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Automatic potentiometric titration in monosegmented flow system exploiting binary search
Analytica Chimica Acta 387 (1999) 165±173
Automatic potentiometric titration in monosegmented ¯ow system exploiting binary search PatrõÂcia B. Martelli, Boaventura F. Reis*, Mauro Korn1, Jose L.F. Costa Lima2 Centro de Energia Nuclear na Agricultura ± Universidade de SaÄo Paulo, PO Box 96, Piracicaba, SP 13400-970, Brazil Received 27 August 1998; received in revised form 5 January 1999; accepted 9 January 1999
Abstract An automatic monosegmented ¯ow system (MSFA) based on the binary search concept to perform potentiometric titration is proposed. A tubular hydrogen ion-selective electrode without inner reference solution, consisting of a conducting epoxy cylinder machined with an axial hole coated with tridodecylamine (TDDA) was employed as a sensor. The titration procedure was implemented by exploiting the binary search approach, after each analytical cycle data were evaluated to decide the variation of the titrant volumetric fraction to be inserted for the next cycle. The ¯ow network comprised three-way solenoid valves controlled by a microcomputer running software in QUICKBASIC 4.5. Combination of binary search and MSFA resulted in an automatic system providing possibilities to perform ¯ow titrations without any operator assistance. The main features of the proposed system were veri®ed by titrating hydrochloric and acetic acid solutions and the feasibility of the approach was ascertained by analyzing vinegar, coke, lemon soda, isotonic, industrial and natural orange juice samples. Results were in agreement with those obtained with a conventional potentiometric titration, and no signi®cant difference at 95% con®dence level was observed. A 1% standard deviation (n9) in results was also observed. # 1999 Elsevier Science B.V. All rights reserved. Keywords: Potentiometric titration; Tubular pH electrode; Monosegmented ¯ow; Binary search; Multicommutation
1. Introduction Titration is a widely used technique to monitor industrial process, presenting as disadvantage the long time required when a manual titrimetric procedure is employed. To overcome this drawback, automatic batch titrators and continuous ¯ow techniques have *Corresponding author. Fax: +55-19-4294610; e-mail: [email protected] 1 Universidade do Estado da Bahia, Salvador ± BA, Brazil. 2 CEQUP/Faculdade de FarmaÂcia ± Universidade do Porto, Portugal.
been proposed. The ®rst automated titration set up was introduced by Zeigel in 1914 [1]; addition of the titrant was done by controlling a burette by means of an electromagnetic device. The requirement of mechanical devices to deliver the titrant solution and to homogenize the mixture in general could make the analytical procedure expensive. This disadvantage could be circumvented by employing continuous ¯ow techniques, that present as advantages high throughput, good precision, and that can be implemented with low cost apparatus. In this sense, the classical work introduced by Blaedel and Laessig [2] can be mentioned; the sample stream was pumped
0003-2670/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S0003-2670(99)00092-6
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at a constant ¯ow rate and the reagent stream was varied linearly up to attain the end point. Following this work, several procedures have been described to carry out titrations in continuous ¯ow systems [3,4]. The manifolds were designed to perform mixing between analyte and titrant solutions into a reaction coil followed by detection. In general, the analyte solution ¯ows at constant ¯ow rate while the titrant solution ¯ow rate is varied up to reach the end point. Another ¯ow system exploiting a gradient titration technique was developed by Fleet and Ho [5] based on the variation of the titrant concentration, while the other parameters were constant. The feasibility of the procedure was veri®ed by titrating sul®de ion with mercuric nitrate solution monitoring with a sul®de selective electrode. Also, a titration gradient based on the triangle-programmed titration technique was developed [6]. The titrant was coulometrically generated in a triangular way by employing a controlled current source. After mixing with the sample stream at constant ¯ow rate, two end points were obtained. The time elapsed between them was directly proportional to the analyte concentration. Since its introduction in 1975 [7], ¯ow injection analysis (FIA) has received considerable interest, and a number of methods have been adapted for routine analysis in different ®elds. The FIA titration technique was introduced by Ruzicka et al. [8] and afterwards several systems have been proposed for different applications [9±11]. A basic difference between ¯ow injection titration and other FIA procedures is the use of peak width rather than peak height as the analytical signal. In the original work [8], the titrant solution concentration was used as a carrier stream. After sample injection, it was mixed with titrant in a gradient chamber, where chemical reactions occurred before detection. In this sense, no reaction stoichiometry was reached as in conventional titrations. The time interval elapsed between signal appearance and its return to the baseline was considered as the analytical parameter. This work showed some advantages such as high sampling rate and good precision. Nevertheless, it requires analytical curves to determine the analyte concentration and the titration curves presented a non-linear behavior. Since this procedure is based on analytical curves, it is considered a pseudo-titration according to the IUPAC de®nition
[12] and also considering the arguments by Pardue and Fields [13]. Ingenious continuous ¯ow titration approaches based on changing the ¯ow rate to generate concentration gradients have been proposed [14,15]. The system comprised two pumps, one running with constant ¯ow rate and the other ¯ow rate was changed in the range from 0 to 5 ml minÿ1. A linear concentration gradient was obtained by varying the ratio of titrant and sample ¯ow rates. Other work employing two peristaltic pumps and exponentially changing the ¯ow rates of titrant and titrand solutions was presented [16]. The authors mentioned as advantage a decrease in the time interval to attain the end point when compared with methods based on linear ¯ow rate variation [14,15]. All the above mentioned titration techniques require calibration curves to obtain the analyte concentration. Flow titrations without calibration runs would be possible if one knows the volumes of sample and titrant which should be constant under ¯ow conditions [17]. In this sense, the work presented by Korn et al. [18] based on the binary search concept ful®lls this requirement. The stoichiometry condition was attained by stepwise varying both sample and titrant volumetric fractions. The sample concentration was obtained directly and no calibration curves were necessary. Dispersion is an inherent feature of the ¯ow system, and as a consequence sample distribution inside the carrier stream presents a gradient pattern, the MSFA can be used to minimize this effect [19]. In a ¯ow system based on this approach, sample aliquots are introduced in the analytical path between two air bubbles in order to minimize the contact of sample solution with carrier solution, resulting in a low dispersion effect. In the present work, an automatic potentiometric titration ¯ow procedure based on the binary search concept [18] employing a monosegmented ¯ow system [19] was developed. A tubular ion-selective electrode for hydrogen ion based on the ionophore tridodecylamine without inner reference solution [20] was employed. The software developed is able to control all steps of the titration procedure with a feedback structure in order to allow loading of sample and titrant solutions into analytical path following application of the binary search. The feasibility of
P.B. Martelli et al. / Analytica Chimica Acta 387 (1999) 165±173
the procedure was demonstrated by the determination of acidity in vinegar, coke, lemon soda, isotonic, industrial and natural orange juice. 2. Theory The potentiometric titration employing binary search as proposed here can be considered as a successive approximations strategy to locate the end
167
point by varying the volumetric fraction of the titrant solution. The signal generated by the electrode when only the carrier solution is ¯owing through the analytical path is registered prior to the analytical cycle and stored as a pre-set potential value (Eb, baseline measurement). This value is adopted as a reference to decide about the titration course to be followed after each run and also to ®nd the titration end point. If the signal generated by running an analytical cycle higher than Eb indicates an
Fig. 1. Schematic representation of the binary search titration: (a) sampling pattern, (b) hypothetical results. Eb ± average readings of the baseline. Eb1Ebks and Eb2Ebÿks.
