Zeroth-order rate law

The rates of nitration of mesitylene-a-sulphonate anion (iii) and iso-durene-a -sulphonate anion (iv) in mixtures of aqueous nitric and perchloric acid followed a zeroth-order rate law. Although the rate of exchange of oxygen could not be measured because of the presence of perchloric acid, these results again show that, under conditions most amenable to its existence and involvement, the nitric acidium ion is ineffective in nitration. 

Chloroanisole and p-nitrophenol, the nitrations of which are susceptible to positive catalysis by nitrous acid, but from which the products are not prone to the oxidation which leads to autocatalysis, were the subjects of a more detailed investigation. With high concentrations of nitric acid and low concentrations of nitrous acid in acetic acid, jp-chloroanisole underwent nitration according to a zeroth-order rate law. The rate was repressed by the addition of a small concentration of nitrous acid according to the usual law rate = AQ(n-a[HN02]atoioh) -The nitration of p-nitrophenol under comparable conditions did not accord to a simple kinetic law, but nitrous acid was shown to anticatalyse the reaction. 

Answer (b) The linear least-squares prescription described in this chapter is used to replace a complex kinetic rate law by a zeroth-order rate law. Hence, the objective function that must be minimized is... 

The latter two conditions indicate that reactant concentration within the catalyst vanishes at the critical spatial coordinate when 0 < criticai < H and it does so with a zero slope. Conditions 2a and 3 are reasonable because reactant A will not diffuse further into the catalyst, to smaller values of r), if it exhibits zero flux at ]criticai. When / critical < 0, couditiou 2b must be employed, which is consistent with the well-known symmetry condition at the center of the catalyst for kinetic rate laws where lEl constant. Zeroth-order reactions are unique because they require one to implement a method of turning ofF the rate of reaction when no reactants are present. Obviously, a zeroth-order rate law always produces the same rate of reaction because reactant molar densities do not appear explicitly in the chemical reaction term. Hence, the mass balance for homogeneous onedimensional diffusion and zeroth-order chemical reaction is solved only over the following range of the independent variable criticai < < 1. when Jiciiacai is... 

Hence, it is not possible to redefine the characteristic length such that the critical value of the intrapellet Damkohler number is the same for all catalyst geometries when the kinetics can be described by a zeroth-order rate law. However, if the characteristic length scale is chosen to be V cataiyst/ extemai, then the effectiveness factor is approximately A for any catalyst shape and rate law in the diffusion-limited regime (A oo). This claim is based on the fact that reactants don t penetrate very deeply into the catalytic pores at large intrapellet Damkohler numbers and the mass transfer/chemical reaction problem is well described by a boundary layer solution in a very thin region near the external surface. Curvature is not important when reactants exist only in a thin shell near T] = I, and consequently, a locally flat description of the problem is appropriate for any geometry. These comments apply equally well to other types of kinetic rate laws. 

The Hougen-Watson model is approximated by the best pseudo-volumetric zeroth-order rate law with kinetic rate constant 0, pseudovoiumetric such that Papp Hw Can be replaced by o.pseudovoiumetric- The questions below are based on pseudo-volumetric zeroth-order kinetics. 

For a particular experiment in a packed catalytic tubular reactor, the chemical kinetics can be approximated by a zeroth-order rate law where the best value for the zeroth-order rate constant is calculated via the formalism on pages 459 and 460. At what value of the intrapeUet Damkohler number Aa. intrapellet does reactant A occupy 75% by volume of the catalyst if the porous pellets are (a) spherical, (b) long cylinders, and (c) wafer-like ... 

The general form of the zeroth-order rate law describing this behavior is ... 

We can consider equation 20.23 in several equivalent ways. Because the rate of disappearance of reactant A is a constant, a plot of [A] versus time is a straight line, as shown in Figure 20.4. Also, we can integrate equation 20.23 to get the integrated zeroth-order rate law... 

For a chemical reaction and zeroth-order rate law of the form... 

Zeroth-order rate law) (6.11a) the concentration of A falls Hnearly until all A has been consumed ... 

Under conditions in which benzene and its homologues were nitrated at the zeroth-order rate, the reactions of the halogenobenzenes ([aromatic] = c. o-1 mol 1 ) obeyed no simple kinetic law. The reactions of fluorobenzene and iodobenzene initially followed the same rates as that of benzene but, as the concentration of the aromatic was depleted by the progress of the reaction, the rate deviated to a dependence on the first power of the concentration of aromatic. The same situation was observed with chloro- andjbromo-benzene, but these compounds could not maintain a zeroth-order dependence as easily as the other halogenobenzenes, and the first-order character of the reaction was more marked. 

These plots illustrate the variations of [A] (left axes, open squares) and of absorbance (right axes, filled squares) during the conversion of A(e = 1000) to P( = 7000) for data following zeroth-order (left), halforder (center), and three-halves-order rate laws. 

