First-order reactions homogeneous

For a first order reaction (-r ) = kC, and Equation 8-147 is then linear, has constant coefficients, and is homogeneous. The solution of Equation 8-147 subject to the boundary conditions of Danckwerts and Wehner and Wilhelm [23] for species A gives... 

The kinetics of resole cure reactions monitored via FTIR suggest that a diffusion mechanism dominates below 140°C. The cure above 140°C exhibits a homogeneous first-order reaction rate. The activation energy of the cure reaction was -"-49.6 kJ/mole.66... 

The black box is closed again. This section assumes that the system is isothermal and homogeneous and that its residence time distribution is known. Reaction yields can be predicted exactly for first-order reactions. For other reactions,... 

Example 15.9 Use residence time theory to predict the fraction unreacted for an isothermal, homogeneous, first-order reaction occurring in a CSTR and aPFR. 

This is an integral along a molecule s path that weighs time and temperature in the manner appropriate to homogeneous but nonisothermal reactions. For a first-order reaction,... 

In the case of 0-pipettes, the collection efficiency also decreases markedly with increasing separation. The situation becomes more complicated when the transferred ion participates in a homogeneous chemical reaction. For the pseudo-first-order reaction a semiquantita-tive description is given by the family of dimensionless working curves calculated for two disks (Fig. 6) [23]. Clearly, at any separation distance the collection efficiency approaches zero when the dimensionless rate constant (a = 2kr /D, where k is the first-order rate constant of the homogeneous ionic reaction) becomes 1. 

A hypothetical reaction with assumed properties was taken, since no real-case reaction was available for demonstration. Liquid-phase operation for a homogeneously catalyzed pseudo-first-order reaction was... 

In homogeneous catalysis, the quantification of catalyst activities is commonly carried out by way of TOF or half-life. From a kinetic point of view, the comparison of different catalyst systems is only reasonable if, by giving a TOF, the reaction is zero order or, by giving a half-time, it is a first-order reaction. Only in those cases is the quantification of activity independent of the substrate concentration utilized ... 

Applying the usual steady-state treatment for consecutive first-order reactions kt at 16 torr pressure over the temperature range 597-701 °C is given by 1.8 x 1011 exp(—47,000/Kr) sec Within experimental error, reactions (1) and (2) were homogeneous processes. However, both k2 and k2 were functions of the total pressure in the system. This dependence is shown in Fig. 1. The methyl zinc decomposition is apparently in its second-order region. Therefore, assuming four effective oscillators and a mean temperature of 1050 °K, = Eohs.+i nRT... 

A continuous flow stirred reactor operates off the decomposition of gaseous ethylene oxide fuel. If the fuel injection temperature is 300 K, the volume of the reactor is 1500 cm3, and the operating pressure is 20 atm, calculate the maximum rate of heat evolution possible in the reactor. Assume that the ethylene oxide follows homogeneous first-order reaction kinetics and that values of the reaction rate constant k are... 

XII. Tricyclic Systems Containing a Cyclobxttane Ring The only system of this kind which appears to have been investigated kinetically in detail is tricyclo[3,3,0,0 ]octane (Srinivasan and Levi, 1964). At temperatures in the range 327 to 366° C the isomerization is a homogeneous first-order reaction. The observed products were 4-vinyl-cyclohexene, butadiene and 1,5-cyclo-octadiene. However, from separate studies on the cyclo-octadiene, it is concluded that the tricyclo-octane first isomerizes to the cyclo-octadiene which then undergoes secondary reactions to yield the other observed products. The observed rate is then the rate of this primaiy reaction, viz. ... 

Consider the system to possess a specific RTD, E(f), and that the reactor is fed with a homogeneous, perfectly mixed feed stream. If a first-order reaction takes place within this reactor the system will be described by linear equations. In this case, the reaction kinetics and the system residence time distribution totally define the conversion of reactant which would be achieved in that system. In other words, any reactor system possessing that particular RTD under consideration would give the same feed conversion... 

The kinetics of a homogeneous liquid reaction are studied in a flow reactor, and to approximate plug flow the 48-cm long reactor is packed with 5-mm nonporous pellets. If the conversion is 99% for a mean residence time of 1 sec, calculate the rate constant for the first-order reaction... 

Many of the reactions discussed in the preceding pages are in fact bimolecular processes, which would normally follow second-order kinetics. However, as aheady discussed, under the regime of LFP they behave as pseudo-first-order reactions. The corresponding rate constants and lifetimes are independent of the initial concentration of transient, and therefore knowledge of extinction coefficients and quantum yields is not needed. Further, it is not important to have a homogenous transient concentration. 

Mass Transfer in Flow along a Flat Plate with Homogeneous First-Order Reaction... 

In the case of A as limiting reactant and a variable-density system, the solution of the model is the same as for first-order irreversible homogeneous reactions of the form A - products (Levenspiel, 1972) ... 

Two important ways in which heterogeneously catalyzed reactions differ from homogeneous counterparts are the definition of the rate constant k and the form of its dependence on temperature T. The heterogeneous rate equation relates the rate of decline of the concentration (or partial pressure) c of a reactant to the fraction / of the catalytic surface area that it covers when adsorbed. Thus, for a first-order reaction,... 

Laboratory experiments, confirmed by data from large scale operations, have shown that ethane decomposition is a homogeneous first order reaction, the rate constant (s ) being given by the equation in SI units 6 ... 

We will consider a dispersed plug-flow reactor in which a homogeneous irreversible first order reaction takes place, the rate equation being 2ft = k, C. The reaction is assumed to be confined to the reaction vessel itself, i.e. it does not occur in the feed and outlet pipes. The temperature, pressure and density of the reaction mixture will be considered uniform throughout. We will also assume that the flow is steady and that sufficient time has elapsed for conditions in the reactor to have reached a steady state. This means that in the general equation for the dispersed plug-flow model (equation 2.13) there is no change in concentration with time i.e. dC/dt = 0. The equation then becomes an ordinary rather than a partial differential equation and, for a reaction of the first order ... 

When homogeneous poisoning occurs, since no reaction will be possible on the poisoned fraction ( , say, as shown in Fig. 3.11) of active surface it is reasonable to suppose that the intrinsic activity of the catalyst is in proportion to the fraction of active surface remaining unpoisoned. To find the ratio of activity of the poisoned catalyst to the activity of an unpoisoned catalyst one would compare the stationary flux of reactant to the particle surface in each case. For a first-order reaction... 

To incorporate mixing by the dispersed plug flow mechanism into the model for the bubble column, we can make use of the equations developed in Chapter 2 for dispersed plug flow accompanied by a first-order chemical reaction. In the case of the very fast gas-liquid reaction, the reactant A is transferred and thus removed from the gas phase at a rate which is proportional to the concentration of A in the gas, i.e. as in a homogeneous first-order reaction. Applied to the two-phase bubble column for steady-state conditions, equation 2.38 becomes ... 

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