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excess of sample solution, then the titrant volumetric fraction must be increased. On the other hand, if a signal lower than Eb indicates an excess of titrant solution, then the titrant volumetric fraction must be decreased. The strategy followed in performing a hypothetical titration employing binary search is represented in Fig. 1. The aliquot volumes of sample and titrant solutions (V1 and V2) are introduced into the system as a time function, so that the volumetric fraction can be related with the previously adjusted time intervals T1 and T2. After sample and titrant aliquots introduction into the analytical path, the microcomputer reads the difference of potential generated by the potentiometer. The collected signal is processed in order to decide either to increase or to decrease the titrant volumetric fraction. As indicated in Fig. 1, the titrant solution volume is varied up to the measured signal was converged to the baseline value according to Eq. (1): Es Eb ks;
(1)
where Es is the signal reading when performing a titration run, Eb the baseline signal, k the arbitrary constant, and s is the baseline standard deviation. The titration procedure ends when the read signal is within the range de®ned by Eq. (1), emphasizing that the stoichiometric condition was attained. As indicated in Fig. 1, equal volumes of the sample and titrant solutions are inserted to perform the ®rst run. If the stoichiometric condition is not attained, the volume of titrant solution is halved and added or subtracted from the last titrant aliquot according to the following equations: V0 V1 =2;
(2)
V2 V1 V0 ;
(3)
V20
(4)
V1 ÿ V0 ;
where V0 is the titrant volume variation, V1 is the titrant volume of the ®rst run, V2 and V20 are the titrant volume for the next run. If the value is higher than the range de®ned by Eq. (1), the concentration of the sample solution is higher than the titrant, then the titrant volumetric fraction must be increased as indicated by Eq. (3); if lower, the titrant solution must be diluted as indicated by Eq. (4). For the next run up to attaining the
stoichiometry condition, the variation of titrant volumetric fraction is calculated as indicated in the following equations: Vn Vnÿ1 =2;
(5)
Vn Vnÿ1 Vn ;
(6)
Vn0
(7)
Vnÿ1 ÿ Vn :
This strategy is followed until the condition established in Eq. (1) is attained. The volumetric fraction of the sample solution is constant to avoid variations of the sample matrix, therefore, when the titrant volumetric fraction was decreased (Eq. (4)), a diluent solution aliquot with a equal volume to that of the variation of titrant was inserted in order to maintain the concentration and ionic strength of the sample zone. All paths followed by the hypothetical titration based on the binary search process up to the ®fth trial is shown in Fig. 1. The end point is between the third and fourth trials and the end point was attained in the ®fth trial. 3. Experimental 3.1. Apparatus The ¯ow manifold was built up by assembling a set of three-way solenoid valves (161T031 ± NResearch), mixing coils of PTFE tubing (0.8 and 1.6 mm i.d.) and transmission lines of polyethylene tubing (0.8 mm i.d.). Signal detection was carried out with a 2002 Crison potentiometer equipped with a double junction electrode (Orion 900029 Ag/AgCl) as a reference electrode. A home-made ¯ow through selective electrode for hydrogen ion [20] was employed as working electrode. The sensor unit was adapted to the ¯ow system by using a cell constructed as described elsewhere [21]. A 486 microcomputer equipped with an electronic interface (Advantech PCL-711S), running software written in QUICKBASIC 4.5, was used to control all steps of the titration procedures. An Ismatec IPC-4 peristaltic pump was employed and variation of pumping rates was performed by using its serial port (RS232) coupled to the microcomputer. An electronic interface [18] was used to match the current intensity required to switch the solenoid valves.
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Fig. 2. Flow diagram of the system for automatic titration. (a) Sampling pattern. V1±V5 ± three-way solenoid valves, B ± coiled reactor (30 cm, i.d. 1.6 mm), C ± carrier stream, S ± sample, T ± titrant, D ± diluent, X ± confluent point, ISE ± ion-selective electrode, REF ± reference electrode, W ± waste, mV ± potentiometer, P ± peristaltic pump, flow rate2.0 ml minÿ1. Dashed lines represent the flow paths when the valves are switched on.
