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pH-stat techniques in titrimetric analysis
Analytica Chimica Acta 470 (2002) 277–288
pH-stat techniques in titrimetric analysis IV. pH-stat monitoring of chelatometric titrations Carlo Maccà a,∗ , Lidia Soldà a , Mirella Zancato b a
Department of Inorganic, Metallorganic and Analytical Chemistry, University of Padua, Via Marzolo 1, I-35131 Padova, Italy b Department of Pharmaceutical Sciences, University of Padua, Via Marzolo 5, I-35131 Padova, Italy Received 11 April 2002; accepted 18 July 2002
Abstract The theory of pH-stat chelatometric titrations recently developed [Anal. Chim. Acta 456 (2002) 313] is experimentally substantiated here. The titrations of four representative doubly charged cations having different behaviour (copper, zinc, calcium, magnesium) are taken as examples. Copper is titratable between pH 3 and 5, zinc between 3 and 6, calcium between 6 and 10, and magnesium between 7 and 10. The shapes of the titration plots agree well with the theory, accounting for simultaneous equilibria involving proton exchange. The technique yields accurate and precise results, which compare favourably with those of other instrumental techniques, in particular photometric titrations. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Titrimetric analysis; Chelatometric titrations; pH-stat titrations; Calcium(II); Copper(II); Magnesium(II); Zinc(II)
1. Introduction Automatic pH-metric titrators frequently include the pH-stat or “Stat” operating function. In this mode, the titrator measures the pH of a test solution and simultaneously counteracts any spontaneous or induced variation (either an increase or a decrease) of this quantity with respect to a pre-selected operating control value by adding the appropriate amount of a suitable reagent (a strong acid or a strong base, respectively). The pH-stat technique [1] is widely used in the chemical and biochemical laboratory when it is necessary to keep under strict control that most important experimental parameter for instance in the course of organic reactions or of biological processes, and in ∗ Corresponding author. Tel.: +39-0498275205; fax: +39-0498275161. E-mail address: [email protected] (C. Macc`a).
studies of reaction rates or of enzyme kinetics [2,3]. Moreover, the measurement of the reactant’s delivery rate provides a direct means for determining reaction rates and performing kinetic analyses [4,5]. In contrast, the use of the pH-stat technique for monitoring volumetric titrations has been very seldom investigated, and is quite unknown in current practice in the analytical laboratory. This paper is part of a series intended to study in more depth the theoretical and practical aspects of this technique in volumetric analysis. The theory and applications of pH-stat monitoring of acid–base titrations [6], respectively, are the object of two recent papers [7,8]. In chelatometric titrations, the use of pH-stat is currently suggested for the mere purpose of keeping the pH at an optimal value, when concentrated buffers could alter the reaction course [9]. At our knowledge, only a single procedure using the pH-stat technique for detecting the titration end point (determination of calcium and magnesium in
0003-2670/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 3 - 2 6 7 0 ( 0 2 ) 0 0 6 9 1 - 8
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skim milk) has so far been described [10]. In the third paper of this series [11], the fundamentals of pH-stat chelatometric titrations have been developed, and the criteria for optimising the experimental conditions have been discussed. Accordingly, such titrations are expected to attain good accuracy and high precision. The purpose of the present work is to substantiate those favourable anticipations by implementing experimental procedures for some representative determinations.
electrode with encapsulated Ag/AgCl reference electrode in 3 M KCl and sleeve junction (Ingold, Urdorf, Switzerland, type 405.60.88.E) was measured with a resolution of 0.1 mV or 0.01 pH. The Stat program allowed choosing either mV or pH as the controlled operational parameter. The measured solution was contained in a 20– 90 cm3 jacketed cell Metrohm (Herisau, Switzerland) type 6.1418.220 and stirred with a PTFE-coated magnetic bar. It was thermostated at 25.0 ± 0.1 ◦ C and fluxed with carbon dioxide-free nitrogen.
