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Anal. Chem. 1984, 56,586-589
a t least a basic understanding of how they work. This understanding prevents misuse of the equipment and as a consequence generates the best possible analytical results. ACKNOWLEDGMENT The authors thank the Chemistry Department Electronics Shop for assistance and the use of equipment. LITERATURE C I T E D (1) Wohltjen, H.; bessy, R. J . Chem. Educ. 1070, 56, 153-156. (2) Binkley, D.; Dessy, R. J. Chem. Educ. 1070, 56, 148-153.
(3) Malmstadt, H. V.; Enke, C. G.; Horllck, G. “Electronic Measurements for Scientists”; W. A. Benjamin: New York, 1974; pp 767-773, 762-763. (4) Graeme, J. G.; Tobey, G. E.; Huelsman, L. P. “Operational Amplifiers-Deslgn and Applications”; McGraw-Hill: New York, 1971; pp 282-316. (5) Shelngold, D. H., Ed. “Transducer Interfacing Handbook”; Analog Devices, Inc.: Norwood, MA, 1980; pp 35-37, 54-65, 127, 137, 147, 181, 195-198, 212, 213, 220-225, 229. (6) Hillburn, J. L.; Johnson, D. E. “Manual of Active Fllter Design”; McGraw-Hill: New York 1973.
RECEIVED for review March 25, 1982. Resubmitted and accepted November 14, 1983.
Computer-Controlled Weight Titrator Based on a Force-Compensation Balance Byron Kratochvil* and J.
E. Nolan
Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2 Cost effective chemical analysis requires accurate and efficient collection and processing of analytical data. The introduction of microprocessors is producing a major impact on these two areas. These devices allow not only the rapid and automatic control of analytical instrumentation but also the routine use of such powerful but mathematically tedious methods of data handling as nonlinear least-squares analysis and simplex optimization. As a result, the ways in which analytical problems can be approached are changing radically (1).
An earlier publication from this laboratory described a computer-controlled gravimetric titrator that was developed primarily to collect data on solutions suitable for the determination of formation Constants (2). This paper reports major changes in the original titrator that provide greater simplicity and flexibility. Titrimetric methods, although not so rapid or easily automated as high-pressure liquid chromatography or various flow-injection techniques, have the advantage of greater precision. This makes them important in some analytical applications. An example is the determination of uranium in procedures for nuclear safeguarding, where a precision of a few parts in 10000 is the norm and where automated titrimetry (3-5) is one of the few satisfactory techniques available. Another exqmple is analysis of standard or certified reference materials. Pungor and co-workers have recently reviewed the field of automated titrimetric analysis (6). A second area where titrations continue to find application is the collection of data for the study of complex equilibria in solutions. Many computer programs have been developed for the deduction of stability constants from titration data (7-10). A computer-controlled titrator can readily collect data of greater precision and more uniform distribution than those obtained manually. Of these advantages, greater precision is the more significant since the amount of information that can be successfully extracted from a titration curve of a complicated system is often limited by the quality of data (9). Our original titrator incorporated a gravimetric approach to titrant delivery. The superiority of metering titrant by weight rather than volume, particularly with respect to precision and accuracy, has been recognized for many years (11). Past attempts to employ this approach in a computer-controlled titrator, however, required complex schemes to mechanically isolate the titrant reservoir (4)or the entire titrant delivery system (2). The advent of stationary-pan digital electronic balances made possible a much simpler design. The principle appears to have been first applied by Moran (3);the
concept was later discussed by Luft (12). We describe here an improved computer-controlled weight titrator that incorporates a stationary-pan balance (Figure 1). Additional features include (1)absorbance-monitoring capabilities, (2) programs for the control of the titrator in three functional modes-potentiometric, photometric, or both, and (3) a new predictor algorithm for potentiometric titrations that efficiently calculates appropriate titrant dosages based on previously observed potential changes. EXPERIMENTAL SECTION Gravimetric Titrant Delivery System. The system (Figure 1)consista of a Mettler PL200 balance (Mettler Instrument Corp., Princeton, NJ), having a range of 160 g and a sensitivity of 1mg, and a 250-mL tubulated plastic bottle connected by 0.0625 in. i.d. Tygon tubing and standard Teflon chromatography fittings to a 12-V dc latching solenoid valve (General Valve Corp., Hanover, NJ, P/N 2-26-900). Another length of Tygon tubing connects the valve to a delivery tip fashioned from a short length of 0.3 mm i.d. Teflon tubing, which has been flared slightly at one end to fit snugly inside the Qgon tubing. The tip is