3.2. Reagents and solutions All solutions were prepared with analytical grade chemicals and distilled deionized water. A buffer solution containing 5.710ÿ5 mol lÿ1 sodium tetraborate plus 2010ÿ5 mol lÿ1 disodium hydrogen phosphate plus 1310ÿ5 mol lÿ1 sodium citrate was used as carrier stream (C). Hydrochloric acid or sodium hydroxide solution was added in order to obtain pH values between 7 and 9. The ionic strength of this solution was adjusted to about 0.1 mol lÿ1 with NaCl. Hydrochloric and acetic acid solutions (S) were prepared from stock solutions (1.0 mol lÿ1) by appropriate dilution. Sodium hydroxide solutions (T) free of CO2 were prepared daily from a saturated sodium hydroxide solution using water boiled for 5 min. Before dilution, an aliquot of the sodium hydroxide stock solution was ®ltered to remove the sodium carbonate precipitated and the ionic strength was adjusted to 0.1 mol lÿ1 with NaCl. While experiments were performed, argon was bubbled through the sodium hydroxide solution to maintain it free of
CO2. As diluent (D) a 0.1 mol lÿ1 NaCl solution was used to maintain the ionic strength in the sample bulk. Vinegar, coke, lemon soda, isotonic, industrial and natural orange juice samples were analyzed without any previous preparation. 3.3. Flow diagram and procedure The ¯ow diagram of the system is shown in Fig. 2, where the solution loading step is performed by synchronizing its start with pumping pulsation. Thus, when the software was run, the microcomputer reads through the PCL-771S analog input the tachometer signal from the peristaltic pump. The ¯ow system was controlled by means of the microcomputer running the software shown in the ¯owchart of Fig. 3. The software also was able to decide about the best course followed in the titration close to the end point. The acquired data were treated in real time to decide straightforwardly about the pathway of the next run to be executed.
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Fig. 3. Software flowchart.
In the con®guration of Fig. 2, all valves are off and only the carrier stream is ¯owing through the analytical path. Afterwards, by switching of the valves V1 and V5 at the same time, an argon volume (VVzt1, Vz, ¯ow rate) is introduced in the analytical path. The aliquots of sample and titrant solutions were inserted in tandem by simultaneously switching on valves V1 and V2 followed by V1 and V3. This cycle should be repeated several times in order to attain the sample volume appropriate to per-
form the titration. Once the solution loading steps are ®nished, valves V1 and V5 are switched on again during a time interval t1 to insert another argon bubble. Under this condition, the analytical path is loaded with a sample string presenting a pattern analogous to that in Fig. 2(a). By switching all valves off, the carrier stream ¯ows again to transport the sample string towards the detector. Solutions mixing and reaction take place in the reaction coil (B). The signals generated by the sensor are read by the micro-
P.B. Martelli et al. / Analytica Chimica Acta 387 (1999) 165±173
computer through the analog input of the PCL-711S interface, which was coupled to the potentiometer analog output. Before inserting the sample string to begin the next run, the microcomputer reads the signal corresponding to the carrier stream (baseline signal) that is used as a reference to ®nd the titration end point. Length of the sample string and sample volume were constant in the analytical path. Then, during the searching procedure to ®nd the end point, the slug of the titrant solution was decreased and a slug of diluent solution was inserted between slugs of the sample and titrant solutions to maintain the string length. The diluent solution slug was introduced by switching valves V1 and V4 on. The analytical path length, sampling string length, sample aliquot volume and gas bubble volume were studied in order to establish better conditions to carry out the titration. The volume of the sampling string was varied from 32 to 640 ml (50% sample solution) by repeating the loading step from 1 to 20. Gas bubble volumes of 10, 20, and 30 ml were inserted by sandwiching the sampling string solution. In this sense, the analytical path length of 30 and 120 cm with inner diameter of 1.6 and 0.8 mm, respectively, were employed. The feasibility of the procedure was veri®ed by titration of HCl and H3COOH with NaOH, and by acidity determination in vinegar, coke, lemon soda, isotonic, industrial and natural orange juice. 4. Results and discussion Selection of the volumetric fraction was based on the molar ratio method, which has been used for determination complex stoichiometry [22]. In this work, it was implemented by binary search as depicted in Fig. 1. The analytical signal should attain a steady state condition in order to improve the decision about the titration course. In this sense, the ¯ow network was designed by exploiting the monosegmented approach owing to its provided facilities to achieved this condition more easier than that based on a usual ¯ow system. Titrant and titrand solutions aliquots were inserted into the analytical path by employing the binary sampling process, thus the reaction coil was loaded
171
Fig. 4. Typical recorded tracings of a binary search titration. Dashed lines (a) indicate the end signal of the first gas bubble and dashed lines (b) indicates the initial signal of the second gas bubble. Curves 1, 2 and 3 correspond to titrant solution slugs of 32, 16 and 24 ml, respectively. Eb ± baseline signal. Eb1Ebks and Eb2Ebÿks. Sample slugs32 ml. Titrant concentration8.7410ÿ2 mol lÿ1 NaOH. Flow rate2.0 ml minÿ1.