If the process of APIO is properly described by Equation (19), which infers the presence of a soluble Fe(III) intermediate species, it will be difficult to analyze this species directly, given the low levels that are expected. We must therefore develop mathematical approaches to estimating the isotopic composition of this component, as was done for DIR. The equations used in the previous chapter (Chapter lOA Beard and Johnson 2004) to describe abiotic Fe(II) oxidation are useful for illustrating possible isotopic fractionations that may occur during APIO. We will assume that the overall oxidation process occurs through a series of first-order rate equations, where relatively slow oxidation of FefTI) to a soluble Fe(III) component occurs, which we will denote as Fe(III)jq for simplicity. The oxidation step is followed by precipitation of Fe(III)jq to ferrihydrite at a much faster rate, which maintains a relatively low level of Fe(III)jq relative to Fe(II)jq. The assumption of first-order kinetics is not strictly valid for the experiments reported in Croal et al. (2004), where decreasing FefTI) contents with time do not closely follow either zeroth-, first-, or second-order rate laws. However, use of a first-order rate law allows us to directly compare calculations here with those that are appropriate for abiologic Fe(II) oxidation, where experimental data are well fit to a first-order rate law (Chapter lOA Beard and Johnson 2004). 

When large concentrations of water are added to the solutions, nitration according to a zeroth-order law is no longer observed. Under these circumstances, water competes successfully with the aromatic for the nitronium ions, and the necessary condition for zeroth-order reaction, namely that all the nitronium ions should react with the aromatic as quickly as they are formed, no longer holds. In these strongly aqueous solutions the rates depend on the concentrations and reactivities of the aromatic compound. This situation is reminiscent of nitration in aqueous nitric acid in which partial zeroth-order kinetics could be observed only in the reactions of some extremely reactive compounds, capable of being introduced into the solution in high concentrations ( 2.2.4). 

Derive the rate law. With a different catalyst, the rate is zeroth-order with respect to [alkene]. How can this be interpreted ... 

Quantitative ESR measurements confirmed that almost all of the total quantity of copper is present as [Cu(RS)] complex during the reaction (65). The kinetic data were consistent with a rate law which is zeroth-order in cysteine concentration ... 

Srinivasan etal.,64 in a phenomenological development, split the etch rate into thermal and photochemical components and used zeroth-order kinetics to calculate the thermal contribution to the etch rate. An averaged time-independent temperature that is proportional to the incident fluence was used to determine the kinetic rate constant. The photochemical component of the etch rate was modeled using, as previously discussed, a Beer s law relationship. The etch depth per pulse is expressed, according to this model, in the form... 

Because HC02H (formic acid) does not appear in the rate law, the rate is independent of the concentration of HC02H, and the reaction is zeroth order in HC02H. Because the exponent on [Br2] (understood) is 1, the reaction is first order in Br2. The reaction is first order overall because the sum of the exponents is 1. 

A zeroth-order reaction of the type A — products is one that has the rate law... 

Beginning with the integrated rate law, derive a general equation for the half-life of a zeroth-order reaction of the type A — Products. How does the length of each half-life compare with the length of the previous one Make the same comparison for first-order and second-order reactions. 

The anticatalytic effect of nitrous acid in nitration The effect of nitrous acid was first observed for zeroth-order nitrations in nitromethane ( 3.2).22 The effect was a true negative catalysis the kinetic order was not affected, and nitrous acid was neither consumed nor produced by the nitration. The same was true for nitration in acetic acid.23 In the zeroth-order nitrations the rate depended on the reciprocal of the square root of the concentration of nitrous acid Aobs = (a + b [HNOJatoioh)-1- First-order nitrations in the organic solvents follow a law of anticatalysis of the same form (but with different constants in the above equation). With both zeroth- and first-order nitrations a more powerful type of anticatalysis set in when higher (> o-i mol 1 1) concentrations of nitrous acid were present. 

In 7-5 % aqueous sulpholan the very reactive compound, anthan-threne, could be nitrated according to a first-order law only with low concentrations of nitric acid, and the reaction was very strongly catalysed by nitrous acid. Under zeroth-order conditions (i.e. in the absence of water and with [HN03] = 5 mol l-1) and with a very small concentration of nitrous acid ([HN02] < 3 x io 5 mol l-1 [urea] = 0-05 mol l-1), where the use of mesitylene gave k0 = 2 ix io-8 mol l-1 s 1 (at 25 °C), the nitration of anthanthrene was too fast to be measured. Clearly, the nitronium ion mechanism could not be operative. With low concentrations of nitric acid ([HN03] < 1 mol l-1) zeroth-order nitration of anthanthrene of the same rate as that for mesitylene could with difficulty be observed often autocatalysis intervened.31... 

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