Concentration as a function of conversion

Now that we have shown how the rate law can be expressed as a function of concentrations, we need only, express concentration as a function of conversion in order to carry out calculations similar to those presented in Chapter 2 to size reactors. If the rate law depends on more than one species, we must relate the concentrations of the different species to each other. This relationship is most easily established with the aid of a stoichiometric table. This table presents the stoichiometric relationships between reacting molecules for a single reaction. That is, it tells us how many molecules of one species will be formed during a chemical reaction when a given number of molecules of another species disappears, These relationships wil be developed for the general reaction... 

Concentration as a function of conversion v/hen no volume change occurs with reaction... 

However, for gas-phase reactions the volumetric flow rate most often changes during the course of the reaction due to a change in the total number of moles or in temperature or pressure. One cannot always use Equation (3-29) to express concentration as a function of conversion for gas-phase reactions. 

The only new twist in calculating reactor volumes or conversions for a recycle reactor is a mole balance at the stream intersections (points P and Q) to express properly the species concentrations as a function of conversion. 

We need V(X) to We now need only to find volume as a function of conversion to obtain the obtain Cj = hj X) species concentration as a function of conversion. 

Figure 19. Membrane flux and instantaneous filtrate IgC concentration as a function of conversion of feed to filtrate (0.45 fjm microporous). The lysate is being concentrated with time.

To summarize these last examples, we have seen that in the design of reactors that are to be operated at conditions (e.g.. temperature and initial concentration) identical to those at which the reaction rate data were obtained, we can size determine the reactor volume) both CSTRs and PFRs alone or in various combinations. In principle, it may be possible to scale up a laboratory-bench or pilot-plant reaction system solely from knowledge of as a function of X or Q. However, for most reactor systems in industry, a, scale-up proce.s.s cannot be achieved in this manner because knowledge of solely as a function of X is seldom, if ever, available under identical conditions. In Chapter 3. we shall see how we can obtain = yfX) from information obtained either in the laboratory or from the literature. This relationship will be developed in a two-step process. In Step 1, we will find the rate law that gives the rate as a function of concentration and in Step 2, we will find the concentrations as a function of conversion. Combining Steps 1 and 2 in Chapter 3. we obtain -/-.v =JiX). We can then use the method.s developed in this chapter along with integral and numerical methods to size reactors. 

Overview. In Chapter 2, we showed that if we had the rate of reaction as a function of conversion, = /(X), we could calculate reactor volumes necessary to achieve a specified conversion for flow systems and the time to achieve a given conversion in a batch system. Unfortunately, one is seldom, if ever, given = yiX) directly from raw data. Not to fear, in this chapter we will show how to obtain the rate of reaction as a function of conversion. This relationship between reaction rate and conversion will be obtained in two steps. In Step 1, Part 1 of this chapter, we define the rate law, which relates the rate of reaction to the concentrations of the reacting species and to temperature. In Step 2, Part 2 of this chapter, we define concentrations for fiow and batch systems and develop a stoichiometric table so that one can write concentrations as a function of conversion. Combining Steps 1 and 2, we see that one can then write the rate as a function conversion and use the techniques in Chapter 2 to design reaction systems. 

Batch Reactors with Variable Volume Although variable volume batch reactors are seldom encountered because they are usually solid steel containers, we will develop the concentrations as a function of conversion because (1) they have been u.sed to collect reaction data for gas-phase reactions, and (2) the development of the equations that express volume as a function of conversion will facilitate analyzing flow systems with variable volumetric flow rates. 

If the rate of reaction is not given explicitly as a function of conversion, we must proceed to level where the rate law must be determined by either finding it in books or journals or by determining it experimentally in the laboratory. Techniques for obtaining and analyzing rate data to determine the reaction order and rate constant are presented in Chapter 5. After the rate law has been established, one has only to use stoichiometry (level ) together with the conditions of the system (e.g.. constant volume, temperature) to express concentration as a function of conversion. 

Since we know the change in the monomer concentration as a function of conversion,... 

In Step 2, described in Chapter 4, we define concentrations for flow and batch systems and develop a stoichiometric table so that one can write concentrations as a function of conversion. 

Overview. In Chapter 3 we described how the rate of reaction, -r, is related to concentration and temperature Step 1). This relationship is step one of a two-step process to find the rate of reaction as a function of conversion. In this chapter we show how concentration can be related to conversion Step 2), and once we do that we will have =/fX) and can design a multitude of reaction systems. We will use stoichiometric tables, along with the definitions of concentration, to find the concentration as a function of conversion. 

For batch systems the reactor is rigid, so Y = Vq and one then uses the stoichiometric table to express concentration as a function of conversion Ca a o aoO... 

First, set up a stoichiometric table using only the symbols (i.e.. 0 , Fj) and then prepare a second table evaluating the species concentrations as a function of conversion for the case when the tola) pressure is 1485 kPa (14.7 atin) and the temperature is constant at 227 C. 

Analysis In this example, we formed a stoichiometric table in terms of molar flow rates. We then showed how to express the concentrations of each species in a gas phase reaction in which there is a change in the total number of moles. Next, we plotted each species concentration as a function of conversion and noted that the concentration of the inert. Ni, was not constant but increased with increasing conversion because of the decrease in the total molar flow rate, Fj, with conversion. 

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