svstem was considerablv less expensive than most commercial syringe pumps aione, andthe components may be used for manv other experiments. We have written alternate versions of the control code in modular form using Turbo Pascal and Quick Basic. Please contact L. Stangeland for information on the lhrbo Pascal software, and D. Anjo concerning the Quick Basic software. The titration data was stored in ASCII format disk files that can be loaded into spread sheets for publication quality graphs. Acknowledgment
We gratefully acknowledge the Royal Norwegian Council for Scientific and Industrial Research for a research fellowship and Telemark Ingeni0rh0gskole for a sabbatical leave. This work was supported by the Office of Research, California State University, Long Beach. We gratellly thank James McKibben who designed and constructed the syringe buret frame.
num: New Ymk, 1915. 2. Feld, W. A,; Shore, C. R.:P m , M. D. I n P o r s o ~ IC w & m in Chmmkfstn;Peter Lykos Ed.;Wiley: New York, 1981;p 88. 3. Cometius,R. D.; Norman, P. R. J C h . Educ. 1885,60,9649. 4.Long.d.W. J. ChemEdm. lML58.658. 6. Vitz,E. W. J. Chem. Edur 198663,804-806. 6. Cofhon, James W. The IBM PC Conneetion: S y k Berkeley, 1984.
Graphical Presentation of Acid-Base Reactions Using a Computer-InterfacedAutotitrator Michele E. lake,' David A. run ow,' and Meng-Chih Su Butler University, Indianapolis, IN 46208
Graphical presentation, with its traditional success in translating difficult concepts to sensible knowledge, remains as a basic tool-perhaps the most primary tool-for the understanding of science. In pursuing graphical presentation, one will probably deal with massive data sets. This can he awkward, if not impossible, without the help of computers. In the past two decades or so, microcomputers have redefined many aspects of science including the manipulation of huge data bases and graphics. It is now possible to paint a better picture of chemical processes and help students to learn chemistry more easily 'Present Address: Indiana University School of Medicine, lndian olis, IN 46202. 'Hogfeidt, E. Graphic Presentation of Equi\b"um Data In Treatise on Analyiical Chemistw, 2nd ed.; Kolthoff. I. M.; Elving, P. J; Eds.; John Wiley: New York, 1979: Pan I, Vol. 2. 3Leharne,S. J. Chem. Ed. 1989.66, A23S-AZ41.
Using Computers to Study Titrations In Real Time
Inspired by some theoretical attempt^,^? this work took on an experimental approach to show the intricacies of acid-base titrations. Although students have heard much about acid-base reactions, their attention has been focused on looking for the titration end point, which is signified by the color change of the indicator. The understanding of chemical changes in the titration process as a whole, particularly on a quantitative basis, has been largely neglected. The goal of this project is to help students see what occurs in the solution at everv . s i -d e step durinz the course ofa titration. Atitration is no longertreatedas the practice of seekingjust one point. It is treated as a lively chemical pmcess that changes continuously throughout its course. After some pilot work, the experiments presented here were incorporated into our sophomore analytical chemistry laboratory. With some basic training in computer use at the beginning of the semester, the students were able to carry out the experiments independently and perform data reduction on the computer. Data acquisition was accomplished by a computer-interfaced experimental setup on a point-to-point basis at the time reactions actually took place. The experimental pmcedure was controlled by a customized program. Several trials can be performed under the same conditions, thus allowing for statistical treatment on experimental results in the later data reduction procedure. In fact, class statistics were also obtained for an overall view of the experiment. Experimental The Equipment
The experimental setup consisted of an autotitration system and a computer-interfaced data acquisition system. The stand-alone autotitrator (Fisher ScientificModel 3951, originally purchased for other use, was connected to a Macintosh IIcx computer through a homemade logic gate circuitry. The circuitry, shown in Figure 1, was necessary for synchronizing the operation of titration and data acquisition. The titration rate was determined by a mechanical plunger driven by a stepper motor. It can he adjusted linearly on the dispenser module of the autotitrator. The pH changes that occurred during the titration were measured by a pair of general-purpose electrodes (Fisher Scientific Models 13-639-3 and 13-639-52), which were connected to the pH meter module of the titration system. Output from the autotitrator was translated to respective digital signals by a 16-bitresolution A/D convertor (Strawberry Tree Inc. Model ACM2-16-8)residing in the computer.
