Density Constant-Volume Systems

2 Plug-Flow Reactors Constant-Density (Constant-Volume) Systems 

What reactor volume is required for the net production rate of D to be at least 12(M) mol/1 (Note This problem is exactly the same as Example 4-4, except that the reactor is a PFR instead of a CSTR.) 

the fractional conversion of A in the effluent from the PFR will be calculated from stoichiometry. Then, this conversion will be used to solve the PFR design equation to obtain the required volume. Once again, a stoichiometric table will be used to relate Ca to Xa- 

Since the inlet flow rates and concentrations are the same as in Example 4-4, and the required production rate of D is also the same, the fractional conversion of A in the stream leaving the PFR must also be the same, i.e., xa = 0.80. 

From Chapter 3, the design equation for an ideal PFR with a homogeneous reaction taking place is, in integrated form. 

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Note that the material balances for fixed beds are valid for die case of constant-density (constant volume) systems. The important term here is the one including the fluid velocity, i.e. the term uJdCIdz. For a variable volume system,... 

For this problem, the stoichiometric table could have been written in a simpler form, if the assumption of constant density had been made before the table was constructed. Table 4-1 is based on using the whole reactor as a control volume. For a constant-density (constant-volume) system, and only for such a system, the stoichiometric table can be written in terms of concentrations. If the control volume is taken to be 1 liter ofsolution, the stoichiometric table becomes as given inTable4-2. 

In this section we discuss the mathematical forms of the integrated rate expression for a few simple combinations of the component rate expressions. The discussion is limited to reactions that occur isothermally in constant density systems, because this simplifies the mathematics and permits one to focus on the basic principles involved. We will again place a V to the right of certain equation numbers to emphasize that such equations are not general but are restricted to constant volume batch reactors. The use of the extent per unit volume in a constant volume system ( ) will also serve to emphasize this restriction. For constant volume systems,... 

For systems of constant density (constant-volume batch and constant-density plug flow) the performance equations are identical, r for plug flow is equivalent to t for the batch reactor, and the equations can be used interchangeably. 

Fluctuations of observables from their average values, unless the observables are constants of motion, are especially important, since they are related to the response fiinctions of the system. For example, the constant volume specific heat of a fluid is a response function related to the fluctuations in the energy of a system at constant N, V and T, where A is the number of particles in a volume V at temperature T. Similarly, fluctuations in the number density (p = N/V) of an open system at constant p, V and T, where p is the chemical potential, are related to the isothemial compressibility iCp which is another response fiinction. Temperature-dependent fluctuations characterize the dynamic equilibrium of themiodynamic systems, in contrast to the equilibrium of purely mechanical bodies in which fluctuations are absent. 

This is a collection of closed systems with the same number of particles A and volume V (constant density) for each system at temperature T. The partition fiinction... 

At constant speed a fan delivers constant volume (m /s) into a fixed system in spite of change in density Pressure and power absorbed vary as change in density. 

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. 

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... 

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. 

For a liquid-phase reaction, or gas-phase reaction at constant temperature and pressure with no change in the total number of moles, the density of the system may be considered to remain constant. In this circumstance, the system volume (V) also remains constant, and the equations for reaction time (12.3-2) and production rate (12.3-6) may then be expressed in terms of concentration, with cA = nAlV ... 

When we mention the constant-volume batch reactor we are really referring to the volume of reaction mixture, and not the volume of reactor. Thus, this term actually means a constant-density reaction system. Most liquid-phase reactions as well as all gas-phase reactions occurring in a constant-volume bomb fall in this class. 

If the rate of the reaction is independent of the concentration of the reacting substance A, then the amount dCA by which the concentration of A decreases in any given unit of time dt is constant throughout the course of the reaction. The rate equation for a constant volume batch system (i.e., constant density) can be expressed as ... 

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