immersed directly in the solution to be titrated. The balance pan and titrant reservoir are enclosed in a Plexiglas balance case constructed locally. The delivery valve is opened and closed by 12-Vdc, 700-mA pulses of opposing polarity (duration -15 ms). The pulses are generated by a power supply designed by the departmental electronics shop. The valve can be operated either by manual means or under remote (computer) control. Computer Hardware and Monitoring Instrumentation. The computer and its related hardware remain essentially unchanged from the previous design (2). Briefly, a PDP 11/03 minicomputer (Digital Equipment Corp., Maynard, MA) is interfaced to the various BCD instrument outputs by a four-channel multiplexer (Figure 2) to a DRVll 16-bit digital 1 / 0 port. Instrumentation connected to the multiplexer includes the balance, a Fisher Accumet 520 pH meter (Fisher Scientific), and a Cary 118C spectrophotometer (Varian Associates, Palo Alto, CA). The BCD outputs of the spectrophotometer digital readout were connected to previously unused multiplexer inputs, and minor wiring changes were made to accommodate the new balance. Absorbances during titrations were monitored by circulating solution from the titration vessel with a Rainin Rabbit peristaltic pump (Rainin Instrument Co., Woburn, MA) through a 1-cm 10-pL flow cell (Hellma Cells Corp., Jamaica, NY) inserted into a thermostated cell compartment in the spectrophotometer. Titrator Control Software. Programs for the PDP-11/03 were written in RT-11 FORTRAN supplemented by high-level 1/0 subroutines from the DECLAB-03 FORTRAN Extensions Package. All programs run under Version 02C of DEC’s RT-11 SJ operating system. Table I outlines the three programs that control various instrument configurations for different experi-
0 1984 American Chemical Society 0003-2700/84/03513-0586$01.50/0
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3. MARCH 1984
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'Table I. Software Configurations and Applications program name BERZEL
monitoring instrumentation pHlmV meter
GRAPHT
spectrophotometer
PISCES
pH/mV meter and spectrophotometer
applications titrant addition criterion analytical solution equilibrium studies equal potential conventional potentiometric potentiometric stability constant end points, determinations (6. 8 ) steps multiparametric curve fitting ( 1 8 ) ,ISE calibration (19) equal titrant conventional photometric . spectrophotometric stability increments end points constant determinations (6, 7) equal potential potentiometriclspectrophotometric steps stability constant determinations (9)
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mental situations. The programs share a common underlying structure; the major components are outlined in F i 3. The control programs were designed to allow the performance of each one to be optimized for a given application by m&cation of varioua operational parameters. These are read from a disk file a t the beginning of a program and include the following: 1. Conditions for Initial Titrant Deliuery. The amount of titrant delivered is determined by the time the valve is open. To
deliver a given weight of titrant, it is therefore nemrmy to know the delivery rate. Once an initial addition has been made. the program can easily keep track of the rate. For the first addition, however, the delivery rate and the amount to be delivered must be specified, otherwise, an arbitrary (default) valve open time (1 8 ) is used. 2. Auemging Criteria. BCD data from each instrument are collected at 0.69 intervals The number of readngs to be avereged can be specified (typically lo), 88 can the maximum acceptable standard deviation for each group of readings from a particular instrument. Specifying a standard deviation of *1 to 2 in the least significant digit for the average of 10 to 20 r e a d provides ~ adequate murance that drift is negligible. Under moat experimental conditions the instruments gave acceptahly stable readings within 10 6. 3. Titrant-Increment Criteria. Titrant increments may be calculated in one of two ways. For applications producing linear titration curves (e.g., photometric), approximately equal increments of titrant are desired, and the valve-open time t d in seconds is given by td
Amd/(h/At)
(1)
where hd is the dmired titrant increment in grams, and Am/At is the titrant delivery rate in grams per second. The specified parameter is Amd. The titrant delivery rate is then maintained by the program atter the initial increment is added. For applications producing sigmoidal titration curves,the problem is more complex. Here Amd must be variable if the data points are to be fairly evenly spaced along the potential axis (13,
588
ANALYTICAL CHEMISTRY, VOL. 56, NO. 3, MARCH 1984
Table 11. Results of Analytical Potentiometric Titrationsa indicator electrode PH
a
titrand 5X 1 g of KHP in 50 mL of H,O 4.621, x -10 g of HCla ( a s ) Cu ISE -1 X 1 to 2 g of std Cu2+(aq) (lmgCuinlOmLofH,O) -1 X mol/g EDTA(aq) 1 to 2 g of std Cuz+(aq) (0.1 mg Cu in 1 0 mL of H,O) All are standardizations of titrant except for titration of HCl.
