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Join With us. For example, 2-butene has four carbon atoms and eight hydrogen atoms; however, the atoms in this compound can form two different arrangements. Therefore, we consider them as two different species, even though each has the same number of atoms of each element. When has a We say that a chemical reaction has taken place when a detectable num- chemical reaction ber of molecules of one or more species have lost their identity and assumed a taken place? In this classical approach to chemical change, it is assumed that the total mass is neither cre- ated nor destroyed when a chemical reaction occurs.
The mass referred to is the total collective mass of all the different species in the system. However, when considering the individual species involved in a particular reaction, we do speak of the rate of disappearance of mass of a particular species. The rate of disappearance of a species, say species A, is the number of A molecules that lose their chemical identity per unit time per unit volume through the breaking and subsequent re-forming of chemical bonds during the course of the reac- tion.
There are three basic ways a species may lose its chemical identity: decomposition, combination, and isomerization. In decomposition, the mole- cule loses its identity by being broken down into smaller molecules, atoms, or atom fragments. A second way that a molecule may lose its chemical identity is through combination with another molecule or atom. In the above reaction, the propylene molecule would lose its chemical identity if the reaction were carried out in the reverse direction, so that it combined with benzene to form cumene.
The rate at which a given chemical reaction proceeds can be expressed in several ways. To illustrate, consider the reaction of chlorobenzene and chloral to produce the banned insecticide DDT dichlorodiphenyl-trichloroethane in the presence of fuming sulfuric acid. What is —rA?
The rate of reaction, —rA, is the number of moles of A e. Example 1—1 Chloral is being consumed at a rate of 10 moles per second per m3 when reacting with chlorobenzene to form DDT and water in the reaction described above. The symbol rj is the rate of formation generation of species j. If species The convention j is a product, then rj will be a positive number. The rate of reaction, —rA, is the rate of disappearance of reactant A and must be a positive number.
Heterogeneous reactions involve more than one phase. In heterogeneous reaction systems, the rate of reaction is usually expressed in measures other than volume, such as reaction surface area or catalyst weight.
For a gas-solid catalytic reaction, the gas molecules must interact with the solid catalyst sur- face for the reaction to take place, as described in Chapter It is the number of moles of species j generated per unit volume per unit time. We can say four things about the reaction rate rj. The chemical reaction rate law is essentially an algebraic equation involving concentration, not a differential equation. Crynes and H. Fogler, eds. Equation states that the rate of disappearance of A is equal to a rate constant k which is a function of temperature times the square The convention of the concentration of A.
As noted earlier, by convention, rA is the rate of for- mation of A; consequently, —rA is the rate of disappearance of A. Throughout this book, the phrase rate of generation means exactly the same as the phrase rate of formation, and these phrases are used interchangeably. The volume enclosed by these boundaries is referred to as the system volume.
We shall perform a mole balance on species j in a system volume, where species j represents the particular chemical species of interest, such as water or NaOH Figure Figure Mole balance on species j in a system volume, V.
If all the system variables e. Figure Dividing up the system volume, V. The total rate of generation within the system volume is the sum of all the rates of generation in each of the subvolumes. The reactor can be charged i. Section 1. It is referred to as the continuous-stirred used for? Equipment on the CRE Web site. It is normally operated at steady state and is assumed to be perfectly mixed; consequently, there is no time dependence or position dependence of the temperature, concentration, or reaction rate inside the CSTR.
That is, every variable is the same at every point inside the reactor. Because the temperature and concentration are identical everywhere within the reaction vessel, they are the same at the exit point as they are elsewhere in the tank.
Thus, the temperature and concentration in the exit stream are modeled as being the same as those inside the reactor. In systems where mixing is highly nonideal, the well-mixed model is inadequate, and we must resort to other modeling techniques, such as residence time distributions, to obtain meaningful results.
This topic of nonideal mixing is discussed in Chapters 16, 17, and 18 on nonideal reactors. We note that the CSTR is modeled such that the conditions in the exit stream e. It consists of a cylindrical pipe and is When is a tubular normally operated at steady state, as is the CSTR. Tubular reactors are used reactor most often used? A schematic and a photograph of industrial tubular reactors are shown in Figure In modeling the tubular reactor, we assume that the concentration varies continuously in the axial direction through the reactor.