2. Experimental
2.1.2. Photometric titrations Photometric titrations were monitored with a Metrohm 662 Photometer equipped with a light-guide measuring cell. The photometric probe could be accommodated in the titration cell through the cover. The stepless wavelength setting is 400–700 nm with a 10 nm resolution. The analogue output is 0–1 V with a 1 mV resolution. The MicroTT 2050 programmable potentiometric titrator was used for adding the titrant EDTA solution and for recording the titration plot by taking the voltage signal from the photometer’s output.
2.1. Apparatus 2.1.1. pH-stat titrations The apparatus required must allow the simultaneous addition of two reactants: the primary titrant (the chelating agent), by stepwise addition of equal, small volume increments, or by continuous addition at a constant volume rate, and the auxiliary titrant (a strong base) under pH-stat control. Single instruments automatically performing all the required operations are not currently available. However, a partly automatic apparatus can easily be assembled by combining a potentiometric (pH-metric) titrator having the pH-stat function with a system for controlled delivery of the primary titrant. The experiments with stepwise delivery of primary titrant here reported were performed with a syringe burette Microbur 2030 (Crison, Barcelona) fitted with a 1 cm3 syringe 1001 TLL (Hamilton, Bonaduz, Switzerland). The resolution of delivered volumes is, 4×10−4 and 1×10−3 cm3 , respectively; accuracy was determined to be better than resolution. The burette was driven by a PC through the proprietary “Bureta” program, modified to repeat additions of constant volume aliquots at fixed time intervals. Experiments with continuous delivery of the primary titrant were performed with the apparatus described in [8]. For delivering the auxiliary titrant under pH-stat control, a microprocessor-controlled programmable potentiometric titrator Crison MicroTT 2050 was used. It was equipped with a Crison Microbur 2030 syringe burette fitted with a 2.5 cm3 1002 TLL syringe (Hamilton) and was connected to an Epson LX-400 printer. The signal from a combination glass
2.2. Reagents All chemicals of analytical grade or better were used as received. The 0.1 or 0.01 M standard solution of metal cations were prepared from high purity metals (Cu), oxides (MgO, ZnO) or salts (CaCO3 ) with the usual procedures [12–15]. The 0.1 M solutions of primary titrant were prepared by weighing analytical grade disodium ethylendinitrilotetraacetate (Na2 H2 Y, EDTA) after desiccation at 80 ◦ C. A 0.1000 M solution of sodium hydroxide low in carbonate (sodium carbonate <0.2%) BDH cat. 191503E was used as the auxiliary titrant. All solutions were prepared with ultrapure water produced with a Milli-Q Plus apparatus (Millipore, Bedford, MA). 2.3. Procedure 2.3.1. pH-stat titrations The measuring electrochemical cell was calibrated separately with pH standards at 4.00 and 7.00. The
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titration cell was filled with 20 cm3 of 0.1 M sodium perchlorate solution containing a suitable buffer at low concentration (generally (1–2) × 10−3 M) and a volume of standard solution of the metal cation containing approximately 50 mol of cation was added. A preliminary adjustment of the solution pH to a value slightly more acidic than the operating value was made either by addition of some drops of diluted acid or (if the standard solution of cation was too acidic) by a preliminary end-point titration with strong base. The exact operating pH value was reached by temporarily activating the Stat function. Finally, the Stat operation and the record of the titration plot were simultaneously started and, after a known time delay (30 or 60 s which allowed to control the stability of pH), the primary titrant addition was begun. Constant volume (24–48 l) stepwise additions at fixed time intervals (30 s–2 min), or continuous additions (minimum rate 0.05 cm3 min−1 ) were carried on until the added primary titrant was 1.5–2 times the equivalence volume (usually corresponding to 0.5 cm3 ). The numerical titration report (displaying time, measured pH or mV, auxiliary titrant volume, single volume increments, temperature) was printed during operation at 10 s intervals. The graphical report (auxiliary titrant volume versus time) was printed after ending the titration. The true titration plot was recalculated by using as the abscissa the primary titrant volume VY and as the ordinate the volume of auxiliary titrant VOH required to reach stationary conditions (pH constant in time at the operating value within the resolution of the pH-stat system, i.e. 0.01 units). The equivalence volume of the primary titrant, Ve , was determined by least-square analysis as the abscissa of the intersection between two straight-line segments. Data was treated with SigmaPlot scientific graphing software (Jandel Scientific, Erkrath, Germany). 2.3.2. Photometric titrations Photometric titrations were performed on a measured volume of standard solution of the analyte cation diluted with 25 ml of buffer at the required pH and containing a suitable indicator. The programmable titrator was operated in the “inflection point” titration mode with constant volume additions. This mode allowed printing and plotting the complete titration record. The input signal was taken from the photometric probe, op-