-
titrant mol/g NaOH(aq) mol/g NaOH(aq) mol/g EDTA(aq)
14). To achieve this goal, the following slope-ratio predictor algorithm was developed:
where
+
where Amd,,+l is the desired increment for the ( n 1)th addition in grams, a d is the desired potential change between incrementa in volts, and Si is the slope for the ith addition, AEi/Ami volts per gram (IEi - Ei-ll)/(mi - mi& where i is n or n - 1: The specified parameter in this case is a d . This algorithm assumes that the relative increase or decrease in the slope of the titration curve is constant from point to point. While not exact, the assumption is adequate for our purposes. In fact, the algorithm provides precise results for all but the most poorly buffered conditions. Addition of the predicted increments is effected by converting A m d to the corresponding valve-open time through eq 1. In both the above cases a balance between the degree of definition of the titration curve and the time of analysis can be achieved by judicious choice of A m d or a d . 4. Equilibration Delay. A delay period can be specified between the end of titrant addition and the beginning of instrument reading. This is useful for slow reactions or slow indicator systems. 5. Criteria for End of Titration. Titrations are completed when a specified absorbance, emf, or weight of titrant delivered is obtained. Each titrator program follows the general flow of control outlined in Figure 3. Once the foregoing operational parameters are established, prompts are issued for an output data file name and an identification code. The programs loop through the subsequent blocks in the figure for each addition of titrant, carrying out the operations appropriate to each stage. The programs can be interrupted at the beginning of each addition cycle for the purpose of updating operational parameters. Reagents and Materials. Fisher potassium hydrogen phthalate of primary-standard grade (lot no. 711435) was used for a series of acid-base test titrations. Carbonate-free NaOH was prepared by dilution of saturated NaOH with distilled, deionized water purged of COPby bubbling with Np Indicator electrodes consisted of a Fisher glass/SCE pair. Complexation test titrations were also carried out by using standard solutions of millimolar copper(I1) prepared from copper shot (Fisher) EDTA titrant was prepared from the didissolved in “OB. sodium salt. Titrations were carried out at pH 6 (acetate buffer) and monitored with Orion Cu(I1) ion-selective and Ag/AgCl reference electrodes. Photometric titrations of the various commercial samples of the indicator dye Calmagite (3-hydroxy-4-[(2-hydroxy-5methylpheny1)azol-1-naphthalenesulfonicacid) (Aldrich,Eastman Kodak, G. Frederick Smith, Fluka) were carried out during the course of another research project. Approximately 1to 2 g of an aqueous solution of each dye lot (nominally 1to 2 mM) was added to 100 mL of a solvent consisting of 50% water/49% acetonitrile/l% concentrated ammonia. (Acetonitrile was added to avoid problems arising from aggregation of the dye molecules, which produced a negative deviation from Beer’s law.) Solutions were then titrated with standard copper(I1) titrant prepared as for the complexation titrations.
