Pseudo nth order

The results of the types of reaetion being eonsidered show that the treatment of kinetie data heeomes rapidly more eomplex as the reaetion order inereases. In eases where the reaetion eonditions are sueh dial the eoneentrations of one or more of the speeies oeeurring in the rate equation remain eonstant, these terms may he ineluded in the rate eonstant k. The reaetions ean he attributed to lower order reaetions. These types of reaetions ean be defined as pseudo-nth order, where n is the sum of the exponents of those eoneentrations that ehange during the reaetion. An example of this type of reaetion is in eatalytie reaetion, where the eatalyst eoneentration remains eonstant during the reaetions. 

What is the total order n of a given reaction What are the most common reaction orders in environmental organic chemistry Does the total order of a given reaction tell you anything about the reaction mechanism What is a pseudo-nth-order rate constant ... 

The decompositions of complex materials are treated as combinations of a series of parallel and/or consecutive pseudo-unimolecular reactions representing the rates of formation of the individual products. Detail is given [99,100] for pseudo-nth order and autocatalytic reaction types. 

When n equals 0, 1, or 2, the reaction is said to be a pseudo-zero-, pseudo-first-, or pseudo-second-order reaction (pseudo-nth-order for higher order reactions), respectively. If the concentration of an additional reactant other than drug D is not constant during the reaction, the reaction order becomes n + 1. 

She has employed resistance measurements to monitor the progress of this reaction. Her exposure to reaction kinetics leads her to suggest that it would be appropriate to assume that the presence of a large excess of ethanol will lead to a rate expression that is pseudo-nth-order in RBr. Sue knows that it is often convenient to obtain data at time intervals separated by a constant time increment and has taken these precautions. She also knows that when monitoring the progress of areaction via physical property measurements, one requires measurements at times zero and infinity. Unfortunately, her measurements at these times are invalid because of an equipment malfunction. She is perplexed and wonders if she will have to repeat the experiment. 

Fast (regime 3) in both phases no depletion (pseudo-nth order in phase I and pseudo-mth Order in phase 2)... 

In determining m, variation in A is not influenced by variation in B. For this, a large excess of B should be employed. The converse should be applied when determining n. When a large excess of one of the reactants was employed, the kinetics reduces from (m x n)th order to pseudo nth order and Equation 7.5 reduces to Equation 7.2. 

When the reaction between components A and B in the liquid phase is mth order in A, and nth order in B, and the concentration of component B is nearly constant throughout the TBR, the reaction is said to be rapid-pseudo-mth order in A. The condition for this situation is 3 < Ha < Ej. The rate of absorption is then expressed by ... 

If the assumptions made above are not valid, and/or information about the rate constants of the investigated reactions is required, model-based approaches have to be used. Most of the model-based measurements of the calorimetric signal are based on the assumption that the reaction occurs in one single step of nth order with only one rate-limiting component concentration in the simplest case, this would be pseudo-first-order kinetics with all components except one in excess. The reaction must be carried out in batch mode (Vr = constant) in order to simplify the determination, and the general reaction model can, therefore, be written as Equation 8.14 with component A being rate limiting ... 

Determination of Integral Method When the concentrations of reactants and products in the cay order for phase change very slowly with time, the pseudo-steady-state forms of the order n balances can be used. For the irreversible nth-order reaction carried out... 

The Hougen-Watson rate law lEinw, with units of moles per area per time, is written on a pseudo-volumetric basis using the internal surface area per mass of catalyst S , and the apparent mass density of the pellet Papp. k is the nth-order kinetic rate constant with units of (volume/mole)" per time when the rate law is expressed on a volumetric basis using molar densities. 

Methodology. Pseudo-first-order kinetic rate constants that are consistent with nth-order kinetics and Hougen-Watson models are calculated as follows ... 

Notice that the molar density of key-limiting reactant A on the external surface of the catalytic pellet is always used as the characteristic quantity to make the molar density of component i dimensionless in all the component mass balances. This chapter focuses on explicit numerical calculations for the effective diffusion coefficient of species i within the internal pores of a catalytic pellet. This information is required before one can evaluate the intrapellet Damkohler number and calculate a numerical value for the effectiveness factor. Hence, 50, effective is called the effective intrapellet diffusion coefficient for species i. When 50, effective appears in the denominator of Ajj, the dimensionless scaling factor is called the intrapellet Damkohler number for species i in reaction j. When the reactor design focuses on the entire packed catalytic tubular reactor in Chapter 22, it will be necessary to calcnlate interpellet axial dispersion coefficients and interpellet Damkohler nnmbers. When there is only one chemical reaction that is characterized by nth-order irreversible kinetics and subscript j is not required, the rate constant in the nnmerator of equation (21-2) is written as instead of kj, which signifies that k has nnits of (volume/mole)"" per time for pseudo-volumetric kinetics. Recall from equation (19-6) on page 493 that second-order kinetic rate constants for a volnmetric rate law based on molar densities in the gas phase adjacent to the internal catalytic surface can be written as... 

The heterogeneous rate law in (22-57) is dimensionalized with pseudo-volumetric nth-order kinetic rate constant k that has units of (volume/mol)" per time. k is typically obtained from equation (22-9) via surface science studies on porous catalysts that are not necessarily packed in a reactor with void space given by interpellet. Obviously, when axial dispersion (i.e., diffusion) is included in the mass balance, one must solve a second-order ODE instead of a first-order differential equation. Second-order chemical kinetics are responsible for the fact that the mass balance is nonlinear. To complicate matters further from the viewpoint of obtaining a numerical solution, one must solve a second-order ODE with split boundary conditions. By definition at the inlet to the plug-flow reactor, I a = 1 at = 0 via equation (22-58). The second boundary condition is d I A/df 0 as 1. This is known classically as the Danckwerts boundary condition in the exit stream (Danckwerts, 1953). For a closed-closed tubular reactor with no axial dispersion or radial variations in molar density upstream and downstream from the packed section of catalytic pellets, Bischoff (1961) has proved rigorously that the Danckwerts boundary condition at the reactor inlet is... 

The parameter has dimensions of (volume/mol)" because >S m/Oapp n,sur ce is a pseudo-volumetric nth-order kinetic rate constant with units of (volume/mol)" /time. In dimensionless notation, equation (30-62) yields the following nonlinear polynomial that relates the molar densities of reactant A in the bulk gas stream and at the external surface of the catalyst ... 

SYSTEMS WITH UNIFORM TEMPERATURE DISTRIBUTION Semenov assumed a pseudo zero order (that is, with no reactant consumption) exothermic reaction following an Arrhenius type rate law — that is, the rate of reaction and therefore the rate of heat production increa.ses exponentially with temperature. Thus for an irreversible nth order reaction A — B at constant volume V the rate of heat production is given by ... 

In Appendix B we show that the action of the pseudo-Liouville operator on the singlet field generates a coupling to the doublet field, and so on. One may show that if the phase-space density fields are defined as in (7.5), if density fields up to the th order are included explicitly in the description, the random forces corresponding to all fields lower than the nth are zero. Hence only the damping matrix corresponding to this /ith-order field is nonzero. As an example, consider the case of singlet and doublet fields that are explicitly treated. In this case, (7.14) reduces to two coupled equations of the form... 

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