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Virtual Titrator A Student-Oriented Instrument David Ritter* and Michael Johnson Department of Chemistry, Southeast Missouri State University, Cape Girardeau, MO 63701 There have been several recent accounts of computer-interfaced titrators (1–11) and noncomputerized titrators (12, 13) in the literature. The titrators have become progressively more capable, and at least one system includes feedback control of the titrant volume by the instrument itself (14). However, while this trend may be desirable for the analytical chemist, it may not be the best for fostering student understanding. A recent article in this Journal (15) clearly describes an example in which the addition of computer assistance that provided too much help to the student actually served to diminish student understanding of the concepts that the experiment was intended to augment. We describe here a titrator system constructed from a computer-interfaced pH meter. The system is distinguished by a different approach. Rather than trying to build the maximum possible capability into the apparatus, we set out to design a system that would increase student involvement in the titration process. We have combined automatic data collection with real-time graphical display and interactive controls to focus attention on the process rather than on the individual bits of data. This titrator system is the first stage of an instrument interfacing project in our physical chemistry laboratory. The goals of the project are to improve student understanding of concepts involved in physical measurement, increase student familiarity with modern technology and instrumentation, upgrade the capabilities of existing premicroprocessor instruments, increase student use of computers, and introduce students to modern data handling techniques. One way to introduce modern instrumentation and methods of measurement into the curriculum is via interfacing precomputer instruments. Chemistry students will benefit from an increased understanding of computer-assisted measurement, data collection, and management. They will certainly encounter increasingly computerized environments in the future. Physical chemistry has its roots in ionic equilibria in solution. Of several recent physical chemistry texts surveyed, all cover the topic of acid–base equilibria (16). Titration of weak acids is a traditional physical chemistry experiment (17). The pK of a substance is an important physical property. In particular, the study of ionic equilibria in solution is extremely important for the understanding of biophysical chemistry.
not learn the VISUAL BASIC language used by the system; they do all of their analysis within the spreadsheet. To help mitigate the potential loss of understanding, we require students to formulate and enter all of their own data analysis functions, rather than having canned algorithms built into the system. In order to successfully use the spreadsheet in this way, students must master the same concepts they would if they were doing the same calculations with their hand-calculator on smaller data sets obtained from a noncomputerized experiment. To further reinforce the titration concepts for the student, real-time data display is used. The pedagogical value of real-time graphical display of information has been demonstrated: a delay of even 30 s between an event and graphical display has been shown to impede learning of concepts (19). The most effective reinforcement occurs when the data are displayed immediately upon measurement. Throughout the course of the titration, as each data point is collected, it is immediately displayed on the computer screen as a graph of pH vs. volume of titrant. In order to focus the student’s attention on relationships between these dependent (pH) and independent (volume) variables, we combine the real-time data display with interactive control over both the addition volume and the time delay between additions of titrant. The student must adjust both the titrant volume and the time between additions during the course of the titration. The program has an upper limit on the number of injections available for the titration; the total number of steps is insufficient to complete the assigned titration
Student-Oriented System We believe that using this system increases student learning through the use of microcomputer enhancements without sacrificing the comprehension traditionally obtained from the precomputer experiments. As the program runs, the pH and cumulative number of stepper motor steps are automatically input into a spreadsheet. After the titration is complete, the students add function coding to their spreadsheet, writing macros to manipulate these raw data (18). The student users do *Corresponding author.
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Figure 1. Block diagram of the instrument.
Journal of Chemical Education • Vol. 74 No. 1 January 1997
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with the smallest shot size. Therefore, the student must use the mouse to manipulate scroll bars on the computer screen to adjust the parameters while the titration progresses. This focus on the titration while it is happening is possible because the program automatically pokes the data into the spreadsheet, rather than requiring the student to record data. All of this works together to build on, without setting aside, the concepts from the noncomputerized experiment. In addition, students begin to understand how computers are well suited to repetitious number crunching. Before doing the titration experiment, many students resist using the spreadsheet to crunch their data from other experiments. However, the titrator generates large data sets. For example, a typical titration may yield approximately 100 data pairs. Students enter a formula once, and then copy it down a column of the spreadsheet, rather than manually repeating each calculation numerous times. After students use the spreadsheet for manipulation of such a large data set, they begin to appreciate its ease of use. Equipment The apparatus consists of a PC-compatible 80386 CPU computer containing a 96-line parallel interface card, an Orion Model 901 Ionanalyzer, and a homemade burette. A Slo-Syn type 230TH translator driver, and a Slo-Syn type M062 stepper motor1 drive the homemade burette system. A schematic diagram is shown in Figure 1. A glass combination pH electrode connected to the Ionanalyzer is used to monitor the pH of the solution; the value is passed from the BCD port on the Ionanalyzer to the parallel-interface card in the computer. The cables connecting the parallel interface card to the Ionanalyzer and the translator driver are homemade. The status of control lines between the parallel interface and the translator-driver are set by the program to control full/half step size and forward/reverse direction, as well as to initiate each step. The translator-driver decodes the information and steps the stepper motor. The student determines the calibration between the number of stepper motor steps and volume delivered by the syringe by massing known deliveries of degassed distilled water. Titration Program To best implement the goals of having real-time display of data with the student interactively controlling the titrator throughout the titration, and automatic linkage of the data to the spreadsheet, we chose to use the Windows operating system. There are several communication protocols available to transfer data between applications within the Windows environment. For the titrator, we use dynamic data exchange (DDE) to set up a cold link between the program and spreadsheet. The program is written in VISUAL BASIC for Windows (VBW). Real-time data display and interactive controls call for a graphical-type user interface. Our graphical user interface consists of three forms, introduction, titrator, and conclusion (Figs. 2–4) that control the functioning of the system. Each of these forms is composed of a number of objects. In the event and object orientation of VISUAL BASIC, each object waits for a particular event to occur to do something. For example, after the program is activated, the introductory form loads and then waits for an action. This facilitates real-time interactive control of the system by the student. When the student clicks on the appropriate box on the introduction form (Fig. 2) to start the system, Quattro
Figure 2. Introduction form.