with a string formed by slugs of titrant in tandem with slugs of titrand. Under this condition, the mixing between solutions could be affected by the reaction coil geometry. Thus, experiments were carried out utilizing two reaction coils with equal volume (600 ml) presenting inner diameters of 0.8 and 1.6 mm. In this way, by maintaining the string volume at 512 ml and the slugs volume at 32 ml, only the inner diameter could affect the mixing condition. The plateau pattern without undulation shown in Fig. 4 indicates that steady state situation and good mixing conditions were attained. Nevertheless, utilizing the 0.8 mm i.d. tubing a recorded signal with undulation was observed, and to obtain similar results the solution slug volumes should be decreased to 4 ml. A low initial volume could affect the ®nal volume variation, thus making the end point location more dif®cult. Moreover, gas bubble segmentation occurred frequently affecting the precision of the measurements. With the 1.6 mm i.d reaction coil, this effect was not observed. The volumes of the two gas bubbles were ®xed at 33 ml and the sampling string was inserted between them. If the volume was smaller than this value, bubbles segmentation occurred affecting the signal stability. The signals were read without bubble removal from the analytical path, and as a conse-
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quence, the generated signals exhibited the ¯uctuations pointed out in Fig. 4 caused by the gas bubbles when they passed through the electrode. The above experiments were carried out by inserting a sample string with a volume of 512 ml. Further experiments showed that a string with a volume of 256 ml yielded a signal of similar magnitude (95%), hence, this volume was employed further. The software was designed to read the signal as a function of time and to display it on the video screen to allow a real time view of the titration. At the same time, a data string of 120 measurements (average of 10 analog/digital converter readings) were generated. Afterwards, the measurements related to the gas bubble were eliminated, and the data were processed to decide about the course of the titration. Also, these data were saved in a ®le to allow further analysis. A baseline value was used as a reference to ®nd the end point of titration. Therefore, the carrier stream solution was passed through the analytical path and 200 measurements of the potentiometer analog output were collected before the beginning of each trial. Afterwards, the mean and standard deviations were calculated. If the r.s.d. was lower than 2%, baseline and r.s.d. values were stored, otherwise the measurements were repeated. As indicated in the model of the binary search titration (Fig. 1), on increasing the number of trials, the measurements tend to the baseline value. The end point titration was found when Eq. (1) was satis®ed. The coef®cient k de®ned as an arbitrary constant was set as 5. The pattern in Fig. 4 indicates a behavior similar to that proposed in the model, so that for
additional trials, the measurements tend to the baseline value. In this ®gure, baseline value and standard deviation were 86.7 and 0.9 mV, respectively. In this sense, the titration end point was reached when the measurement (Es) was comprised in the 82.2±91.2 mV range. In Fig. 4, only three trials of the titration are shown corresponding to titrant solution slugs volume 32, 16 and 24 ml. The potential difference of curve 3 was larger than 91.2 mV, thus for the next trial the titrant slug volume should be 28 ml. In this situation, the volume variation was 4 ml and for the next trial it should be 2 ml. This value must be added if the measurement was higher than 91.2 mV or subtracted if the measurement was lower than 82.2 mV, as indicated by Eqs. (6) and (7). This strategy of slug variation was continued to locate the end point or till it attained the smallest variation that was pre-set as 0.3 ml (loading time variation of 0.01 s). After the operational conditions were established, the feasibility of the approach was assessed by analyzing samples of vinegar, coke, lemon soda, isotonic, industrial and natural orange juice, yielding the results in Table 1. Accuracy was checked by applying the paired t-test with those data obtained by a conventional titrimetric procedure [22], and no signi®cant differences at the 95% con®dence level were observed. A relative standard deviation of 1% (n9) was achieved. The time elapsed for performing one trial was 30 s, therefore, the overall time to carry out the entire titration depends on the required number of trials. For the analyzed sample (Table 1), the minimum number of trials was 5 and the maximum 8.
Table 1 Mean values and uncertainties (n3) for acidity determination in vinegar, coke, lemon soda, isotonic, industrial and natural orange juice samples Sample
FIA (10ÿ2 mol lÿ1)
Reference methoda (10ÿ2 mol lÿ1)
White vinegar White vinegar Color vinegar Color vinegar Coke Lemon soda Isotonic Orange juice (natural) Orange juice (industrial)
7.250.03 7.210.02 7.580.01 7.290.02 0.4630.03 2.640.04 3.550.01 9.080.01 8.880.01
7.430.03 7.220.01 7.580.02 7.280.05 0.4690.07 2.580.07 4.090.01 9.080.03 8.760.04
a
Conventional potentiometric titration with glass electrode.
P.B. Martelli et al. / Analytica Chimica Acta 387 (1999) 165±173
5. Conclusions The proposed system was able to perform all steps required for the titration without any operator assistance. The combination of the binary search concept and the monosegmented ¯ow approach provided possibilities to locate the titration end point with good precision. The acidity of the samples was determined without using analytical curves. The system can work without removing the gas bubbles. Their passage through the electrode cause signal ¯uctuations which do no affect the analytical signal. Acknowledgements The authors are grateful to E.A.G. Zagatto for critical comments. FAPESP, FINEP/PRONEX, CAPES and CNPq are thanked for ®nancial support. References [1] H. Zeigel, Z. Anal. Chem. 53 (1914) 755. [2] W.J. Blaedel, R.H. Laessig, Anal. Chem. 36 (1964) 1617. [3] W.J. Blaedel, R.H. Laessig, Anal. Chem. 37 (1965) 332.