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Figure 1. Schematic diagram of logic gate circuitry in the experimental setup. Volume 69 Number 4 April 1992
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The ~ictorialand intuitive nature of the program follows the & r e n t development in scientific compuGg for intua fun itive -programmine. - This makes learninp -to program . process. Handling the Data
After the ex~eriment.extensive data reduction was handled by spreadsheet programs (Microsoft EXCEL 2.2). A typical data set of this work can easily require a thousand points. The successful use of spreadsheets in manipulating massive data has been well-demonstrated in all areas of chemistry in this JournaL4 In our studv the onlv inout data were the DHvalues a t each stage of'titrationUandthe~orres~ondin~volume of titrant. With a few mathematical formulas describing the relationship between involved species, which will be detailed in the following section, experimental concentration diagrams were derived to show the composition of the solution a t all staees of the titration. Based on the derived concentration diagram, a set of experimental thermodynamic constants were obtained. Finally, using the experimental constants and textbook theories. we eenerated calculated titration curves to compare with theexperimental curves for better understanding of acid-base reactions. This modelinp process involved so& 20 steps of operation on a spreadsh&t. It was greatly simplified by the use of EXCEL Macm programming that allows several steps of operation to be grouped as one keystroke. One of the major goals in this project was to show students an overall picture of acid-base reactions. With Macintosh's high-quality graphing capability, plotting a diagram of thousands of points became a trivial routine. An exceptional, cost&ffective graphing program, DeltaGraph 1.5 by Delta Point, was used in our laboratory to produce desktop publishable graphs. This program can communicate with almost all Macintosh software now on the market. and thus makes data transfer between a b ~ l i cations muih easier. All the experimental diagramsAl;resented here were eenerated directly with" hv DeltaGra~h out further modifi&tions.
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lure 2. Example of the mntrol software as displayed on the mmter monitor. Each icon contains a set of operations with programIble oarameters. Bv linkina selected icons in a seauential manner 11 IS bet neo by tnekonne; ng ones, we can nstrun the mmputer perlorm tne oesred experment ana to log the data at tne same
Results And Discussion Titration Curves
Four types of acid-base reactions were carried out in our titration studies: strong acid, weak acid, polyprotic base,
Acquiring the Data
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All the sienals were taken.. ~rocessed.and stored in the computer at the same time the experiment was underway. In other words, real-time data acquisition was used. Using the control software that came with the A D convertor, we were able to watch the titration curves build on the computer monitor as the experiment was carried out. The data acquisition control software (Strawberry Tree Inc. Analog Connection WorkBench 3.0)is a powerful and user-friendly object-oriented programming application. Fieure 2 shows an examole of the Droaam used in this stcdy. By connecting the icons (basii f&ctional blocks) in a certain wav. we can instruct WorkBench to ~erforma wide variety of tasks to fit the desired needs. Even a t the undergraduate sophomore level, our students learned to use WorkBench fluently in a short time. %ee, for example, Parker, 0. J.; Breneman, G. L. J. Chern. Ed. 1990,67,A5-A6.
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Figure 3. Experimentaltitration curve of 0.10 M CH3COOHby 0.10 M NaOh. The ower trace IS a scaleup of the first der valive of the pH wllh respect to the vo m e of titrant
where C. and VnAare the initial concentration and the volume of acetic acid before the titration, and C, is the concentration of acetic acid at the solution volume V.I, during the titration. Equations 2 and 3 are the results of mass balance and charge balance.
Fig~re4. Experimental titration cuwe of 0.10 M Na2C03by 0.10 M HCI. The lower trace is a scaleup ot tne first oerlvatve of pH with respect to the volume of t trant. and nonaqueous systems. Only the results obtained with weak acid and polyprotic base (Figures 3 and 4) are included here for discussion. All concentrations were appmximately 0.10 M. The titrants were standardized with respect to primary standards. Indicators and a chart &order were also used to verify the progress of titrations. However, no attempt was made to adjust the ionic strength of the solution. As part of our teaching laboratory, these results proved to be hiehlv re~mducibleand consistent to within our experimental errors. As can be seen in the figures, the first derivatives of the pH clearly point out the titration end points on the resulting titration diagrams. They are also obvious on the computer monitor during the actual experimental course.
