First-order rate

Fig. 3. Decay of the H202 concentration versus time during the anaerobic oxidation reaction with cysteine in the presence of CuS04. First stage of constant rate (first-order in [Cu]) during the period of oxidation, second stage of increasing rate after completion of the oxidation of cysteine to cystine. Reprinted from Journal of Molecular catalysis, vol. 11, Zwart, J. van Wolput, J. H. M. C. van der Cammen, J. C. J. M. Koningsberger, D. C. Accumulation and Reactions of H202 During the Copper Ion Catalyzed Autoxidation of Cysteine in Alkaline Medium, p. 69, Copyright (2002), with permission from Elsevier Science.

Fig. 10 a, b. Column experiments using different flow rates, first order model TOC concentration released vs a time b pore volume... 

Research with pilot scale units has shown that the major resistances to mass transfer of reactant to catalyst are within the liquid film surrounding the wetted catalyst particles and also intraparticle diffusion. A description of these resistances is afforded by Fig. 14. Equating the rate of mass transfer across the liquid film to the reaction rate, first order in hydrogen concentration... 

A sample CFSTR of volume VR has one inlet stream rate u, containing A at concentration CA0 and a second inlet stream of rate au, containing B at concentration CBO, The reaction is A + B ——>2P with the rate first order with respect to both A and B. Obtain an expression for the concentration of A at the reactor exit in terms of VR and the conditions in the feed streams. 

Figure 10. Effectiveness factor ij as a function of the Weisz modulus ji. Combined influence of intraparticle and interphase mass transfer and interphase heat transfer on the effective reaction rate (first order, irreversible reaction in a sphere, Biot number Bim = 100, Arrhenius number y — 20, modified Prater number ( as a parameter).

Cook and Moore35 studied gas absorption theoretically using a finite-rate first-order chemical reaction with a large heat effect. They assumed linear boundary conditions (i.e., interfacial temperature was assumed to be a linear function of time and the interfacial concentration was assumed to be a linear function of interfacial temperature) and a linear relationship between the kinetic constant and the temperature. They formulated the differential difference equations and solved them successively. The calculations were used to analyze absorption of C02 in NaOH solutions. They concluded that, for some reaction conditions, compensating effects of temperature on rate constant and solubility would make the absorption rate independent of heat effects. 

Moreover, eqn 6.13 can be applied to a reversible catalytic reaction in which the catalyst acts as a co-reactant in an early step and is restored as a co-product in a later one. Its concentration, Q, then appears in both the numerator and denominator on the right-hand side of eqn 6.13, and so cancels, in accordance with the requirement that the presence of a catalyst does not affect equilibrium. In the rate equation developed from eqns 6.4 to 6.6, Crat appears as co-factor in both terms of the numerator. This makes the rate first-order in the catalyst, provided CMl does not also appear in some terms of denominator, as it will unless the catalyst reacts in the first step and is reformed in the last, as is usually true. 

Figure 10.4. Rate of methyl methacrylate chain polymerization. Left rate first order in monomer (redox initiator) [36] right rate approximately half order in initiator (benzoyl peroxide) [37].

In this expression = 6.37 x 10 L/mol s at 25 C. The reverse reaction rate (first-order) is given by /f = k (FeSO ). The equilibrium constant is = 205/mol, from which (because = kjk and assuming the principle of detailed balancing) we compute k = 31/s. Calculated rates and concentrations for this reaction as a function of time are given in Fig. 2.8. Note that the overall rate R in Fig. 2.8[b]) equals the difference ( + - / ). 

EFFECT OF PORE DIFFUSION ON REACTION RATE First-Order Reaction... 

A similar approach can be used to estimate atmospheric degradation rates first-order rate constant, fep expressed as follows ... 

Insertion of the dienes CH2=CRCR =CH2 into the Fe—H bond in [Cp(OC)2FeH] occurs with rates first order in [complex] and [diene] but independent of An inverse primary H/D isotope effect is observed and... 

The quadrupling of the hydrogen ion concentration results in a quadrupling of the rate (first-order kinetic behaviour) the halving of the bromate concentration results in the rate being reduced by a factor of 2 (first-order kinetic behaviour). This is equivalent to the overall rate being doubled. 

For a certain concentration at the surface of the unreacted core, Ca c, and rate constant related to the surface area (m s ), the chemical reaction rate (first-order reaction) is given by... 

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