First order irreversible series reactions

Consider the first order series reactions [4] A —— B — — C. The governing equations for this reaction scheme can be written as 

A Maple procedure for solving equations (2.8) subject to the initial conditions is 

Start the Maple program with a restart command to clear all variables. 

Call Maple s linear algebra package by using the with(linalg) command. 

Call Maple s plotting package by using the with(plots) command. 

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Consider the first-order irreversible series reaction A—carried out in an ideal CSTR to maximise the production of product B. Show that the space time x for maximum production of B is Xmax = 1/yjk and the maximum product concentration is... 

The first-order irreversible exothermic reaction A —> B occurs in the liquid phase of one or more stirred-tank reactors in series. In a series configuration all reactors have the same volume and operate at the same specified temperature. A height- to-diameter ratio of 2 is assumed in the design. The reaction rate is... 

Consider a train of five CSTRs in series that have the same volume and operate at the same temperature. One first-order irreversible chemical reaction occurs in each CSTR where reactant A decomposes to products. Two mass-transfer-rate processes are operative in each reactor. The time constant for convective mass transfer across the inlet and outlet planes of each CSTR is designated by the residence time x = Vjq. The time constant for a first-order irreversible chemical reaction is given >y X = l/k. The ratio of these two time constants,... 

Matrix Analysis. Startup behavior of a series of n CSTRs in series with first-order irreversible chemical reaction is described by n coupled ODEs. These equations ... 

One should compare the analytical solution given by equation (2-15) with the Laplace transform and matrix results for startup behavior of a series of n CSTRs with first-order irreversible chemical reaction. The three solutions are equivalent. An alternative proof of the analytical solution that does not require mathematical rigor is based on graphical comparison of the numerical results in Figure 2-3 with the solution given by equation (2-15). The numerical and analytical solutions are indistinguishable. 

Example 4.13 treated the case of a piston flow reactor inside a recycle loop. Replace the PER with two equal-volume stirred tanks in series. The reaction remains first order, irreversible, and at constant density. 

It is readily apparent that equation 8.3.21 reduces to the basic design equation (equation 8.3.7) when steady-state conditions prevail. Under the presumptions that CA in undergoes a step change at time zero and that the system is isothermal, equation 8.3.21 has been solved for various reaction rate expressions. In the case of first-order reactions, solutions are available for both multiple identical CSTR s in series and individual CSTR s (12). In the case of a first-order irreversible reaction in a single CSTR, equation 8.3.21 becomes... 

For the case where all of the series reactions obey first-order irreversible kinetics, equations 5.3.4, 5.3.6, 5.3.9, and 5.3.10 describe the variations of the species concentrations with time in an isothermal well-mixed batch reactor. For series reactions where the kinetics do not obey simple first-order or pseudo first-order kinetics, the rate expressions can seldom be solved in closed form, and it is necessary to resort to numerical methods to determine the time dependence of various species concentrations. Irrespective of the particular reaction rate expressions involved, there will be a specific time... 

A series of experiments were performed using various sizes of catalyst spheres. The reaction was first order irreversible. The first two columns of the table record the diameter dp in cm and the rate in mol/(h)(cc). The surface concentration was Cs = 0.0002 mol/cc. Find the true specific rate and the effective diffusivity. 

Consider a two-step first-order irreversible reactions in series... 

The simplest sets of reactions involve series or parallel first-order irreversible reactions. We will first consider these cases because they have simple analytical solutions and are useful prototypes of more complicated reaction sets. These can be considered in the energy diagrams similar to those we discussed in the previous chapter for single reactions. 

An industrial system consists of a nonisothermal CSTR (with a cooling jacket) and a tubular adiabatic reactor in series. The reaction is a first-order irreversible reaction ... 

A series of first order irreversible reactions is one in which an intermediate is formed that can then further react. A generalized series reaction is... 

Consider the series first order irreversible reaction of the form A —>B—>C in a constant density CFSTR. The material balance of component A is uCA0 = uCA + Vr. The material balance of component B is uCB0 = uCB + (k2CB - kiCA)VR. The material balance of component C is uCco = uCc - k2CBVR. Assuming that CBO = Cco = 0, then the exit concentration of components A, B, and C are... 

Table 1 Conversion of a system of CSTRs in series (total volume = 0.6 m3, volumetric flow rate = 0.1 m3 h ) for a first-order irreversible reaction with kinetic constant equal to 0.25 h 1...

If you have a CSTR and a PFR (both of the same volume) available to carry out an irreversible, first-order, liquid-phase reaction, how would you connect them in series (in what order) to maximize the conversion ... 

A chemical reaction takes place in a series of four continuous stirred tank reactors arranged as shown. The chemical reaction is a first-order irreversible reaction of the type. 

Figure 4.13 Illustration of the conversion in a series of CSTR for a first-order irreversible reaction with a constant total residence time and a variable number of units in the series. The total residence time is 1 (arbitrary units) and the rate constant is in the same time units.

For first-order irreversible reactions and Danckwerts residence time distribution Huang and Kuo derived two solutions one for long exposure times that expresses the concentration gradients in trigonometric function series and the following solution for rather short exposure times, obtained by Laplace transforms ... 

For a first-order irreversible reaction A-PFR connected in series, show that the overall conversion is independent of which reactor precedes when the reactor volumes are equal. 

A first-order irreversible reaction A B is described by a tanks-in-series model. The total volume (and total residence time) of the system is fixed, but the number of tanks can be changed. Which limit approaches C utlcoK as the number of tanks approaches infinity Prove this mathematically. 

For two, first-order, irreversible reactions in series, with no intermediate (R) in the feed... 

Example 4.12 used N stirred tanks in series to achieve a 1000-fold reduction in the concentration of a reactant that decomposes by first-order kinetics. Show how much worse the CSTRs would be if the 1000-fold reduction had to be achieved by dimerization i.e., by a second order of the single reactant type. The reaction is irreversible and density is constant. 

Irreversible Reactions in Series. We first consider consecutive unimolecular-type first-order reactions such as... 

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