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AciaLBase Neutralization
To extract significant physical insight fmm experimental titration curves. one must consider in detail the reactions that occur in a titration course. Since our objective was to expand the scope of knowledge learned in the laboratory, we begin our discussion at the textbook level and stay closely with the experimental approach, with a minimal number of assumptions. Parallel to this work, an excellent theoretical approach by Leharne3 is recommended for those who are interested in the development of the methodology used here. In the following discussion, we use an acetic acid titration as an example for the background theory in deriving concentration diagrams. Let [HA] = [CH3COOH1
and
DeterminingKK,and K, Among the variables used above, C., VHA,Vsalnand [Nat1 are experimental measurements, and [Ht1 is derived from the pH measurement. K. and K, are thermodynamic constants that must be determined experimentally.Therefore, in pursuing the composition of the solution, knowing the concentrations of HAand A- at every stage of the titration is desired. In fact, an aqueous acid-base titration of a monoprotic system like this can be easily understood in terms of the dissociation of the species being titrated. The degree of acid dissociation a,which is derived from eq 4, is defined as
It links two important parameters of a titration in a simple way, as described below. pa=pH-p&
(6)
At a = 1,half of the acid has dissociated, giving [*I=
[Al
Then the titration arrives at the system p i n t , at which PH = PK, Therefore, the thermodynamic constant K., which governs almost all the chemistry of a titration, can be obtained empirically for the given &mperature and experimental conditions. It was our experience that the experimental KO value may deviate from the literature vaiue enough to cause substantial errors. Furthermore, the hydmnium ion concentration and hydroxide ion concentration can be experimentally determined following the above equations, so K, can he derived under the experimental conditions. Like K., K, may deviate significantly from the well-assumed value of 10-14in textbooks. The concept of system point provides a direct means of obtaining K, from the experimental titration curve without using elaborate calculations. Alternatively, system points can be located on the titration curve midway between the initial point and the end point. At the midway point, half of the equivalence volume of titrant has been added, which causes the dissociation of half of the acetic acid. The concentrations of both dissociated and undissociated acid are equal at this point, that is,
1
[HA] = [A7 = -C, 2
[ A 1 = [CH3C00-I
for undissociated and dissociated acetic acid in the solution.. res~ectivelv.The relationship between the wantities of species involved in the titration can he descrided by the following formulas. &
coxv,=cmxv,, CHA= [HA] + [A1 [Natl
+ WI = [OK1 + [A7
Accordine to ea 6. the DHof the solution at this ~ o i nreDt to 6e resents tLe p& h e & value thus obtained identical to the one found bv rigorous mathematical derivation based on eqs 1-5.
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(1)
Concentration Diagrams
(2)
Two concentration diagrams, Figures 5 and 6, are derived based on the experimental titration curves of Figures 3 and 4 for weak acid and plyprotic systems, respectively.
(3)
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Log W I and log [OH-] are also plotted in the same fi ure. Both form straight lines and cross each other at
The dopes of log [H'l and log [OH-] are -1 and +1, respt tively, which follow the theoretical prediction of Hogfeld
Furthermore, it can be proved that log [H+lis parallel the linear part of log [HA]by cornparingthe slopes of bot The end point is located at the intersection of Log [HA] and lag [OK] where
F~gure5 Concentrat on d~agramof 0 10 M CH3COOH tnrated by 0 10 M NaOH Tne condmons for tnls dlagram are based on the t trauon
curve of Figure 4
Aconcentration diagram reveals much detail of the chemistry in the solution as the titration progresses. It is plotted as the logarithm of the concentration for the species involved in the titration against the solution pH (or pOH). In Figure 5, a concentration diagram of 0.10 M acetic acid titrated by 0.10 M sodium hydroxide includes the concentration of both the undissociated and the dissociated acid, [HA] and [A-I. Most of the acid remains undissociated a t the first part of the titration. Thus,
[HA] = [ O m As indicated in Figure 5, fewer data points were taken this region because the change in pH around the end poi is swift, but the sampling rate for the pH is held consta throughout the entire experiment. Figure 6 shows the concentration diagram of sodium ca bonate titrated by hydrochloric acid. It was derived fro the experimental titration curve of Figure 4. The diagra was plotted against pOH instead of pH because the sol tion started in the basic region. Despite its complicated a pearance, the concentration diagram contains the baa features of those in acetic acid. Two system points are located a t the intersections of log
and log [HCOJ
and a t until the solution pH reaches the system point. The projection of this point on the pH coordinate gives the pKa. After the system point has been reached, the concentration of undissociated acid drops linearly on this logarithmic plot. In other words, it decreases exponentially while more titrant is being added. The solution becomes dominated by the dissociated acid. Thus,
log [HCOJ and log [H2C031 for pKal and pKbz, respectively. The crossing point of log [coil and log EI2CO~I indicates the middle point of two system points, that is,
Again, the plots of log [HI] and log [OH-] intersect a t
The slopes are more complex in the polyprotic system Following the trace of log [CO:-], we see that it decreas, linearlv as more titrant is added to the svstem. whi~ causesin increase in pOH. This can be seen on F&e 6 . a parallel segment of the plot of log IC0:-I to log IOH-I b tween two svstem points. Bevond the second svstem wir the slope of the ~ ~ ~ [ C trace O P Iis doubly decreased as pr dicted by the theory.2 log [co?] = pKbl - pOH +log [HCOJ r pKbl + pK,,
- 2pOH + log C ,
[COFI= -2
d log d pOH
F gure 6. Concentrat on aiagram d 0.10 M Na2C0, tlirated by 0.10 M HCI. The con0 ttons for th s dlagram are based on the titration curve of Figure 5.
