The zeroth order reaction

The flux of flie adsorbed species to die catalyst from flie gaseous phase affects die catalytic activity because die fractional coverage by die reactants on die surface of die catalyst, which is determined by die heat of adsorption, also determines die amount of uncovered surface and hence die reactive area of die catalyst. Strong adsorption of a reactant usually leads to high coverage, accompanied by a low mobility of die adsorbed species on die surface, which 

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The kinetic effect of increased pressure is also in agreement with the proposed mechanism. A pressure of 2000 atm increased the first-order rates of nitration of toluene in acetic acid at 20 °C and in nitromethane at 0 °C by a factor of about 2, and increased the rates of the zeroth-order nitrations of p-dichlorobenzene in nitromethane at 0 °C and of chlorobenzene and benzene in acetic acid at 0 °C by a factor of about 559. The products of the equilibrium (21a) have a smaller volume than the reactants and hence an increase in pressure speeds up the rate by increasing the formation of H2NO. Likewise, the heterolysis of the nitric acidium ion in equilibrium (22) and the reaction of the nitronium ion with the aromatic are processes both of which have a volume decrease, consequently the first-order reactions are also speeded up and to a greater extent than the zeroth-order reactions. 

Consider the zeroth-order reaction A---- product, (a) Write... 

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. 

First-order nitrations in nitromethane are also markedly accelerated by addition of sulphuric acid, the effect being very similar to that observed with zeroth-order reactions. 

Unlike the effect of sulphuric acid upon nitration in nitric acid ( 2.2.3 where zeroth-order reactions are unknown), the form of the catalysis of zeroth-order nitration in nitromethane by added sulphuric acid does not deviate from a first-order dependence with low concentrations of catalyst. ... 

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). 

The catalysis was very strong, for in the absence of nitrous acid nitration was very slow. The rate of the catalysed reaction increased steeply with the concentration of nitric acid, but not as steeply as the zeroth-order rate of nitration, for at high acidities the general nitronium ion mechanism of nitration intervened. 

The effect of nitrous acid on the nitration of mesitylene in acetic acid was also investigated. In solutions containing 5-7 mol 1 of nitric acid and < c. 0-014 mol of nitrous acid, the rate was independent of the concentration of the aromatic. As the concentration of nitrous acid was increased, the catalysed reaction intervened, and superimposed a first-order reaction on the zeroth-order one. The catalysed reaction could not be made sufficiently dominant to impose a truly first-order rate. Because the kinetic order was intermediate the importance of the catalysed reaction was gauged by following initial rates, and it was shown that in a solution containing 5-7 mol 1 of nitric acid and 0-5 mol 1 of nitrous acid, the catalysed reaction was initially twice as important as the general nitronium ion mechanism. 

The addition of sulphuric acid increased the rate of nitration of benzene, and under the influence of this additive the rate became proportional to the first powers of the concentrations of aromatic, acetyl nitrate and sulphuric acid. Sulphuric acid markedly catalysed the zeroth-order nitration and acetoxylation of o-xylene without affecting the kinetic form of the reaction. ... 

The evidence outlined strongly suggests that nitration via nitrosation accompanies the general mechanism of nitration in these media in the reactions of very reactive compounds.i Proof that phenol, even in solutions prepared from pure nitric acid, underwent nitration by a special mechanism came from examining rates of reaction of phenol and mesi-tylene under zeroth-order conditions. The variation in the initial rates with the concentration of aromatic (fig. 5.2) shows that mesitylene (o-2-0 4 mol 1 ) reacts at the zeroth-order rate, whereas phenol is nitrated considerably faster by a process which is first order in the concentration of aromatic. It is noteworthy that in these solutions the concentration of nitrous acid was below the level of detection (< c. 5 X mol... 

Anisole] = 0 4 mol 1 zeroth-order reactions, except for that with added nitrate, which was of the first order with respect to the concentration of anisole. 

Differential temperature method. A differential method has been applied to a study of the iodination of acetone, a pseudo-zeroth-order reaction when [(CHj)2CO] [I2].26 It allows the determination of AW to much higher accuracy than otherwise. The reaction rate is expressed mathematically as... 

Figure 4. Entrance region polymer weight fraction (relative to value at the tube centerline) profiles in the tube cross section for a zeroth order reaction and uniform viscosity at GrSc = 10 and = 0.05 and 0.1.

FIGURE 6.9 Plots of the total current density vs. (or K ) for (1) first-order and (2) zeroth-order reactions. 

Another approach widely used for nonadiabatic reactions is the diabatic one. The channel Hamiltonians Hex and H determining the zeroth-order Born-Oppenheimer electron states of the donor A and acceptor B and the perturbations Vt and Vf leading to the forward and reverse electron transitions, respectively, are separated... 

Eqs. (19) and (20) were derived applying the steady-state approximation to the oxidized Fe-TAML species and using the mass balance equation [Fe-TAML] = 1 + [oxidized Fe-TAML] ([Fe-TAML] is the total concentration of all iron species, which is significantly lower than the concentrations of H2O2 and ED). The oxidation of ruthenium dye 8 is a zeroth-order reaction in 8. This implies that n[ED] i+ [H202]( i+ m). Eq. (19) becomes very simple, i.e.,... 

This is commonly called the Arrhenius equation. Table 4.1 gives typical values for fuels in terms of the specific rate constant, k. In Equation (4.1), m("r is taken as positive for the mass rate of fuel consumed per unit volume. Henceforth, in the text we will adopt this new sign convention to avoid the minus sign we were carrying in Chapter 3. The quantity A is called the pre-exponential factor and must have appropriate units to give the correct units to m("r. The exponents n and m as well as A must be arrived at by experimental means. The sum (n + m) is called the order of the reaction. Often a zeroth-order reaction is considered, and it will suffice for our tutorial purposes. 

Raising a mixture of fuel and oxidizer to a given temperature might result in a combustion reaction according to the Arrhenius rate equation, Equation (4.1). This will depend on the ability to sustain a critical temperature and on the concentration of fuel and oxidizer. As the reaction proceeds, we use up both fuel and oxidizer, so the rate will slow down according to Arrhenius. Consequently, at some point, combustion will cease. Let us ignore the effect of concentration, i.e. we will take a zeroth-order reaction, and examine the concept of a critical temperature for combustion. We follow an approach due to Semenov [3],... 

An example of a zeroth-order reaction is Reaction l-9f, 2H20(aq) H30+(aq) + OH (aq). For zeroth-order reactions, the concentrations of the reactants do not vary (which is why they are zeroth-order reactions). Use the reaction rate progress parameter Then... 

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