evolving on their own. Every simulation has a message line warning of this limitation. The mechanical device cited above (13)does show collisions and could be used in tandem with this program, as their strengths complement each other. The program runs on MS-DOS computers. It was written to detect and use VGA, EGA, CGA, ATT 400,or Hercules graphics adapters and has been tested on VGA, EGA, and Hercules-equipped computers. The other graphics modes were tested with a VGA driver simulating each mode. Copies of the program and source code (Turbo Pascal 5.5,Borland International) may be obtained by sending a formatted diskette and a stamped, self-addressed mailer to the author.
Heat Balancing of a Reactor Using a Spreadsheet Patrick L. M. Wong and James R. Manuel Department of Metallurgy University of South Australia The Levels. S. A. 5095. Australia In teaching introductory chemical metallurgy, one common example used to illustrate the use of heat capacity and Hess's Law is the heat balancing of a reactor for the roasting of calcium carbonate. This involves some repetitive integration of the heat capacities involved. This exercise is also an excellent means of illustrating the amount of fuel that can be saved if the flue gas is used to preheat the incoming air required for combustion. Using a computer spreadsheet to perform multiple calculations allows the parameters of interest to be systematically varied by entering a range of values, for feed air temperature and flue gas temperature, in successive cells of two columns. It is assumed that students already have a basic knowledge of spreadsheet operation. Otherwise, this may need to be introduced beforehand. In this case, Microsoft Excel' was used. The basic problem, that of understanding of the thermodynamics of heat balancing a reactor, is thus extended to demonstrate the following concepts:
Feed Temperature
Calcine Temperature
Flue Gas Temperature
Figure 4. Path diagram used forenergy balancing of the decomposition of calcium carbonate. The simplified reactor is illustrated in Figure 3. The students were asked to calculate the number of moles of methane per mole of calcium carbonate required initially to complete the process. Following that they were to calculate the number of moles of methane saved if the flue gas is used to preheat the incoming air, such that the temperature of the flue gas is decreased to 500 K and the incoming air is preheated to 373 K. The assumptions made in the calculations are that there is no heat loss in the system, no decomposition of HzO(g)at high temperature and that the decomposition of calcium carbonate to calcium oxide is complete.
1. an introduction to the basic principles of computer model-
Formulation of the Problem The problem can be formulated in several ways. Most students found the problem easiest to understand if the heat balance was considered in terms of feed component basis and the corresponding path diagrams. This experience is similar to that described by Ebenezer, who found that "concept mapping" is the most effective way to give an overview of a unit (14);in this case, a thermodynamic system. Adiagram can be drawn for each feed component. Figure 4 gives the path diagram for CaCO&). With reference to this diagram, let HI,Hz, Hs and Ha be the enthalpies of the reactions indicated and HT1be the total enthalpy of the system for the decomposition of calcium carbonate. Therefore:
2. the use of a computer spreadsheet as a tool in modelling.
HT1=H1+H2+H3+H4
ling in chemical systems
(1)
The application of a spreadsheet to this type of straightforward problem helps to make the principles of computer modelling and its application to more complex systems easier to understand.
t--Air, 298 K
The heat capacity functions can be obtained from Rao (15).The integrated equation is usually expressed in the form shown below, which can be easily entered into the spreadsheet:
Figure 3. Asimplified diagram of a reactor for the roasting of calcium carbonate, with feed temperature 298 K, and flue gas temperature 1000 K.
MicrosoflCorporation: Redmond, 'Microsofl Excel for windowsTM; WA.
Volume 71 Number 9 September 1994
785
Feed Temperature
H T ~ 4
2
Feed Temperature
,
Flue Gas Temperature
2
1
, -I
HZ4
&
C02 + 2H2(g)
CH4(g) + 02@)