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erated either in the absorbance or transmittance mode. Very small (10 l) additions were made, and a strict stability criterion (signal drifting less than 1 mV in 10 s) was chosen, in order to reach the best precision and accuracy even when the signal change at the end point was abrupt or the complexation reaction was slow. 3. Results and discussion 3.1. The pH-stat titration plot and the choice of operating pH In pH-stat chelatometric titrations of metal cations, the addition of primary titrant (EDTA or another suitable chelating agent) is accompanied by the addition of the auxiliary titrant (a strong base solution) at a rate suitable to maintain the pH constant at a pre-selected value by neutralising the acidity delivered by EDTA. The titration plot shows the added volume of strong base, VOH , against the volume of EDTA, VY . When the chelation of the titrand cation is complete, the delivery of acidity by EDTA does stop or change rate, depending on the operating pH. Therefore, in the correspondence of the equivalence point the titration plot’s slope also changes. If the conditions are suitable, it is expected that the change of slope is easily appreciable. The dependence of the titration plot’s shape on the nature of the reactants and on pH has been discussed in detail [11]. Two main aspects of the titration plot do condition the feasibility of a titration: the extent of slope change and its sharpness. The extent of slope change depends on the difference between the net number of protons delivered by EDTA before and after the equivalence point. Its sharpness, in turn, depends on the quantitativity of the chelation reaction. Both are strongly influenced by pH [11]. According to the primary reaction: Mm+ + H2 Y2− → MYm−4 + 2H+
(1)
the slope of the titration plot before the equivalence point ideally corresponds to 2 mol of strong base per mole of EDTA. However, competing reactions involving proton exchange, whose extent depends on pH, can decrease this ratio [11]. The slope after the equivalence point, ideally null after the completion of
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reaction (1), is dictated by the degree of protonation of the unreacted ligand at the operating pH. At pH increasing over about 5, the prevailing form is HY3− ; at still higher pH it is Y4− . Therefore, a finite and increasing amount of base is consumed to deprotonate the excess titrant, H2 Y2− ; the relative amount gradually approaches the maximum value of 2 mol of auxiliary titrant per mole of primary titrant in excess. In consequence, the change of slope at the equivalence point vanishes at a pH is larger than about 11.5 [11]. In turn, the quantitativity of the chelation reaction depends on the conditional stability constant of the chelate complex KMY in the reaction medium. This quantity is heavily conditioned by the dependence of the degree of protonation of EDTA anion on pH [16]. Competing ligands decreasing the free-cation fraction of the unreacted metal may also have an appreciable effect. The overall trend is towards a decrease of KMY on decreasing pH. As the reaction becomes less and less quantitative, the slope change occurs in a larger and larger interval around the equivalence point, thus impairing the sharpness of the equivalence point. For every analyte cation, a compromise value of pH for the two contrasting effects must be found. This optimum value can be accurately forecast if the stability constant of the chelate complex and the equilibrium constants of the competing reactions are known with sufficient accuracy [11]. It must be noted that pH does not need to be known with the greatest accuracy, as long as it lies in the wanted range and is kept rigorously constant during each single titration. For quantitative determinations, calibration of the measuring cell with usual pH standards is quite acceptable. 3.2. Choice of the instrumental and other experimental parameters The experimental parameters to be set at the beginning of each titration are either of chemical or of instrumental nature. The chemical parameters are operating pH and buffer power of the supporting solution. The instrumental ones are addition rate, equilibration time and control band [8]. The choice of pH is dictated by the criteria discussed in Section 3.1. The buffering power of the measured solution regulates the sensitivity of the pH-static response, i.e. the deviation of pH from the operat-