Figure 3. Titrator form.
Figure 4. Conclusion form.
Pro for Windows (QPW) is automatically started, the appropriate QPW worksheet is activated, and a DDE cold link is established between the titrator form and the QPW worksheet. After the student clicks on the introductory form box, the titrator form, Figure 3, is displayed on the screen. This form has two groups of controls: the autotitrator controls are below the graphics box, and the manual controls are above. The LOAD and INJECT buttons are used to slew the syringe either in or out by the amount displayed in the NUMBER OF SHOTS box. These are used to flush and load the syringe with the titrant. The READ button reads the current value of the Ionanalyzer and displays it in the VALUE box. The BCD coded value read from the Ionanalyzer via the parallel card is translated into the corresponding pH value by
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the program. During the course of the titration each reading is inserted into the appropriate cell of the spreadsheet automatically by the DDE cold link protocol. The cold link updates the spreadsheet by poking the pH and number of stepper motor steps into the appropriate locations each time the value is read from the Ionanalyzer. The END button is used to close the titrator form and display the conclusion form, Figure 4. These manual controls are used in preparing for the titration. The group of controls below the graphics box are used to operate the autotitrator. The three variable controls are adjusted by the attached scroll bars: the NUMBER OF STEPS FOR THE TITRATION SAMPLE limits the total number of shots for a titration, the TITRATION SPEED control determines the length of time between shots of titrant, and the SHOT SIZE control determines the volume of titrant added in each shot. We initially found that students tended to overcompensate in control adjustments. We then added thirty beeps of the speaker between each injection to give the student immediate auditory feedback to changes in the timer control, allowing them to judge the magnitude of their corrections between shots. The sound immediately changes in direct proportion to changes in the timing. The START and STOP buttons begin and end the autotitration. A mouse click on the START command button on the titrator form (Fig. 3) starts the titration. When the command button sub recognizes that the appropriate mouse click has occurred, it invokes the code to start the titration. Students’ attention must remain focused on the experiment in order to complete the titration with a welldefined endpoint. Both TITRATION SPEED and SHOT SIZE are controlled by the student throughout the titration. At the start of the titration, the student minimizes the time delay between shots and increases the size of each shot. An appropriate delay must be chosen to match the electrode response to the size of the injection. The student watches the Ionanalyzer digital display to determine the optimum time delay between various sizes of shots. As the titration progresses, a graph of pH vs. volume added takes shape in the graphics box in the center of the form, Figure 3. The graph is updated as each data point is added immediately after the measurement. The real-time display of the data in a graphical format provides the immediate visual feedback that allows effective control of the timing and size of each shot of titrant. The student watches the progression of the titration in the graphics box. When the inflection indicating approach of the end point begins to show on the graph, the student gradually increases the time delay between shots and decreases the shot size as necessary for good definition of the endpoint. In this manner, the titration is accomplished in a relatively short time while still allowing excellent definition of the endpoint(s). Students enjoy using the mouse to control the titrator. When the titration is complete, the spreadsheet contains two columns of numbers: the cumulative number of stepper motor steps to deliver the volume of titrant and the corresponding pH values. Students must then convert the steps to volume. They do this by first massing deliveries of degassed distilled water from the burette, and calculating the proportionality between shot size and volume. They then add the appropriate formulas to the worksheet to convert the steps into volumes. The spreadsheet is then used to generate a finished graph, Figure 5. They construct first and second derivative curves by taking differences between successive values and dividing them, Figure 6. Students determine the equivalence
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points for the titration from the derivative curves (20). After finding the equivalence point(s) and concentration, students can determine an approximate value for the pK a from the pH at halfway to the equivalence point, Figure 5 (21). For a more rigorous analysis, the data on the spreadsheet may be modeled with the quartic equation for the diprotic system over the pH range. Student set up a model on the spreadsheet to compare to their data, and display both on a graph of pH vs. volume of titrant (22, 23). Rather than solve the equation for the concentration of acid, we use Freiser’s method (24) of using alphas to calculate the theoretical volume of titrant at each point. The pKa is also calculated at each
Figure 5. Plot from student titration of phosphoric acid with sodium hydroxide.
