First order isothermal constant volume

Maple can be used to determine the sensitivity equations (see Example A.2 of Rawlings and Ekerdt) for a first order, isothermal constant volume reactor model where... 

Example 14.1 Consider a first-order reaction occurring in a CSTR where the inlet concentration of reactant has been held constant at uq for f < 0. At time f = 0, the inlet concentration is changed to Up Find the outlet response for t > 0 assuming isothermal, constant-volume, constant-density operation. 

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). 

In Chapter 3, the analytical method of solving kinetic schemes in a batch system was considered. Generally, industrial realistic schemes are complex and obtaining analytical solutions can be very difficult. Because this is often the case for such systems as isothermal, constant volume batch reactors and semibatch systems, the designer must review an alternative to the analytical technique, namely a numerical method, to obtain a solution. For systems such as the batch, semibatch, and plug flow reactors, sets of simultaneous, first order ordinary differential equations are often necessary to obtain the required solutions. Transient situations often arise in the case of continuous flow stirred tank reactors, and the use of numerical techniques is the most convenient and appropriate method. 

TABLE 7-2 Consecutive and Parallel First-Order Reactions in an Isothermal Constant-Volume Ideal Batch or Plug Flow Reactor. 

Table 7-2 and Figs. 7-3 and 7-4 show the analytical solution of the integrals for two simple first-order reaction systems in an isothermal constant-volume batch reactor or plug flow reactor. Table 7-3 shows the analytical solution for the same reaction systems in an isothermal constant-density CSTR. 

Exercise 7.1.8, A solution of substance A of concentration is fed at a rate q to an isothermal, constant-volume stirred tank reactor of volume y. Substance A undergoes consecutive first order reactions A —B —... 

Consider the differential equation describing a first-order, isothermal, irreyersible reaction in a constant-volume batch reactor... 

Consider the gas-phase decomposition A B -b C in an isothermal tubular reactor. The tube i.d. is 1 in. There is no packing. The pressure drop is 1 psi with the outlet at atmospheric pressure. The gas flow rate is O.OSSCF/s. The molecular weights of B and C are 48 and 52, respectively. The entering gas contains 50% A and 50% inerts by volume. The operating temperature is 700°C. The cracking reaction is first order with a rate constant of 0.93 s . How long is the tube and what... 

Determine the time required for 80% conversion of 7.5 mol A in a 15-L constant-volume batch reactor operating isothermally at 300 K. The reaction is first-order with respect to A, with kA = 0.05 min-1 at 300 K. 

For an isothermal first-order reaction taking place in a constant-volume BR but at varying density in a PFR, it can be shown that the times are also equal this is not the case for other orders of reaction (see problem 17-8). 

For a relatively small amount of dispersion, what value of Pei would result in a 10% increase in volume (V) relative to that of a PFR (Vpf) for the same conversion (/a) and throughput (q) Assume the reaction, A - products, is first-order, and isothermal, steady-state, constant-density operation and the reaction number, Mai = at, is 2.5. For this purpose, first show, using equation 20.2-10, for the axial-dispersion model with relatively large Per, that the % increase s 100(V - V pfWpf = 100MAi/Pei. 

The system is sketched in Fig. 3.1 and is a simple extension of the CSTR considered in Example 2.3. Product B is produced and reactant A is consumed in each of the three perfectly mixed reactors by a first-order reaction occurring in the liquid. For the moment let us assume that the temperatures and holdups (volumes) of the three tanks can be different, but both temperatures and the liquid volumes are assumed to be constant (isothermal and constant holdup). Density is assumed constant throughout the system, which is a binary mixture of A and B. 

The new Liquid Lightning reactor is a single, isothermal, constant-holdup CSTR in which the concentration of ethanol, C, is controlled by manual changes in the feed concentration, Cq. Ethanol undergoes an irreversible first-order reaction at a specific reaction rate k = 0.25/day. The volume of the reactor is 100 barrels, and the throughput is 25 barrels/day. 

Suppose a first-order reaction (n = 1) is preformed in an isothermal batch reactor of constant volume V. Write a material balance Table 3-17 ... 

The gas-phase decomposition of sulfuryl chloride, S02C12 — S02 + Cl2, is thought to follow a first order rate law. The reaction is performed in a constant volume, isothermal batch reactor, and the concentration of S02C12 is measured at several reaction times, with the following results. 

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