173
[4] J.M. Calatayud, P.C. FalcoÂ, M. Albert, Analyst 112 (1987) 1063. [5] B. Fleet, A.Y.W. Ho, Anal. Chem. 46 (1974) 9. [6] G. Nagy, Z. FeheÂr, K. ToÂth, E. Pungor, Anal. Chim. Acta 91 (1977) 97. [7] J. Ruzicka, E.H. Hansen, Anal. Chim. Acta 78 (1975) 145. [8] J. Ruzicka, E.H. Hansen, H. Mosbaek, Anal. Chim. Acta 98 (1977) 235. [9] J.F. Tyson, Analyst 112 (1987) 523. [10] J.F. van Staden, H. Plessis, Anal. Commun. 34 (1997) 147. [11] G.D. Clark, J. Zable, J. Ruzicka, G.D. Christian, Talanta 38 (1991) 119. [12] H.M.N. Irving, H. Freiser, T.S. West, Pure Appl. Chem. 18 (1969) 427. [13] H.L. Pardue, B. Fields, Anal. Chim. Acta 124 (1981) 39. [14] J. Marcos, A. Rios, M. ValcaÂrcel, Anal. Chim. Acta 261 (1992) 489. [15] J. Marcos, A. Rios, M. ValcaÂrcel, Anal. Chim. Acta 261 (1992) 495. [16] C.H. Yarnitzky, N. Klein, O. Cohen, Talanta 40 (1993) 1937. [17] J. Bartroli, L. Alerm, Anal. Lett. 28 (1995) 1483. [18] M. Korn, L.F.B.P. Gouveia, E. Oliveira, B.F. Reis, Anal. Chim. Acta 313 (1995) 177. [19] C. Pasquini, W.A. Oliveira, Anal. Chem. 57 (1985) 2575. [20] P.B. Martelli, B.F. Reis, E.A.G. Zagatto, J.L.F.C. Lima, R.A. Lapa, Quim. Nova 21 (1998) 133. [21] S. Alegret, J. Alonso, J. Bartroli, A.A.S.C. Machado, J.L.F.C. Lima, J.M. Paulis, Quim. Anal. 6 (1987) 278. [22] D.A. Skoog, D.M. West, F.J. Holler, Fundamentals of Analytical Chemistry, 7th ed., Orlando, 1996.
Automatic potentiometric titration in monosegmented ¯ow system exploiting binary search PatrõÂcia B. Martelli, Boaventura F. Reis*, Mauro Korn1, Jose L.F. Costa Lima2 Centro de Energia Nuclear na Agricultura ± Universidade de SaÄo Paulo, PO Box 96, Piracicaba, SP 13400-970, Brazil Received 27 August 1998; received in revised form 5 January 1999; accepted 9 January 1999
Abstract An automatic monosegmented ¯ow system (MSFA) based on the binary search concept to perform potentiometric titration is proposed. A tubular hydrogen ion-selective electrode without inner reference solution, consisting of a conducting epoxy cylinder machined with an axial hole coated with tridodecylamine (TDDA) was employed as a sensor. The titration procedure was implemented by exploiting the binary search approach, after each analytical cycle data were evaluated to decide the variation of the titrant volumetric fraction to be inserted for the next cycle. The ¯ow network comprised three-way solenoid valves controlled by a microcomputer running software in QUICKBASIC 4.5. Combination of binary search and MSFA resulted in an automatic system providing possibilities to perform ¯ow titrations without any operator assistance. The main features of the proposed system were veri®ed by titrating hydrochloric and acetic acid solutions and the feasibility of the approach was ascertained by analyzing vinegar, coke, lemon soda, isotonic, industrial and natural orange juice samples. Results were in agreement with those obtained with a conventional potentiometric titration, and no signi®cant difference at 95% con®dence level was observed. A 1% standard deviation (n9) in results was also observed. # 1999 Elsevier Science B.V. All rights reserved. Keywords: Potentiometric titration; Tubular pH electrode; Monosegmented ¯ow; Binary search; Multicommutation
1. Introduction Titration is a widely used technique to monitor industrial process, presenting as disadvantage the long time required when a manual titrimetric procedure is employed. To overcome this drawback, automatic batch titrators and continuous ¯ow techniques have *Corresponding author. Fax: +55-19-4294610; e-mail: [email protected] 1 Universidade do Estado da Bahia, Salvador ± BA, Brazil. 2 CEQUP/Faculdade de FarmaÂcia ± Universidade do Porto, Portugal.
been proposed. The ®rst automated titration set up was introduced by Zeigel in 1914 [1]; addition of the titrant was done by controlling a burette by means of an electromagnetic device. The requirement of mechanical devices to deliver the titrant solution and to homogenize the mixture in general could make the analytical procedure expensive. This disadvantage could be circumvented by employing continuous ¯ow techniques, that present as advantages high throughput, good precision, and that can be implemented with low cost apparatus. In this sense, the classical work introduced by Blaedel and Laessig [2] can be mentioned; the sample stream was pumped
0003-2670/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S0003-2670(99)00092-6
166
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at a constant ¯ow rate and the reagent stream was varied linearly up to attain the end point. Following this work, several procedures have been described to carry out titrations in continuous ¯ow systems [3,4]. The manifolds were designed to perform mixing between analyte and titrant solutions into a reaction coil followed by detection. In general, the analyte solution ¯ows at constant ¯ow rate while the titrant solution ¯ow rate is varied up to reach the end point. Another ¯ow system exploiting a gradient titration technique was developed by Fleet and Ho [5] based on the variation of the titrant concentration, while the other parameters were constant. The feasibility of the procedure was veri®ed by titrating sul®de ion with mercuric nitrate solution monitoring with a sul®de selective electrode. Also, a titration gradient based on the triangle-programmed titration technique was developed [6]. The titrant was coulometrically generated in a triangular way by employing a controlled current source. After mixing with the sample stream at constant ¯ow rate, two end points were obtained. The time elapsed between them was directly proportional to the analyte concentration. Since its introduction in 1975 [7], ¯ow injection analysis (FIA) has received considerable interest, and a number of methods have been adapted for routine analysis in different ®elds. The FIA titration technique was introduced by Ruzicka et al. [8] and afterwards several systems have been proposed for different applications [9±11]. A basic difference between ¯ow injection titration and other FIA procedures is the use of peak width rather than peak height as the analytical signal. In the original work [8], the titrant solution concentration was used as a carrier stream. After sample injection, it was mixed with titrant in a gradient chamber, where chemical reactions occurred before detection. In this sense, no reaction stoichiometry was reached as in conventional titrations. The time interval elapsed between signal appearance and its return to the baseline was considered as the analytical parameter. This work showed some advantages such as high sampling rate and good precision. Nevertheless, it requires analytical curves to determine the analyte concentration and the titration curves presented a non-linear behavior. Since this procedure is based on analytical curves, it is considered a pseudo-titration according to the IUPAC de®nition