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The same p a t h of change was also observed in the i creasing rate of log [HCOi], where the slope changes fro +2 to +1 after oassinn the first svstem point. The concentration iiagrams shown hire were based on on the experimental data. No simdification or assumptic was made in deriving the diagrams. The experiment
and [A7 = [Na7 + [H7 based on mass balance. At the equivalence point and after it, the concentration of undissoiiated acid &n be calculated, similar to the derivation ofhydmnium concentration above, by the following formula
where b'=Kb-m and
Figure 7. Comparison of the experimental and calculated titration curves. Open and filled circles represent theoretical and experimental curves. res~ectivelv.The lower trace shows the differencebetween the two. ' however, were restricted to constant temperature, and only the acid-base reactions involved in the titration were considered. These conditions are necessary when comparisons are made with the theoretical data, as will be discussed below.
From the concentration of HA, the mass balance provides the concentration of dissociated acid and hydroxide ion. [A1 = Cm- [HA]
and The hydronium ion concentration can then be determined as
Theoretical Titration Curve of Acetic Acid
Once a set of exoerimental thermodvnamic constants have been determined, through the conskuction of concentration diagrams, computer simulations based on solution theory can be camed out to explore the chemical insight of the titrations. Aeain. acetic acid titration is used as an example to illustrate the simulation process. The necessary thermodynamic constants, including K. and K,, with the experimental conditions of Figure 3, yield the theoretical titration curve shown in Fimre 7. Usingthc methods in ou;~extbook,~we can calculate the oH of the solution in a titration bv considerine the eauilib;ia present in the system. ~urthermore,atitration is treated as if it were composed of two stages: one stage before the equivalence point, and another stage a t the equivalence point and aRer it. Before the equivalence point, the hydronium ion eoncentration is derived by solving a quadratic equation, which was derived from eq 4, for K. [Hi] = (b + db" + 4 7 4
)
where b = K,
+ [Natl
and rn = Cm- [Na'l
In this stage, the composition of the solution can be easily calculated to give [HAI=m-[m
In Figure 7, the lower trace indicates the difference in pH between the experimental curve and the calculated curve. The correlation of the two is excellent throughout the entire titration except during the initial stages. This may be due to the relatively low dielectric constant of acetic acid in water. We susned that the electrode resnonse is not reliable in describini the characteristics of the solution in this reeion. However. further investieation is needed to resolve tGs discrepan&.
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Conclusion
The feedback from the students appeared quite positive. Thev develooed a clear oicture of the acid-base reaction bv witnessingthe chemical changes as the titration Progressed. In addition, students gained much confidence in using computers to enhance their problem-solving skills through this hands-on pmied. This oroied was a fruitful learning experience forboth the students and the instructor from the time of its design - to the oractical procedure in the teaching laboratory.
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Acknowledament
The support of this project from Butler AcademicGrants and the chemistry department is greatly appreciated. We thank the chemistry students in the analytical classes for their helpful suggestions. Snwg, 0.A,: West, 0 M.: Ho ler, F. J. Fundamentals ofAnalyiica1 Chemrstry. 51n ed : Saunders Col ege: New York. 1988.
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