The first-order series reactions A B, B C have activation energies of 8 and 10 kcal/mole, respeetively. In a 1 liter batch reactor at 100°C the selectivity to B is 50% and the conversion is 50% in a reaetion time of 10 min with = 1 mole/liter. The solvent is water and the reactor can be pressurized as needed to maintain liquids at any temperature. [Pg.200]

First-order kinetics. Consider a first-order reaction studied with a series of initial concentrations, as depicted here. Show that the initial rate tangents come to a common intercept t" on the x axis, and find an expression for what time this is. [Pg.44]

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 [Pg.324]

Use the F(t) curve for two identical CSTR s in series and the segregated flow model to predict the conversion achieved for a first-order reaction with k = 0.4 ksec-1. The space time for an individual reactor is 0.9 ksec. Check your results using an analysis for two CSTR s in series. [Pg.421]

In the reaction scheme in series (sixth row in Table 2.1), the required product is often the intermediate I, and its concentration has a maximum at time t, which can be taken as the optimal batch time, When the system follows a first-order kinetics not affected by chemical equilibrium (Fig. 2.5), it can be easily shown that t depends on the values of the rate constants through the following expression [Pg.18]

That is, A decays exponentially with time determined by (kl7[B]0), as if it were a first-order reaction. Thus under these so-called pseudo-first-order conditions, a plot of ln[A] against time for a given value of [B]0 should be linear with a slope equal to ( — I7[B]0). These plots are carried out for a series of concentrations of [B](l and the values of the corresponding decays determined. Finally, the absolute rate constant of interest, kl7, is the slope of a plot of the absolute values of these decay rates against the corresponding values of [B] . Some examples are discussed below. [Pg.142]

This program is designed to simulate the resulting residence time distributions based on a cascade of 1 to N tanks-in-series. Also, simulations with nth-order reaction can be run and the steady-state conversion obtained. A pulse input disturbance of tracer is programmed here, as in example CSTRPULSE, to obtain the residence time distribution E curve and from this the conversion for first order reaction. [Pg.333]

Example 4.5 Derive the state space representation of two continuous flow stirred-tank reactors in series (CSTR-in-series). Chemical reaction is first order in both reactors. The reactor volumes are fixed, but the volumetric flow rate and inlet concentration are functions of time. [Pg.68]

Imagine a first-order reaction taking place in such a system under conditions where rk, i.e. VkjQ, is 10 and R is 5. Using the technique previously adopted in Sect. 5.1 and outlined in Appendix 2, we can readily calculate that this system would achieve 96.3% conversion of reactant. Under these conditions, the recycle reactor volume turns out to be 3.03 times that of an ideal PFR required for the same duty. This type of calculation allows Fig. 14 to be constructed this is similar in form to Fig. 12, but lines of constant for the tanks-in-series model have been replaced by lines of constant recycle ratio for the recycle model. From a size consideration alone, the choice of a PFR recycle reactor is not particularly [Pg.258]

A first-order liquid-phase reaction takes place in a baffled stirred vessel of 2 volume under conditions when the flow rate is constant at 605 dm min and the reaction rate coefficient is 2.723 min the conversion of species A is 98%. Verify that this performance lies between that expected from either a PFR or a CSTR. Tracer impulse response tests are conducted on the reactor and the data in Table 6 recorded. Fit the tanks-in-series model to this data by (A) matching the moments, and (B) evaluating N from the time at which the maximum tracer response is observed. Give conversion predictions from the tanks-in-series model in each case. [Pg.251]

When cyclopropane (C3H , see 1) is heated to 500.°C (773 K), it changes into an isomer, propene (see 2). The following data show the concentration of cyclopropane at a series of times after the start of the reaction. Confirm that the reaction is first order in C3H6 and calculate the rate constant. [Pg.662]

From the data of runs Cl to C20 and D1 to D20, calculate x, the number of moles of sucrose hydrolyzed in each time interval. If the reaction were zero order in sucrose, then we would expect that (x/0.003) = kf, where x/0.003 is the concentration of either of the product species in mol L units. Prepare a graph of the results obtained in these two series of runs, plotting x versus t, and indicate whether the data are consistent with the hypothesis that the reaction is zero order in sucrose. Note that, even if a reaction starts out being zero order in sucrose, this cannot continue indefinitely. Indeed, we expect the inversion reaction to become first order in sucrose when (S) becomes sufficiently small. [Pg.281]

Tanks-in-series reactor configurations provide a means of approaching the conversion of a tubular reactor. In modelling, they are employed for describing axial mixing in non-ideal tubular reactors. Residence time distributions, as measured by tracers, can be used to characterise reactors, to establish models and to calculate conversions for first-order reactions. [Pg.405]

Reactor capacity per unit volume appears to depend on four resistances in series the gas-phase transfer resistance, two liquid-phase transfer resistances, and the kinetic resistance. The highest resistance limits the capacity of the reactor. The four resistances have the unit of time and each one individually represents the time constant of the particular process under study. For example, 1 lkjigl is the time constant for the transfer of A from the bulk of the gas through the gas film to the gas-liquid interface. The same holds for the three other resistances. For a first-order reaction in a batch reactor, for example, the concentration after a certain time is given by C/C0 = exp(-r/r), in which r = 1/ A is the reaction time constant. For processes in series the individual time constants can be added to find the overall time constant of the total process. [Pg.64]

A series of cyano(arylcarbamoyl)phosphorus ylides (6) and cyano(arylthiocarbamo-yl)phosphorus ylides (7) have been prepared and fully characterized.33 Pyrolytic reaction products obtained by FVP have shown that thermal extrusion of PI13PO or PI13PS occurs (Scheme 5). Kinetic study of the gas-phase pyrolysis of each ylide by a static method showed that these reactions are unimolecular and first order with no significant substituent effect, but the thiocarbamoyl ylides (7) react 40-65 times more rapidly than their carbamoyl analogues (6). [Pg.312]

Equation (19-22) indicates that, for a nominal 90 percent conversion, an ideal CSTR will need nearly 4 times the residence time (or volume) of a PFR. This result is also worth bearing in mind when batch reactor experiments are converted to a battery of ideal CSTRs in series in the field. The performance of a completely mixed batch reactor and a steady-state PFR having the same residence time is the same [Eqs. (19-5) and (19-19)]. At a given residence time, if a batch reactor provides a nominal 90 percent conversion for a first-order reaction, a single ideal CSTR will only provide a conversion of 70 percent. The above discussion addresses conversion. Product selectivity in complex reaction networks may be profoundly affected by dispersion. This aspect has been addressed from the standpoint of parallel and consecutive reaction networks in Sec. 7. [Pg.9]

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 [Pg.278]

Concentration-time curves. Much of Sections 3.1 and 3.2 was devoted to mathematical techniques for describing or simulating concentration as a function of time. Experimental concentration-time curves for reactants, intermediates, and products can be compared with computed curves for reasonable kinetic schemes. Absolute concentrations are most useful, but even instrument responses (such as absorbances) are very helpful. One hopes to identify characteristic features such as the formation and decay of intermediates, approach to an equilibrium state, induction periods, an autocatalytic growth phase, or simple kinetic behavior of certain phases of the reaction. Recall, for example, that for a series first-order reaction scheme, the loss of the initial reactant is simple first-order. Approximations to simple behavior may suggest justifiable mathematical assumptions that can simplify the quantitative description. [Pg.120]

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