Constant-Volume Reactors

For a batch reactor (constant volume), the design equations (Eq. 7.1.1) are... 

E5.3 A reaction R + S is carried out in a batch reactor (constant volume). The experiment was started with several initial concentrations and when half of the concentration was reached, the corresponding time was measured. The following table gives the values for two different temperatures. Determine the order of the reaction, the specific rate, and the activation energy. 

The gas phase decomposition A B -r 2C is conducted in a constant volume reactor. Runs 1 through 5 were conducted at 100°C run 6 was performed at 110°C (Table 3-15). Determine (1) the reaction order and the rate constant, and (2) the activation energy and frequency factor for this reaction. 

Suppose the reaction is performed in a batch reactor of constant volume V(m ) at a constant temperature T(K), beginning with pure A... 

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. 

The ideal, constant-volume batch reactor satisfies the following component balance ... 

This reaction can be elementary if = 1 or 2. More generally, it is complex. Noninteger values for n are often found when fitting rate data empirically, sometimes for sound kinetic reasons, as will be seen in Section 2.5.3. For an isothermal, constant-volume batch reactor. 

The feed is charged all at once to a batch reactor, and the products are removed together, with the mass in the system being held constant during the reaction step. Such reactors usually operate at nearly constant volume. The reason for this is that most batch reactors are liquid-phase reactors, and liquid densities tend to be insensitive to composition. The ideal batch reactor considered so far is perfectly mixed, isothermal, and operates at constant density. We now relax the assumption of constant density but retain the other simplifying assumptions of perfect mixing and isothermal operation. 

The following reactions are occurring in a constant-volume, isothermal batch reactor ... 

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. 

Example 7.4 The following data have been obtained in a constant-volume, isothermal reactor for a reaction with known stoichiometry A B - - C. The initial concentration of component A was 2200 mol/m. No B or C was charged to the reactor. 

Example 7.5 Suppose the consecutive reactions 2A B C are elementary. Determine the rate constants from the following experimental data obtained with an isothermal, constant-volume batch reactor ... 

A simpler method arbitrarily picks values for oq and reacts this material in a batch reactor at constant V and T. When the reaction is complete, P is calculated from the molar density of the equilibrium mixture. As an example, set = 22.2 (P=l atm) and react to completion. The long-time results from integrating the constant-volume batch equations are a = 5.53, 5 = c= 16.63, = 38.79mol/m, and y =0.143. The pressure at equili-... 

This result is perfectly general for a constant-volume reactor. It continues to apply when p, Cp, and H are expressed in mass units, as is normally the case for liquid systems. The current example has a high level of inerts so that the molar density shows little variation. The approximate heat balance... 

The reactor operates at constant volume, constant density, constant flow rate, and isothermally. The only difference between the two products is the addition of component C to the feed when Product II is made. 

The complex chemical reaction, shown below, is carried out in an isothermal, constant-volume, batch reactor. All the reactions follow simple first-order kinetic rate relationships, in which the rate of reaction is directly proportional to concentration (Fig. 1.3). 

The dynamic error existing between and Cr depends on the relative magnitudes of the respective time constants. For the reactor, assuming a first-order, constant volume reaction... 

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... 

Consider a simple first-order exothermie reaction, A —> B, carried out in a single, constant-volume, continuous stirred-tank reactor (Fig. 3.12), with constant jacket coolant temperature, where r = - k Ca,. 

For a batch reactor, under constant volume conditions, the component mass balance equation can be represented by... 

The liquid phase hydrolysis reaction of acetic anhydride to form acetic acid is carried out in a constant volume, adiabatic batch reactor. The reaction is exothermic with the following stoichiometry... 

Figure 5.58. The reactor for exaiuple HOMPOLY is a constant-volume stirred tank.

Physical Methods that have been Used to Monitor Reaction Kinetics. In this section some physical property measurements of general utility are discussed. One of the oldest and most useful techniques used in kinetics studies involves the measurement of the total pressure in an isothermal constant volume reactor. This technique is primarily used to follow the course of homogeneous gas phase reactions that involve a change in the total number of gaseous molecules present in the reaction vessel (e.g., the hydrogenation of propylene). 

The following data were recorded in an isothermal (552 °C) constant volume reactor. 

The reaction takes place in the gas phase in an isothermal constant volume reactor. Determine the order of the reaction and the reaction rate constant. The order may be assumed to be an integer. 

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