (to afford the zero-order dependence on oxidant concentration) or the oxidation step may be slower (to give the first-order dependence). The second-order dependence on oxidant concentration for acetone and nitroethane cannot involve slow oxidation of a free radical and no ready alternative explanation is available. Maltz showed that the rate of oxidation of isobutanal equals the rate of enolisation, and that two main paths of oxidation are followed subsequent to enolisation leading either to tetramethyldihydropyrazine and a poly-aquocyanoiron(II) species or to isobutyric acid. 

A kinetic study of the hydrodefluorination of C F H in the presence of EtjSiH indicated a first-order dependence on both [fluoroarene] and [ruthenium precursor] and a zero-order dependence on the concentration of alkylsilane, implying that the rate-limiting step in the catalytic cycle involves activation of the fluoroarene. The regioselectivity for hydrodefluorination of partially fluorinated substrates such as CgFjH has been accounted for by an initial C-H bond activation as shown in the... 

This mechanism can only be regarded as of limited utility since it does not take into account the zero order dependence on catalyst that is observed under some conditions. More investigation is needed to expand the understanding of the system over a wider range of conditions using a rigorous statistical design to try and determine the extent of interactions between the different reaction parameters. 

The MO concentrations versus time profiles were fitted to second order polynomial equations and the parameters estimated by nonlinear regression analysis. The initial rates of reactions were obtained by taking the derivative at t=0. The reaction is first order with respect to hydrogen pressure changing to zero order dependence above about 3.45 MPa hydrogen pressure. This was attributed to saturation of the catalyst sites. Experiments were conducted in which HPLC grade MIBK was added to the initial reactant mixture, there was no evidence of product inhibition. 

Figure 3 shows the results of varying the CO pressure. The maximum activity appears to lie near 600 psi for benzaldehyde reduction. Figure 3 is an attempt to elucidate an apparent reaction order with respect to the arithmetically averaged CO pressure. At pressures less than 400 psi, the order is nearly first order. The situation at higher pressures is not clear however, it is reasonable to speculate that the dominant aspects of the kinetics shift at these pressures. The data suggest the shift is to zero-order dependance. 

The effects of benzaldehyde concentrations on turnover frequency are anomalous. Our results indicate that benzaldehyde hydrogenation turnover frequency is independent of benzaldehyde concentration (an apparent zero-order dependence). However, the data in Table 2 indicate otherwise. If the reaction were independent of aldehyde concentration, the rate data should be independent of the type of aldehyde used. This is especially true with p-tolualdehyde and p-anisaldehyde where the structural changes to the aldehyde (addition of p-methyl or p-methoxy) should influence the reactivity of the aldehyde functionality only through electronic effects. Thus, we are forced to conclude that the aldehyde is involved in the rate determining step even though the concentration study does not support its presence. 

While this mechanism involves lower formal coordination numbers than that of Scheme 19.8 a, its shortcoming is a zero-order dependence on [H2] that must be accompanied by a zero-order reaction dependence on [C=C],... 

An informative set of calculations was carried out by Brandt et al, coupled to experimental studies that demonstrated first-order dependence of the turnover rate on both catalyst and H2, and zero-order dependence on alkene (a-methyl-(E)-stilbene) concentration [71]. The incentive for this investigation was the absence of any characterized advanced intermediates on the catalytic pathway. As a result of the computation, a catalytic cycle (for ethene) was proposed in which H2 addition to iridium was followed by alkene coordination and migratory insertion. The critical difference in this study was the proposal that a second molecule of H2 is involved that facilitates formation of the Ir alkylhydride intermediate. In addition, the reductive elimination of R-H and re-addition of H2 are concerted. This postulate was subsequently challenged. For hydrogenation of styrene by the standard Pfaltz catalyst, ES-MS analysis of the intermediates formed at different stages in the catalytic cycle revealed only Ir(I) and Ir(III) species, supporting a cycle (at least under low-pressure conditions in the gas... 

