Zeroth order kinetics

Employing simplifications arising from the use of asymptotic forms of the electronic basis functions and the zeroth-order kinetic energy operator, we obtain... 

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). 

Recent experiments have shown that the concentration of aromatic compound needed to maintain zeroth-order kinetics (see below) was much greater than for nitrations with solutions of nitric acid in some inert organic solvents reactions which were first order in the concentration of the aromatic were obtained when [ArH] < c. 2 x io mol 1 . ... 

Nitrations of the zeroth order are maintained with much greater difficulty in solutions of acetyl nitrate in acetic anhydride than in solutions of nitric acid in inert organic solvents, as has already been mentioned. Thus, in the former solutions, the rates of nitration of mesi-tylene deviated towards a dependence on the first power of its concentration when this was < c. o-05-o-i mol 1 , whereas in nitration with nitric acid in sulpholan, zeroth-order kinetics could be observed in solutions containing as little as 10 mol 1 of mesitylene ( 3.2.1). 

In general, nitrations in nitromethane show a greater tendency towards zeroth-order kinetics, so that, for example, whereas benzene gives first-order kinetics on nitration by 7.0 M nitric acid in acetic acid (Table 13), in nitro-... 

Mesitylene was studied using the range 5-7 M nitric acid, and when the nitrous acid concentration is small (< 0.014 M) nitronium ion nitration appears to occur, giving zeroth-order kinetics weakly retarded by nitrous acid. At rather higher nitrous acid concentrations the reaction is catalysed by nitrous acid and the kinetics go over to first-order (at constant nitrous acid concentration). 

Zeroth-order kinetics. The rate of bromination of acetone in acidic aqueous solution is governed by the enolization step. With [(CH3>2CO]o s> [B lo, the reaction rate is... 

Zero-point energy, 215 Zeroth-order kinetics, 28... 

Figure 3(a) shows rates of NH decomposition on clean polycrystalline Rh. As with NO decomposition the rate obeys zeroth order kinetics at low temperature and first order kinetics at higher temperature. 

A flat material of thickness is placed on a hot plate of controlled temperature Tb. The material is energetic and exothermic with a heat of combustion of Ahc and its reaction is governed by zeroth-order kinetics, Ae E RT the mass loss rate per unit volume. Notation is as used in the text. The differential equation governing the process to ignition is given as... 

Trace amounts of Cu(II) were reported to catalyze the oxidation of I-to I2 (156) and the phosphinate ion (H2P02) to peroxodiphosphate ion (PDP), which could be present as P20g, HP20 or H2P20f (757). Individual kinetic traces showed some unusual patterns in these reactions, such as the variation between first- and zeroth-order kinetics with respect to the formation of I2 under very similar conditions, or an autocatalytic feature in the concentration profiles of PDP, but these events were not studied in detail. The catalytic effect was interpreted in terms of a Cu(II) / Cu(I) redox cycle and the superoxide ion radical,... 

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... 

The gas-phase reaction A —> 3B obeys zeroth-order kinetics with r = 0.25 moles/liter h at 200°C. Starting with pure. 4 at 1 atm calculate the time for 95% of the. 4 to be reacted away in... 

To see selectivities for other rate expressions, let us consider the same reactions with zeroth-order kinetics. 

Note that with zeroth-order kinetics the rate of formation of a species goes to zero when the concentration of the reactant forming is goes to zero. We write Cb,ca O to indicate the value of Cg when goes to zero because after that time no more B is being formed. You should plot these functions and compare them with curves for first-order kinetics. 

For zeroth-order kinetics the maximum selectivities are identical, and for negative-order kinetics the CSTR wiU give a higher maximum selectivity. [What type of reactor will be better if one reaction is positive order and the other negative order ]... 

Calculate the conversion of A B, r = kC in two CSTRs using the residence time distribution and compare the result with that obtained by integrating the CSTR mass balances. Repeat this problem for zeroth-order kinetics. 

The generic shape of the desorption peak for TPD, zeroth order kinetics. (Parameters A=10 s , E = 100 kJ/mol, initial coverage 0.95.)... 

Sciortino, F., Bansil, R., Stanley, E.H., Alstrom, P. (1993). Interference of phase separation and gelation a zeroth-order kinetic model. Physical Review E, 47, 4615 1618. 

This evidence is not compelling partly because the transition to a zeroth-order form is not complete and partly because high concentrations of substrates have, in other reactions, produced a spurious transition to a zeroth-order form as a result of medium effects (Marziano et al., 1974). However, if the zeroth-order kinetics arise from medium effects, the rate coefficient for the formation of the electrophile must be even greater than the value of 617 moH s-1 dm3 quoted above. 

Fig. 2.9 Examples of temperature-programmed desorption following zeroth-, first- and second-order kinetics. Each curve corresponds to a different initial coverage of the adsorbate. Ag/Ru(001) Silver forms islands on the ruthenium substrate. Desorption of Ag from the edges of these islands gives rise to zeroth-order kinetics note the exponential increase of the low-temperature sides of the peak, as expected from Eq. (2-15). Desorption from the second layer of silver occurs at lower temperatures, indicating that Ag-Ag bonds are weaker than Ag-Ru bonds [20]. CO/Rh(111) At coverages...

Derive the zeroth-order kinetics model expression in Eq. 6.3 from the von Smoluchowski rate law. (Hint Choose a suitable representation for N(t) and for the rate coefficient kmn in Eq. 6.10.)... 

Figure 6.11 holds for a slab. Similar figures can be obtained for other catalyst geometries. This is illustrated in Figure 6.13 where the effectiveness factor is plotted versus 8 for zeroth-order kinetics in an infinite slab, infinite cylinder and a sphere. Figure 6.13 has been constructed on the basis of the formulae given in Table 6.6. Hence, the discussion that follows is not restricted to a slab, but holds for any arbitrary catalyst geometry. 

Figure 6.13 Effectiveness factor r versus Thiele modulus 8 of Equation 6.48 for zeroth-order kinetics in an infinitely long slab, an infinitely long cylinder and a sphere.

Table 6.6 Effectiveness factor tj as a function of the Thiele modulus 8 (given by Equation 6.48) for zeroth-order kinetics an infinite slab, an infinite cylinder and sphere...

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