298 K 298 K Figure 5. Path diagram for combustion of methane.
Flue Gas Temperature Figure 6. Path diagram for nitrogen gas heating
where Hz is the enthalpy of component Z, TI and Tz are the initial and final temperatures, respectively, and a , b, and c are constants. Figures 5 and 6 show similar path diagrams for the CH4(g)combustion and Nz heating. Let Hnand Hnbe the total enthalpies of the combustion system and nitrogen heating system respectively, assuming that the mole % of oxygen in air is 21% and that of nitrogen is 79%. The final equation is then expressed (in spreadsheet notation) as: 0.0 = HT1+X*HTZ+ 0.79/0.21*2X*HT3
(7)
where X is the number of moles of CH4 required to complete the decomposition reaction. Rearranging this gives: X = -HTl/H,
+ 7.52 HT3
(8) In the spreadsheet, the temperatures of the inlet air, calcine and flue gas are the variables. Once the spreadsheet is set up, the number of moles of CHdg) can be automatically calculated when those temperatures are changed. At this point, some basic principles of heat transfer are introduced to the students.
Student Response Most students found it very interesting to see the amount of fuel that can be saved simulv . -bv ureheatine the incoming air. At a later stage, once the students gainv&fidence in using the spreadsheet, multiple components can be introduced to the system to make it more realistic. Afew students who were not familiar with spreadsheets found their use, through the local network server, frustrating for this type of problem. Firstly, it was necessary to queue to use the computers in the pool. Secondly, in the event of the program crashing, it took several minutes to reboot on the network.%Students who have little interest in computers tend to he intolerant of factors such as these. This exercise does. however. demonstrate the correct use of computers in modelling; that is to save time in carrying out relativelv comulex.. reuetitive calculations. It remains . necessary to understand the parameters controlling the system in order to obtain a correct result. Once a system is set up, however, there is more freedom to explore the changes induced by varying different parameters as well as the option, via the spreadsheet, of graphical presentation of results. . A
A
Enhanced Latimer Potential Diagrams Via Spreadsheets Henry Freiser University of Arizona Tucson, AZ 85721 One of the great landmark texts in inorganic chemistry is the classic text by Wendell M. Latimer, Oxidation Potentials aka The Oxidation States of the Elements and Their Potentials in Aqueous Solutions (161,first published in 1938, and recently updated (17).For over the last half century, these monographs have provided the most authoritative source on redox equilibrium parameters. A particularlv useful feature for elements havine more than one oxiiation state in aqueous solution is a so-called Latimer uotential diaeram. listine the standard or formal eouilibiium potentyals associffted with changes in oxidation states. Two such diagrams, describing the formal potentials for the uranium system, one a t pH = 0 and one at pH = 1 are shown in Figure 7. From such diagrams, one would(or, more accurately, should) be able to distinguish between stable species and those which would disproportionate into those of higher and lower, oxidation states. For example, from Figure 7, one should he able to deduce that UW) would disproportionate to U(N) and U(V1). Utilizing the data given in a Latimer potential diagram to draw such conclusions does Dose a uroblem for some. however. --In this paper, use of computer spreadsheets is shown to dramatically simplify such problems. Furthermore, the spreadsheet approach also enhances the quality and the extent of the information obtained. even when onlv Dart of the data given in the Latimer diagram is available.' In uriuciule.,the values of the standard (or formal) uotentials between successive oxidation states describe the redox equilibria of a component having multiple oxidation states in aqueous solution, and we should be able to deduce the rest, i. e., the values of the potentials of nonadjacent oxidation states. This is simply a consequence of chemical equilihrium. Doing this by traditional methods, however, can he something of a puzzler, especially for people who are not called upon to do this often. The process is simplified by modifying the familiar Nernst equation, in whichpe , obtained by dividing E and E" by 0.0592:
.
.
pe = p e o + (lln) log [OxlilRedli
?his exercise was carried out using the locally sewed student microcomputer pool, running on an MS-DOS platform, with Microsof! windowsTM3.1. The problems mentioned with programs crashing were probably due to the limited memory (2Mb)of the 386 SX workstations. The time taken to reboot was related to the type of network cards installed. The workstations have now been upgraded, with faster CPU's, more memory (8Mb),and new network cards, so that this type of problem no longer occurs. 786
Journal of Chemical Education
L
~
~
(1)
The analogy between eq. 1and the acid-base buffer equations is reassuring to the student. To follow the analogy further, let us define a set of fractions for the redox system. These are analogous to the a values commonly used for acid-base and metal complexation, but to avoid confusion they will he designated as f. In the usual meaning of a, the sum of the fvalues of all of the species in the system equals
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