Figure 6. First and second derivative curves obtained from the titration curve.
Figure 7. Student data with theoretical fit for titration of potassium hydrogen phthalate with sodium hydroxide.
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point. The pK a’s over the range from 20% to 80% of the volume at the equivalence point are then averaged (25) to yield a value for the average pK a. This average pKa is then used to generate the theoretical curve (see Fig. 7). Students add the appropriate functions to their spreadsheet and use the pKa’s and concentration of the acid determined from the titration for the theoretical fit. Conclusion The close integration of real-time graphical display, interactive controls, and linkage to the spreadsheet is easily accomplished by using VISUAL BASIC for Windows programming. The automated data collection eliminates the worst drudgery of the premicrocomputer experiment, but the real-time graphical display of data integrated together with interactive controls compel students to keep their attention focused on the pH–volume relationship. The use of a spreadsheet for data analysis also eliminates the drudgery of repetitive calculations, but student comprehension appears to be undiminished. We attribute this to the fact that the students must enter their own formulas for the calculation into the spreadsheet, and they must therefore master the same calculations as for the premicrocomputer experiment. In this way, our goals have largely been met. Note 1. Superior Electric Corp., Bristol, CT.
Literature Cited 1. 2. 3. 4.
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5. Greenspan, P. D.; Burchfield, D. E.; Veening, H. J. Chem. Educ. 1985, 62, 688. 6. Meyer, E. F. J. Chem. Educ. 1992, 69, A158. 7. Amend, J. R.; Tucker, K. A.; Furstenau, R. P. J. Chem. Educ. 1991, 68, 857. 8. McMahon, J. J.; Braca, P. R. J. Chem. Educ. 1992, 69, A156. 9. Chau, F. T. Comput. Chem. 1990, 14, 69. 10. Braithwaite, A.; Hills, C. C.; Smith, F. J. Comp. Appl. Lab. 1984, 2, 115. 11. Chipperfield, J. R.; Roscoe, R. M.; Webster, D. E. Anal. Proc. 1983, 20, 127. 12. Lingane, J. J. Electroanalytical Chemistry, 2nd ed.; John Wiley: New York, 1958; Chapter 8. 13. Lynch J. A.; Narramore, J. D. J. Chem. Educ. 1990, 67, 533. 14. Stangeland, L. J.; Anjo, D. M. J. Chem. Educ. 1992, 69, 296. 15. Sprague, E. D.; Ridgway, T. H. J. Chem. Educ. 1993, 70, 909. 16. Alberty, R. A.; Silbey, R. J. Physical Chemistry, 1st ed.; John Wiley: New York, 1992; Chapter 9; Mortimer, R. G. Physical Chemistry; Benjamin/Cummins: Redwood City, CA, 1993; Chapter 7; Atkins, P. W. Physical Chemistry, 5th ed., W. H.Freeman: New York, 1994; Chapter 9. 17. Daniels, F.; Williams, J. W.; Bender, P.; Alberty, R. A.; Cornwell, C. D.; Harriman, J. E. Experimental Physical Chemistry, 7th ed.; McGraw-Hill: New York, 1970; Experiment 30. 18. Scientific computation and mathematical modeling by means of spreadsheets has a long history. For example, see: Hayes, B. Sci. Am. 1983, 249(4), 22; Rosenberg, R. M.; Hobbs, E. V. J. Chem. Educ. 1985, 62, 140; Durham, B. J. Chem. Educ. 1990, 67, 416. 19. Brasell, H. J. Res. Sci. Teach. 1987, 24, 385. 20. Skoog, D. A.; West, D. M. Fundamentals of Analytical Chemistry, 3rd ed.; Holt: New York, 1976; p 408; Daniels, F.; Williams, J. W.; Bender, P.; Alberty, R. A.; Cornwell, C. D.; Harriman, J. E. Experimental Physical Chemistry, 7th ed., McGraw-Hill: New York, 1970; Experiment 30. 21. Cawley, J. J. J. Chem. Educ. 1993, 70, 596. 22. Breneman, G. L.; Parker, O. J. J. Chem. Educ. 1992, 69, 46. 23. Lake, M. E.; Grunow, D. A.; Su, M. J. Chem. Educ. 1992, 69, 299.; Partanen, J. I.; Karki, M. H. J. Chem. Educ. 1994, 71, A120. 24. Freiser, H. Concepts and Calculations in Analytical Chemistry: A Spreadsheet Approach; CRC: Boca Raton, FL; 1992; Chapter 8. 25. Albert, A.; Serjent, E.P. The Determination of Ionization Constants, 2nd ed.; Chapman and Hall: London, 1971; Chapter 2.
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