no. of titns 6 6 5 5
mean result, mol/g 4.621, x
re1 std dev, PPt 0.38
5.040,
X
0.68
1.015,
X
0.5
1.054, X
0.4
RESULTS AND DISCUSSION Analytical Potentiometric Titrations. Results for the potentiometric acid-base and complexation titrations are presented in Table 11. End points were determined from calculated first derivative curves. Although the weights of titrant and, in some cases, of sample measured considerably less than those employed in conventional manual volumetric titrations (down to almost an order of magnitude less), the precision of the results is as good as and a t times nearly an order of magnitude superior to those obtained volumetrically. The observed precision is typical of that expected for gravimetric titrations. In theory, with the balance used (1-mg sensitivity) it should be possible to deliver 1-g quantities with a precision of 1 ppt. In practice, care is required to achieve such precision; in particular, the delivery tubing must be securely anchored within the balance case and must be allowed to relax for several minutes before the titration is begun. The observed high precision may be attributed in part to the superior end-point definition afforded by the computercollected titration curves. Because the instrument can reliably deliver increments as small a~ 2 mg, a large number of points can be obtained, particularly in the end-point region, simply by specifying a small desired potential step ( a d ) , say 0.05 pH unit. Since analysis time increases linearly with the number of points collected, and since the number of points required for adequate definition of the end point depends on the sharpness of the break, efficient analytical titrations require optimization of a d . Once a well-defined curve has been obtained for a given titration, optimization is straightforward. Under conditions of rapid electrode response the titrator can collect three to four data points per minute. The time required for the titrations described typically ranged from 8 to 10 min. The use of increments of equal potential rather than equal titrant has been recognized for some time as the preferred way of defining titration curves for either analytical purposes (13) or equilibrium studies (14). A variety of predictor algorithms have been proposed for the purpose of collecting equal-potential increment curves (5, 13-15). Although most appear to be reasonably effective in overall definition, some are more rapid and efficient in locating end points. Although a definitive comparison has not been undertaken, control programs based on the sloperatio algorithm presented in eq 2 have been in use in our laboratory for approximately 2 years. During that time the algorithm has provided results with a precision and accuracy similar to those shown in Table I1 in a variety of applications where sigmoidal curves are generated (16). Analytical Photometric Titrations. Results for titrations conducted in the photometric mode are presented in Table 111. The precision obtained is consistent with the balance sensitivity and the relatively small amounts involved. The photometric titrations took approximately 20 min each because of the slow mixing and equilibration caused by circulation of the solution through the flow cell of the spectrophotometer. The photometric end points were determined by linear least-squares analysis of the computer-collected curves. Well-defined titration curves were obtained with a relative standard deviation in the slope of 0.2 to 1.0 ppt.
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Anal. Chem. 1984, 56,589-591
Table 111. Results of Analytical Photometric Titrations of Calmagite with Cu(II)= calmagite, re1 std dev, source % PPt company A 56.3 1.1 B 51.0 4.0 54.4 2.8 C 70.8 1.5 D purified ( 2 0 ) 91.8 2.4 a For each titration 5 pmol of calmagite was taken and 2 g of titrant was required. Results are the mean of six determinations in each set.
-
-
Beyond chemical considerations, the linearity of the curves reflects the low level of drift in the instrumentation and also the benefits of signal averaging.
CONCLUSIONS The computer-controlled gravimetric titrator described here is well suited to (a) analytical applications where high precision is required and (b) the study of complexation equilibria in solution. In addition, the system can be programmed to support other applications such as the high-speed Gran titrations proposed by Yamaguchi and Kusugama (17) and the “standard-less” titrations proposed by Barry, Meites, and Campbell (18). Further refinements in the titrator-control software, particularly in the areas of computer optimization of the operational parameters involved in data collection, are under way. The titrator-control applications discussed here can be implemented on virtually any computer or microprocessor.
The amount of data collected is small, the necessary calculations are simple, and the timing and execution-speed requirements are minimal.
ACKNOWLEDGMENT This work was supported by the Natural Sciences Engineering and Research Council of Canada and by the University of Alberta.
