A Constant-Volume Batch Reactor

A constant volume batch reactor is used to convert reactant, A, to product, B, via an endothermic reaction, with simple stoichiometry, A - B. The reaction kinetics are second-order with respect to A, thus 

From the reaction stoichiometry product B is formed at exactly the same rate as that at which reactant A is decomposed. 

For the second-order reaction, the term representing the rate of heat production by reaction simplifies to 

This gives the resultant heat balance equation as 

The component material balance, when coupled with the heat balance equation and temperature dependence of the kinetic rate coefficient, via the Arrhenius relation, provide the dynamic model for the system. Batch reactor simulation examples are provided by BATCHD, COMPREAC, BATCOM, CASTOR, HYDROL and RELUY. 

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Assuming that the reactions are first order in a constant volume batch reactor, the rate equations for components A, B, C, and D, respectively, are ... 

The reaction rate ( rco) for a constant volume batch reactor system is equal to the rate of mass transfer (r coy. 

Although many industrial reactions are carried out in flow reactors, this procedure is not often used in mechanistic work. Most experiments in the liquid phase that are carried out for that purpose use a constant-volume batch reactor. Thus, we shall not consider the kinetics of reactions in flow reactors, which only complicate the algebraic treatments. Because the reaction volume in solution reactions is very nearly constant, the rate is expressed as the change in the concentration of a reactant or product per unit time. Reaction rates and derived constants are preferably expressed with the second as the unit of time, even when the working unit in the laboratory is an hour or a microsecond. Molarity (mol L-1 or mol dm"3, sometimes abbreviated M) is the preferred unit of concentration. Therefore, the reaction rate, or velocity, symbolized in this book as v, has the units mol L-1 s-1. 

Suppose a homogeneous, gas-phase reaction occurs in a constant-volume batch reactor. Assume ideal gas behavior and suppose pure A is charged to the reactor. 

The reaction is essentially irreversible, and its rate in a constant volume batch reactor is given by... 

From experiments in a constant volume batch reactor at 791 °K, it is known that the time... 

Pure phosphine is to be admitted to a constant volume batch reactor and allowed to undergo decomposition according to the above reaction. If pure phosphine enters at 672 °C and the initial pressure is 1 atm, determine the times necessary to decompose 20% of the original phosphine for both isothermal and adiabatic operation. 

The standard heat of reaction is — 11.63 kJ/mole. Determine the times necessary to achieve 90% conversion in a constant volume batch reactor under adiabatic conditions and under isothermal conditions. 

They were obtained by means of a constant-volume batch reactor.)... 

For a reaction represented by A - products, in which the rate, ( — rA), is proportional to cA, with a proportionality constant kA, show that the time (t) required to achieve a specified fractional conversion of A (/A) is independent of the initial concentration of reactant cAo. Assume reaction occurs in a constant-volume batch reactor. 

Use a spreadsheet or equivalent computer program to calculate the concentration of product C as the reaction proceeds with time (/) in a constant-volume batch reactor (try the parameter values supplied below). You may use a simple numerical integration scheme such as Acc =... 

The hydrolysis of methyl bromide (CffiBr) in dilute aqueous solution may be followed by titrating samples with AgNCfy The volumes of AgNC>3 solution (V) required for 10 cm3 samples at 330 K in a particular experiment in a constant-volume batch reactor were as follows... 

The rate of decomposition of gaseous ethylene oxide (QFUO), to CH4 and CO, has been studied by Mueller and Walters (1951) by determination of the fraction (/A) of oxide (A) reacted after a definite time interval (f) in a constant-volume batch reactor. In a series of experiments, the initial pressure of the oxide (P 0) was varied. Some of the results are as follows ... 

The rate of reaction between hydrocyanic acid (HCN) and acetaldehyde (CH3CHO) to give acetaldehyde cyanohydrin has been studied in a constant-volume batch reactor at 25°C in dilute aqueous solution, buffered to keep the pH constant (Svirbely and Roth, 1953). The reaction is... 

Some of the data they obtained for a solution equimolar in reactants (ca = 0.757 mol L 1) in a constant-volume batch reactor are as follows (/j is the fraction of B unconverted at time t) ... 

We derive the kinetics consequences for this scheme for reaction in a constant-volume batch reactor, the results also being applicable to a PFR for a constant-density system. The results for a CSTR differ from this, and are explored in Example 18-4. 

Assuming that reaction occurs in a constant-volume batch reactor at a fixed temperature, and that at time zero only A and B are present, calculate (not necessarily in the order listed) (a) ki and k2 (b) cAo and cB(, at time zero (c) cp at 40 min (d) at 20 min. 

Assuming that reaction occurs at constant r in a constant-volume batch reactor, calculate k, cc at t, and jfc2 state the units of k and ki. 

Suppose reaction 8.3-1 with rate law given by equation 8.3-2 is carried out in a constant-volume batch reactor (or a constant-density PFR) at constant 7... 

For a constant-volume batch reactor operated at constant T and pH, an exact solution can be obtained numerically (but not analytically) from the two-step mechanism in Section 10.2.1 for the concentrations of the four species S, E, ES, and P as functions of time t, without the assumptions of fast and slow steps. An approximate analytical solution, in the form of a rate law, can be obtained, applicable to this and other reactor types, by use of the stationary-state hypothesis (SSH). We consider these in turn. 

For a first-order reaction, the integrated form of the rate equation for a constant volume batch reactor, from Table 1.1 in Volume 3, is ... 

The reaction system, 2A = B = > C, has been studied in a constant volume, batch reactor with the tabulated results. Assuming the orders conform to the stoichiometry, find the specific rates. 

If b — c, the relative production rates for B and C will depend on the rate coefficients only. Improvements in the relative yield of B can now be achieved only by changing the reaction temperature or by using a catalyst. The reactor flow pattern will not affect the product distribution but it wiU affect the conversion of A. In a constant-volume batch reactor, if... 

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