Consequently, the reaction rate, which is a function of con- centration for all but zero-order reactions, will also vary axially. Figure b Tubular reactor photo. Longitudinal tubular reactor. McGraw-Hill, Inc. That is, there is no radial variation in reaction rate, and the reactor is referred to as a plug-flow reactor PFR. Plug flow—no radial variations in velocity, concentration, temperature, or reaction rate Also see PRS and Visual Encyclope- dia of Equipment.
However, we see that by applying Equation , the result would yield the same equation i. As the reac- tants proceed down the reactor, A is consumed by chemical reaction and B is produced. The greater the mass of a given catalyst, the greater the reactive surface area. Consequently, the reaction rate is based on mass of solid catalyst, W, rather than on reactor volume, V.
Figure shows a schematic of an industrial catalytic reactor with vertical tubes packed with solid catalyst. Figure Longitudinal catalytic packed-bed reactor. The derivation of the design equation PBR Mole Balance for a packed-bed catalytic reactor PBR will be carried out in a manner analo- gous to the development of the tubular design equation.
To accomplish this der- ivation, we simply replace the volume coordinate in Equation with the catalyst mass i. Example 1—2 How Large Is It?
Solution 1. Sketch CA as a function of V. CA0 CA 0. Calculate V. Again using Equation E We see that a reactor volume of 0. The more species A consumed and converted to product B, the larger must be the reactor volume V.
The purpose of the example was to give a vision of the types of calculations we will be carrying out as we study chemical reaction engineering CRE. There are also links to view reactors on different Web sites. Susan Montgomery and her students at the University of Michigan. Chapter 1 Summary 23 The CRE Web site describes industrial reactors, along with typical feed and operating conditions.
The goal of this text is to weave the fundamentals of chemical reaction engineering into a structure or algorithm that is easy to use and apply to a variety of problems. By convention, —rA is the rate of disappearance of species A and rA is the rate of formation of species A. Mole balances on species A in four common reactors are shown in Table S Summary Notes 2.
Web Material A. Problem-Solving Algorithm B. Getting Unstuck on a Problem This Web site gives tips on how to overcome mental barriers in problem solving. Smog in L. Web module includes a Living Example Problem. Getting Unstuck C. Interactive Computer Games A. Quiz Show I 4. The reactor portion of this encyclopedia is included on the CRE Web site. Before solving the problems, state or sketch qualitatively the expected results or trends. Write a paragraph describing both the content goals and the intellectual goals of the course and text.
Look at the QuickTime videos. Write a paragraph describing two or more of the reactors. What similarities and differences do you observe between the reactors on the Web e. How do the used reactor prices compare with those in Table ? Go on a scavenger hunt using the summary notes for Chapter 1 on the Web site. Take a quick look at the Web Modules and list the ones that you feel are the most novel applications of CRE.
QA What does a negative number for the rate of formation of species e. What does a positive number signify? QA What assumptions were made in the derivation of the design equation for: a The batch reactor BR? Problems PA a Revisit Example Rework this example using Equation on page Explain why. Suggest two ways to work this problem incorrectly. Play this game and then record your performance number, which indicates your mastery of the material.
The feed is only A and B in equimolar proportions. Which of the following sets of equations gives the correct set of mole balances on A, B, and C?
Species A and B are disappearing and species C is being formed. Circle the correct answer where all the mole balances are correct. We shall use this system volume to model the accumulation and depletion of air pollutants. We shall perform an unsteady-state mole balance Equation 1—4 on CO as it is depleted from the basin area by a Santa Ana wind.
Santa Ana winds are high-velocity winds that originate in the Mojave Desert just to the northeast of Los Angeles.
Use the data in the module to work parts 1—12 a through h given in the module. Load the Living Exam- ple Polymath code and explore the problem. These equation solvers will be used extensively in later chapters. Also, plot the number of foxes versus the number of rabbits. Explain why the curves look the way they do.
Enrico Fermi was an Italian physicist who received the Nobel Prize for his work on nuclear processes. He used a process to set bounds on the answer by saying it is probably larger than one number and smaller than another, and arrived at an answer that was within a factor of Need an account?
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