[12] and also considering the arguments by Pardue and Fields [13]. Ingenious continuous ¯ow titration approaches based on changing the ¯ow rate to generate concentration gradients have been proposed [14,15]. The system comprised two pumps, one running with constant ¯ow rate and the other ¯ow rate was changed in the range from 0 to 5 ml minÿ1. A linear concentration gradient was obtained by varying the ratio of titrant and sample ¯ow rates. Other work employing two peristaltic pumps and exponentially changing the ¯ow rates of titrant and titrand solutions was presented [16]. The authors mentioned as advantage a decrease in the time interval to attain the end point when compared with methods based on linear ¯ow rate variation [14,15]. All the above mentioned titration techniques require calibration curves to obtain the analyte concentration. Flow titrations without calibration runs would be possible if one knows the volumes of sample and titrant which should be constant under ¯ow conditions [17]. In this sense, the work presented by Korn et al. [18] based on the binary search concept ful®lls this requirement. The stoichiometry condition was attained by stepwise varying both sample and titrant volumetric fractions. The sample concentration was obtained directly and no calibration curves were necessary. Dispersion is an inherent feature of the ¯ow system, and as a consequence sample distribution inside the carrier stream presents a gradient pattern, the MSFA can be used to minimize this effect [19]. In a ¯ow system based on this approach, sample aliquots are introduced in the analytical path between two air bubbles in order to minimize the contact of sample solution with carrier solution, resulting in a low dispersion effect. In the present work, an automatic potentiometric titration ¯ow procedure based on the binary search concept [18] employing a monosegmented ¯ow system [19] was developed. A tubular ion-selective electrode for hydrogen ion based on the ionophore tridodecylamine without inner reference solution [20] was employed. The software developed is able to control all steps of the titration procedure with a feedback structure in order to allow loading of sample and titrant solutions into analytical path following application of the binary search. The feasibility of
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the procedure was demonstrated by the determination of acidity in vinegar, coke, lemon soda, isotonic, industrial and natural orange juice. 2. Theory The potentiometric titration employing binary search as proposed here can be considered as a successive approximations strategy to locate the end
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point by varying the volumetric fraction of the titrant solution. The signal generated by the electrode when only the carrier solution is ¯owing through the analytical path is registered prior to the analytical cycle and stored as a pre-set potential value (Eb, baseline measurement). This value is adopted as a reference to decide about the titration course to be followed after each run and also to ®nd the titration end point. If the signal generated by running an analytical cycle higher than Eb indicates an
Fig. 1. Schematic representation of the binary search titration: (a) sampling pattern, (b) hypothetical results. Eb ± average readings of the baseline. Eb1Ebks and Eb2Ebÿks.
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excess of sample solution, then the titrant volumetric fraction must be increased. On the other hand, if a signal lower than Eb indicates an excess of titrant solution, then the titrant volumetric fraction must be decreased. The strategy followed in performing a hypothetical titration employing binary search is represented in Fig. 1. The aliquot volumes of sample and titrant solutions (V1 and V2) are introduced into the system as a time function, so that the volumetric fraction can be related with the previously adjusted time intervals T1 and T2. After sample and titrant aliquots introduction into the analytical path, the microcomputer reads the difference of potential generated by the potentiometer. The collected signal is processed in order to decide either to increase or to decrease the titrant volumetric fraction. As indicated in Fig. 1, the titrant solution volume is varied up to the measured signal was converged to the baseline value according to Eq. (1): Es Eb ks;
(1)
where Es is the signal reading when performing a titration run, Eb the baseline signal, k the arbitrary constant, and s is the baseline standard deviation. The titration procedure ends when the read signal is within the range de®ned by Eq. (1), emphasizing that the stoichiometric condition was attained. As indicated in Fig. 1, equal volumes of the sample and titrant solutions are inserted to perform the ®rst run. If the stoichiometric condition is not attained, the volume of titrant solution is halved and added or subtracted from the last titrant aliquot according to the following equations: V0 V1 =2;
(2)
V2 V1 V0 ;
(3)
V20
(4)
V1 ÿ V0 ;
where V0 is the titrant volume variation, V1 is the titrant volume of the ®rst run, V2 and V20 are the titrant volume for the next run. If the value is higher than the range de®ned by Eq. (1), the concentration of the sample solution is higher than the titrant, then the titrant volumetric fraction must be increased as indicated by Eq. (3); if lower, the titrant solution must be diluted as indicated by Eq. (4). For the next run up to attaining the
stoichiometry condition, the variation of titrant volumetric fraction is calculated as indicated in the following equations: Vn Vnÿ1 =2;
(5)
Vn Vnÿ1 Vn ;
(6)
Vn0
(7)
Vnÿ1 ÿ Vn :
This strategy is followed until the condition established in Eq. (1) is attained. The volumetric fraction of the sample solution is constant to avoid variations of the sample matrix, therefore, when the titrant volumetric fraction was decreased (Eq. (4)), a diluent solution aliquot with a equal volume to that of the variation of titrant was inserted in order to maintain the concentration and ionic strength of the sample zone. All paths followed by the hypothetical titration based on the binary search process up to the ®fth trial is shown in Fig. 1. The end point is between the third and fourth trials and the end point was attained in the ®fth trial. 3. Experimental 3.1. Apparatus The ¯ow manifold was built up by assembling a set of three-way solenoid valves (161T031 ± NResearch), mixing coils of PTFE tubing (0.8 and 1.6 mm i.d.) and transmission lines of polyethylene tubing (0.8 mm i.d.). Signal detection was carried out with a 2002 Crison potentiometer equipped with a double junction electrode (Orion 900029 Ag/AgCl) as a reference electrode. A home-made ¯ow through selective electrode for hydrogen ion [20] was employed as working electrode. The sensor unit was adapted to the ¯ow system by using a cell constructed as described elsewhere [21]. A 486 microcomputer equipped with an electronic interface (Advantech PCL-711S), running software written in QUICKBASIC 4.5, was used to control all steps of the titration procedures. An Ismatec IPC-4 peristaltic pump was employed and variation of pumping rates was performed by using its serial port (RS232) coupled to the microcomputer. An electronic interface [18] was used to match the current intensity required to switch the solenoid valves.