The above, together with the fact that a fourfold variation of [CN ] for the [WO(OH)(CN)4]3 complex showed zero-order dependence on free cyanide concentration further points to a dissociative activation for the cyanide exchange process, also in the case of the mono oxo (classic 16-electron) [MO(X)(CN)4]m species. 

While claiming no finality for their mechanism, the authors pointed out that it accounted satisfactorily for the zero-order dependence on NC13 concentration, the intensity exponent of unity and many other characteristics of the reaction. However, a serious defect lies in the apparent absence of any effect of pressure on the rate of diffusion of NC14 to the reaction vessel surface. Such an effect would be expected under their conditions and it would yield a dependence of the reaction rate on total pressure opposite to that observed. 

The weathering of silicates has been investigated extensively in recent decades. It is more difficult to characterize the surface chemistry of crystalline mixed oxides. Furthermore, in many instances the dissolution of a silicate mineral is incipiently incongruent. This initial incongruent dissolution step is often followed by a congruent dissolution controlled surface reaction. The rate dependence of albite and olivine illustrates the typical enhancement of the dissolution rate by surface protonation and surface deprotonation. A zero order dependence on [H+] has often been reported near the pHpzc this is generally interpreted in terms of a hydration reaction of the surface (last term in Eq. 5.16). 

The acceleration of the reaction between benzyl chloride and metal acetates in acetonitrile has been studied using several crown ethers (Dorn et al., 1977 Knochel et al., 1975). Very surprisingly, the overall reaction was found to be first order in the presence of cryptands and second order in the presence of crown ethers. The order in benzyl chloride was one in both cases, indicating a zero-order dependence on acetate concentration for the cryptand-catalysed reaction. Unfortunately, the authors did not give all the details of the experiments on which these conclusions were based. Hence, no explanation can be offered for the apparent discrepancy between their results and those of Cambillau et al. (1976, 1978), who observed a first-order dependence on the concentration of metal acetoacetates in alkylations, irrespective of whether or not they were performed in the presence of crown ethers or cryptands. 

The reaction of benzene with Cu(II) and Fe(III)-exchanged hectorites at elevated temperatures produced a variety of organic radical products, depending on the concentration of water in the reaction medium and the reaction time (90). The formation of free radicals was accompanied by a reduction in oxidation state of the metals, a process that had a zero-order dependence on the metal ion concentration. Under anhydrous conditions the free radicals appeared to populate sites in the interlayer region, the activation energies under these conditions being lower than in the hydrated samples. 

At lower PPh3 concentrations where the predominant resting state observed by in situ studies is (PPh3)2Rh(CO)2H, species 3c and 3t are formed by CO dissociation, which is likewise inhibited by increased CO concentration. Consistent with this mechanism is the recent determination that dissociation/association of CO is reversible and faster than hydroformylation for arylphosphines (see 8.3). An inverse order in CO pressure and a zero order dependency on H2 pressure was reported by several authors [32,42,43], Under standard conditions, we propose that the best starting point for the kinetics is an equation of the type ... 

The rate equation for the reaction scheme in Figure 13.17 shows a zero order dependence in aryl iodide and base, a first order in alkene, and a square root order in the palladium concentration. We can conclude from this that either the complexation of acrylate to palladium or its insertion in the palladium-aryl bond is rate-determining. 

It follows therefore that, under hydrogen pressures >4atm, and K are independent of the hydrogen concentration this indicates a zero-order dependence on hydrogen pressure, such that the reaction depends only on the concentration of 1-decene in the ionic liquid. 

The HCo(CO)4 complex is therefore inferred to be involved in initial hydrogen transfer to carbon monoxide. This step was initially proposed to comprise rate-determining hydrogen atom transfer from HCo(CO)4 to free CO, affording a formyl radical, HtO subsequent reaction with further HCo(CO)4 would lead to the observed products (35). However, kinetic observations (the zero-order dependence on CO partial pressure) were later made which are inconsistent with such a process (36). 

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