LITERATURE CITED Meltes, L. CRC Crit. Rev. Anal. Chem. 1979, 8 , 1. Guevremont, R.; Kratochvll, B. Anal. Chem. 1978, 5 0 , 1945. Moran, B. W. Trans. Am. Nucl. SOC. 1978, 30, 270. Tamberg, T. Fresenlus’ Z . Anal. Chem. 1978, 291, 124. Slanlna, J.; Bakker, F.; Lautenbag, C.; Llngerak, W. A.; Sier, T. Mikrochlm. Acta 1978, 519. Punaor. E.:Feher. 2.:Naoy, -. G.; Toth. K. CRC Crlt. Rev. Anal. Chem. 1983, 14, 175. Gans, P. A&. Mol. Relaxation Interact. Processes 1980, 18, 139. McBryde, W. A. E. Talanta 1974, 2 7 , 979. Leggett, D. J. Am. Lab. (FairfleM, Conn.) 1982, 14 (l),29. Alcock, R. M.; Hartley, F. R.; Rogers, D. E. J . Chem. SOC.,Delton Trans. 1978, 115. Kratochvll, B.; Makra, C. Am. Lab. (Fairflekf, Conn.) 1983, 15 (1). 22. Lufi, L. Talanta 1980, 2 7 , 221. Chrlstlansen, T. F.; Busch. J. E.; Krogh, S. C. Anal. Chem. 1976, 4 8 ,
1051. Leggett. D. J. Anal. Chem. 1978, 5 0 , 718. Ebel, S.; Reyer, B. Fresenius’ Z . Anal. Chem. 1982, 312, 346. Kratochvll, B.; Maitra, C. Can. J . Chem. 1982, 6 0 , 2387. Yamaguchl, S.;Kusuyama, T. Fresenlus’ Z . Anal. Chem. 1979, 295,
256. Barry, D. M.; Meltes, L.; Campbell, B. H. Anal. Chim. Acta 1974, 6 9 ,
143. Martin, C. R.; Frelser, H. Anal. Chem. 1979, 5 1 , 803. Kratochvll, B.; Nolan, J.; Cantwell, F. F.; Fulton, R. B. Can. J . Chem. 1981, 5 9 , 2539.
RECEIVED for review August 9, 1983. Accepted October 20, 1983.
Welght Tltrimetry with Equivalence Point Detection by Differential Electrolytic Potentiometry Pablo Cofr6* and Georgina Copia
Facultad de Quimica, Pcntificia Universidad Catdlica de Chile, Casilla 114-0, Santiago, Chile Weight titrations have been known for a long time. They have recently been reviewed (1))and their advantage of higher precision over volumetric titrations has been pointed out by different authors (1-3). However, we could get no real advantage from this technique, if we did not have the titration end point located with the same high precision. Differential electrolytic potentiometry (DEP) has been thoroughly studied as an end-point location technique (4). When applied to argentimetry ( 5 ) ) a precision of 0.04% is obtained. In this work, we make an appraisal of the practical precision and accuracy obtained by the classical gravimetric method, precipitating silver as AgCl, and the weight titration of silver with KBr, using DEP. Results obtained are really promising and have encouraged us to apply the method to real samples. This will be the subject of a future paper.
Weighing of the syringe was done with a Sartorius Model 1602 MP electronic analytical balance. Weighing of 1L bottles for solution preparation was done with a Sartorius Model 1404 MP8 top-loading balance. Twin silver wire electrodes (0.5 cm2)were made as described elsewhere (6). The constant current source was assembled as described in the literature (7). The potential difference between indicator electrodes was monitored by means of a Metrohm Model E510 pH meter attached to a Metrohm Model Labograph E478 strip chart recorder. Reagents. All chemicals were reagent grade. Procedure. Twin silver electrodes were activated by immersion in 1:l (v/v) nitric acidwater for a few seconds and then cathodiied for 1min, with a 3-V dry cell in 1:lOO (v/v) nitric acid-water with a platinum anode. Electrodes were immersed in the sample solution only when titration was completed to 95-98%. The titration was stopped when the first decrease in potential difference was observed. Titration curves were obtained by using the pipet-dilution method (8).
EXPERIMENTAL SECTION Apparatus. A disposable syringe was used as a weighing buret with a siliconized capillary tube attached to the needle. Drop weight delivered was 2-5 mg.
RESULTS AND DISCUSSION Electrode Response. This was investigated by voltammetry, and results found are shown in Figure 1. Curves A
0003-2700/84/0356-0589$01.50/0
0 1984 American Chemical Society