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Fig. 2. Flow diagram of the system for automatic titration. (a) Sampling pattern. V1±V5 ± three-way solenoid valves, B ± coiled reactor (30 cm, i.d. 1.6 mm), C ± carrier stream, S ± sample, T ± titrant, D ± diluent, X ± confluent point, ISE ± ion-selective electrode, REF ± reference electrode, W ± waste, mV ± potentiometer, P ± peristaltic pump, flow rate2.0 ml minÿ1. Dashed lines represent the flow paths when the valves are switched on.
3.2. Reagents and solutions All solutions were prepared with analytical grade chemicals and distilled deionized water. A buffer solution containing 5.710ÿ5 mol lÿ1 sodium tetraborate plus 2010ÿ5 mol lÿ1 disodium hydrogen phosphate plus 1310ÿ5 mol lÿ1 sodium citrate was used as carrier stream (C). Hydrochloric acid or sodium hydroxide solution was added in order to obtain pH values between 7 and 9. The ionic strength of this solution was adjusted to about 0.1 mol lÿ1 with NaCl. Hydrochloric and acetic acid solutions (S) were prepared from stock solutions (1.0 mol lÿ1) by appropriate dilution. Sodium hydroxide solutions (T) free of CO2 were prepared daily from a saturated sodium hydroxide solution using water boiled for 5 min. Before dilution, an aliquot of the sodium hydroxide stock solution was ®ltered to remove the sodium carbonate precipitated and the ionic strength was adjusted to 0.1 mol lÿ1 with NaCl. While experiments were performed, argon was bubbled through the sodium hydroxide solution to maintain it free of
CO2. As diluent (D) a 0.1 mol lÿ1 NaCl solution was used to maintain the ionic strength in the sample bulk. Vinegar, coke, lemon soda, isotonic, industrial and natural orange juice samples were analyzed without any previous preparation. 3.3. Flow diagram and procedure The ¯ow diagram of the system is shown in Fig. 2, where the solution loading step is performed by synchronizing its start with pumping pulsation. Thus, when the software was run, the microcomputer reads through the PCL-771S analog input the tachometer signal from the peristaltic pump. The ¯ow system was controlled by means of the microcomputer running the software shown in the ¯owchart of Fig. 3. The software also was able to decide about the best course followed in the titration close to the end point. The acquired data were treated in real time to decide straightforwardly about the pathway of the next run to be executed.
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Fig. 3. Software flowchart.
In the con®guration of Fig. 2, all valves are off and only the carrier stream is ¯owing through the analytical path. Afterwards, by switching of the valves V1 and V5 at the same time, an argon volume (VVzt1, Vz, ¯ow rate) is introduced in the analytical path. The aliquots of sample and titrant solutions were inserted in tandem by simultaneously switching on valves V1 and V2 followed by V1 and V3. This cycle should be repeated several times in order to attain the sample volume appropriate to per-
form the titration. Once the solution loading steps are ®nished, valves V1 and V5 are switched on again during a time interval t1 to insert another argon bubble. Under this condition, the analytical path is loaded with a sample string presenting a pattern analogous to that in Fig. 2(a). By switching all valves off, the carrier stream ¯ows again to transport the sample string towards the detector. Solutions mixing and reaction take place in the reaction coil (B). The signals generated by the sensor are read by the micro-
P.B. Martelli et al. / Analytica Chimica Acta 387 (1999) 165±173
computer through the analog input of the PCL-711S interface, which was coupled to the potentiometer analog output. Before inserting the sample string to begin the next run, the microcomputer reads the signal corresponding to the carrier stream (baseline signal) that is used as a reference to ®nd the titration end point. Length of the sample string and sample volume were constant in the analytical path. Then, during the searching procedure to ®nd the end point, the slug of the titrant solution was decreased and a slug of diluent solution was inserted between slugs of the sample and titrant solutions to maintain the string length. The diluent solution slug was introduced by switching valves V1 and V4 on. The analytical path length, sampling string length, sample aliquot volume and gas bubble volume were studied in order to establish better conditions to carry out the titration. The volume of the sampling string was varied from 32 to 640 ml (50% sample solution) by repeating the loading step from 1 to 20. Gas bubble volumes of 10, 20, and 30 ml were inserted by sandwiching the sampling string solution. In this sense, the analytical path length of 30 and 120 cm with inner diameter of 1.6 and 0.8 mm, respectively, were employed. The feasibility of the procedure was veri®ed by titration of HCl and H3COOH with NaOH, and by acidity determination in vinegar, coke, lemon soda, isotonic, industrial and natural orange juice. 4. Results and discussion Selection of the volumetric fraction was based on the molar ratio method, which has been used for determination complex stoichiometry [22]. In this work, it was implemented by binary search as depicted in Fig. 1. The analytical signal should attain a steady state condition in order to improve the decision about the titration course. In this sense, the ¯ow network was designed by exploiting the monosegmented approach owing to its provided facilities to achieved this condition more easier than that based on a usual ¯ow system. Titrant and titrand solutions aliquots were inserted into the analytical path by employing the binary sampling process, thus the reaction coil was loaded
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Fig. 4. Typical recorded tracings of a binary search titration. Dashed lines (a) indicate the end signal of the first gas bubble and dashed lines (b) indicates the initial signal of the second gas bubble. Curves 1, 2 and 3 correspond to titrant solution slugs of 32, 16 and 24 ml, respectively. Eb ± baseline signal. Eb1Ebks and Eb2Ebÿks. Sample slugs32 ml. Titrant concentration8.7410ÿ2 mol lÿ1 NaOH. Flow rate2.0 ml minÿ1.
