Constant-Volume Batch Reaction Systems

Another example of a constant-volume gas-phase isothermal reaction occuns when the number of moles of products equals the number of moles of reactants. The water-gas shift reaction, important in coal gasification and many other processes, is one of ihe.se  

In this reaction. 2 mo of reactant forms 2 mol of product. When the number of reactant molecules forms an equal number of product molecules at the same temperature and pressure, the volume of the reacting mixture will not change if the conditions are such that the ideal gas law is applicable, or if the compressibility factors of the products and reactants are approximately equal. 

For liquid-phase reaction.s taking place in solution, the solvent usually dominates the situation. As a result, changes in the density of the solute do not 

For the constant-volume systems described earlier. Equation (3-25) ca be simplified to give the following expres.sions relating concentration and con version  

To summarize for liquid-phase reactions (or as we will soon see for isoiherma and isobaric gas-phase reactions with no change in the total number of moles) we can use a rate law for reaction (2-2) such as -r - k/,jC,, Cs obtait - A t iat is, 

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Consider the reaction A — products. The rate equation in a constant volume batch reaction system gives... 

The concept of a a mole balance on species A in a constant-volume batch reaction system c<> half life. f i. is bined with the rate law results in the following expression very imponani in... 

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

An elegant, general solution for first-order networks has been provided in a classic publication by Wei and Prater [22]. In essence, the mathematics are developed for a reaction system with any number of participants that are all connected with one another by direct first-order pathways. For example, in a system with five participants, each of these can undergo four reactions, for a total of twenty first-order steps. Matrix methods are used to obtain concentration histories in constant-volume batch reactions, and a procedure is described for determination of all rate coefficients from such batch... 

Consider the reaction A B. The rate equation for a constant volume batch system is ... 

Assuming that the reaction is second order in a constant volume batch system, the rate equation is... 

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,... 

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. 

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. 

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 ... 

Consider elementary reactions A— B and A———> C. The rate equations for these reactions for a constant volume batch system (i.e., constant density) are... 

Paraldehyde decomposition is represented by (CH3CHO)3 ———> 3CH3CHO. The stoichiometry of the reaction is of the form A — ->3B. Assuming that the reaction is first order, then the rate equation for a constant volume batch system is ... 

Some authors [120—122] have collected simple kinetic systems and attempted to solve the corresponding characteristic equations explicitly in the case of an isothermal, constant volume batch reactor. In view of the fact that most reaction mechanisms are not simple ones or are not considered in these collections or are not amenable to an explicit solution and that types of reactors other than the isothermal batch reactor are used in kinetics, this approach (involving, furthermore, standard mathematics) will not be discussed further here. 

Constant-volume batch reactors are found very frequently in industry. In pai -ticular, the laboratory bomb reactor for gas-phase reactions is widely used for obtaining reaction rate information on a small scale. Liquid-phase reactions in which the volume change during reaction is insignificant are frequently carried out in batch reactors when small-scale production is desired or operating difficulties rule out the use of continuous systems. For a constant-volume batch reactor. Equation (2-5) can be arranged into the form... 

This irreversible reaction has an elementary rate law and is carried out in aqueous ethanol. Therefore, like almost all liquid-phase reactions, the density remains almost constant throughout the reaction. It is a general principle that for most liquid-phase reactions, the volume V for a batch reaction system and the volumetric flow rate v for a continuous-flow system will not change appreciably during the course of a chemical reaction. 

P3-14b Reconsider the decomposition of nitrogen tetroxide discussed in Example 3-8. The reaction is to be Carried out in PER and aiso in a constant-volume batch reactor at 2 atm and 340 K. Only Nj04 and an inert I are to be fed to the reactors, Plot the equilibrium conversion as a function of inert mole fraction in the feed for both a constant-volume batch reactor and a plug Sow reactor, Why is the equilibrium conve ton lower for the batch system than the flow system in Example 3-87 Will this lower equilibrium conversion result always be the case for batch systems ... 

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. 

To determine reaction rate parameters from the experimental data, the following differential equation was used to describe the reaction system in a constant-volume batch reactor assuming a pseudo-first-order equation for propylene epoxidation ... 

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