with a string formed by slugs of titrant in tandem with slugs of titrand. Under this condition, the mixing between solutions could be affected by the reaction coil geometry. Thus, experiments were carried out utilizing two reaction coils with equal volume (600 ml) presenting inner diameters of 0.8 and 1.6 mm. In this way, by maintaining the string volume at 512 ml and the slugs volume at 32 ml, only the inner diameter could affect the mixing condition. The plateau pattern without undulation shown in Fig. 4 indicates that steady state situation and good mixing conditions were attained. Nevertheless, utilizing the 0.8 mm i.d. tubing a recorded signal with undulation was observed, and to obtain similar results the solution slug volumes should be decreased to 4 ml. A low initial volume could affect the ®nal volume variation, thus making the end point location more dif®cult. Moreover, gas bubble segmentation occurred frequently affecting the precision of the measurements. With the 1.6 mm i.d reaction coil, this effect was not observed. The volumes of the two gas bubbles were ®xed at 33 ml and the sampling string was inserted between them. If the volume was smaller than this value, bubbles segmentation occurred affecting the signal stability. The signals were read without bubble removal from the analytical path, and as a conse-
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quence, the generated signals exhibited the ¯uctuations pointed out in Fig. 4 caused by the gas bubbles when they passed through the electrode. The above experiments were carried out by inserting a sample string with a volume of 512 ml. Further experiments showed that a string with a volume of 256 ml yielded a signal of similar magnitude (95%), hence, this volume was employed further. The software was designed to read the signal as a function of time and to display it on the video screen to allow a real time view of the titration. At the same time, a data string of 120 measurements (average of 10 analog/digital converter readings) were generated. Afterwards, the measurements related to the gas bubble were eliminated, and the data were processed to decide about the course of the titration. Also, these data were saved in a ®le to allow further analysis. A baseline value was used as a reference to ®nd the end point of titration. Therefore, the carrier stream solution was passed through the analytical path and 200 measurements of the potentiometer analog output were collected before the beginning of each trial. Afterwards, the mean and standard deviations were calculated. If the r.s.d. was lower than 2%, baseline and r.s.d. values were stored, otherwise the measurements were repeated. As indicated in the model of the binary search titration (Fig. 1), on increasing the number of trials, the measurements tend to the baseline value. The end point titration was found when Eq. (1) was satis®ed. The coef®cient k de®ned as an arbitrary constant was set as 5. The pattern in Fig. 4 indicates a behavior similar to that proposed in the model, so that for
additional trials, the measurements tend to the baseline value. In this ®gure, baseline value and standard deviation were 86.7 and 0.9 mV, respectively. In this sense, the titration end point was reached when the measurement (Es) was comprised in the 82.2±91.2 mV range. In Fig. 4, only three trials of the titration are shown corresponding to titrant solution slugs volume 32, 16 and 24 ml. The potential difference of curve 3 was larger than 91.2 mV, thus for the next trial the titrant slug volume should be 28 ml. In this situation, the volume variation was 4 ml and for the next trial it should be 2 ml. This value must be added if the measurement was higher than 91.2 mV or subtracted if the measurement was lower than 82.2 mV, as indicated by Eqs. (6) and (7). This strategy of slug variation was continued to locate the end point or till it attained the smallest variation that was pre-set as 0.3 ml (loading time variation of 0.01 s). After the operational conditions were established, the feasibility of the approach was assessed by analyzing samples of vinegar, coke, lemon soda, isotonic, industrial and natural orange juice, yielding the results in Table 1. Accuracy was checked by applying the paired t-test with those data obtained by a conventional titrimetric procedure [22], and no signi®cant differences at the 95% con®dence level were observed. A relative standard deviation of 1% (n9) was achieved. The time elapsed for performing one trial was 30 s, therefore, the overall time to carry out the entire titration depends on the required number of trials. For the analyzed sample (Table 1), the minimum number of trials was 5 and the maximum 8.
Table 1 Mean values and uncertainties (n3) for acidity determination in vinegar, coke, lemon soda, isotonic, industrial and natural orange juice samples Sample
FIA (10ÿ2 mol lÿ1)
Reference methoda (10ÿ2 mol lÿ1)
White vinegar White vinegar Color vinegar Color vinegar Coke Lemon soda Isotonic Orange juice (natural) Orange juice (industrial)
7.250.03 7.210.02 7.580.01 7.290.02 0.4630.03 2.640.04 3.550.01 9.080.01 8.880.01
7.430.03 7.220.01 7.580.02 7.280.05 0.4690.07 2.580.07 4.090.01 9.080.03 8.760.04
a
Conventional potentiometric titration with glass electrode.
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5. Conclusions The proposed system was able to perform all steps required for the titration without any operator assistance. The combination of the binary search concept and the monosegmented ¯ow approach provided possibilities to locate the titration end point with good precision. The acidity of the samples was determined without using analytical curves. The system can work without removing the gas bubbles. Their passage through the electrode cause signal ¯uctuations which do no affect the analytical signal. Acknowledgements The authors are grateful to E.A.G. Zagatto for critical comments. FAPESP, FINEP/PRONEX, CAPES and CNPq are thanked for ®nancial support. References [1] H. Zeigel, Z. Anal. Chem. 53 (1914) 755. [2] W.J. Blaedel, R.H. Laessig, Anal. Chem. 36 (1964) 1617. [3] W.J. Blaedel, R.H. Laessig, Anal. Chem. 37 (1965) 332.
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