ing value caused by unbalanced titrants ratio. In the absence of any buffer, EDTA addition, particularly when discontinuous, could cause sudden and large pH changes, hindering the pH-static control. A too high buffering power would instead cover the titrant’s action. Both effects cause large random errors [8]. With synthetic samples, optimum conditions are realised by adding a suitable buffer pair. The approach to the choice of the instrumental parameters is similar to the one discussed in detail for acid–base pH-stat titrations [8]; in the present instance, however, it is much more dependent on the nature of the chemical system involved. Indeed, an important peculiarity of chelation reactions is that they are more or less appreciably slow, at variance with neutralisation, which is generally fast. When the reaction is fast, the practical ratedetermining stage can be, alternatively, the mixing of reactants, the electrode response, or the ability of the pH-stat device to keep pace with the acidity change. This last is mostly conditioned by the instrumental parameters set. By acid–base titrations, it was quite generally possible to operate with continuous, although moderately slow, addition of titrand (which in acid–base titrations operationally takes the place of the primary titrant). In contrast, preliminary experiments did show that complexometric reactions with continuous additions, although yielding apparently satisfactory linear segmented plots, were frequently affected by appreciable systematic errors. These were removed by operating with constant additions at fixed time intervals. With this procedure, the plot of auxiliary titrant volume against time together with the numerical record of both quantities and pH (see Section 2.3) allowed to verify point by point the time necessary to reach equilibrium conditions (Fig. 1). The size of the added aliquots (1/20 to 1/10 of the equivalence volume), and thus their number, was chosen to satisfy the somewhat contrasting requirement of efficient pH-stat control, good least-squares evaluation of data and reasonable total titration time. The time between two subsequent additions, set after the results of a preliminary titration, was just long enough to allow the reaction to reach equilibrium after each addition (Fig. 1). The size of additions also has a role in dictating the instrumental parameters specific of the pH-stat operational mode, i.e. equilibration time and control band
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Fig. 1A shows a typical graphical titration record (volume of auxiliary titrant against time) for an appreciably slow reaction (copper(II) at pH 3). Fig. 1B shows the corresponding pattern of pH as recorded in the numerical titration report (see Section 2.3). Stepwise additions of EDTA were made at 1 min intervals; pH was measured at 2 s intervals and recorded every 10 s. The patterns of both plots of pH and NaOH volume against time show that 30–45 s were required to reach stationary conditions after each addition of primary titrant. After the equivalence point, the measured solution is no any more under pH-stat control, because the excess EDTA behaves as a weak base (it hydrolyses by about 30%) and slowly increases the solution pH [11]. 3.3. The auxiliary titrant
Fig. 1. (A) Recorded plot of the volume of auxiliary titrant (0.1000 M NaOH) against time for a pH-stat titration at pH 3.00 of 48.64 mol of copper(II) in approximately 20 ml of supporting solution (0.1 M sodium perchlorate containing 2 × 10−3 M formate buffer). Aliquots of 48 l of 0.1 M of EDTA were added at 1 min intervals. Equilibration time 2 s; control band 2 pH units. (B) The corresponding plot of measured pH against time.
[8]. The equilibration time is the time after which in the Stat mode the meter is made to accept the measured signal as stable and ideally corresponding to the equilibrium emf of the measuring cell when stationary conditions are reached. Given the fast response of the physical measuring system, an equilibration time of 2 s was sufficient. The choice of the control band [8] is possibly less critical than in acid–base titrations, because the reaction and, consequently, the delivery of acidity, are moderately slow and do not require fast compensation of large pH changes if the size of added primary titrant aliquots is small. The purposely added pH buffer (see above) helped to damp pH from swinging.
For determining the metal cation contained in the sample solution, it is not necessary to know accurately the titre of the auxiliary titrant solution. Indeed, the titre of the strong base only decides on the experimental slopes (cm3 /cm3 ) of the two segments composing the titration plot without altering the abscissa of their intersection, i.e. the equivalence volume of the primary titrant. In principle, if the reacting strength of the secondary titrant is accurately determined [7,8] and the real path of the overall reaction (cation+chelating agent+base) with its exact stoichiometry [11] is known, the amount of analyte can also be determined from the end-point volume of the auxiliary titrant. Much more interesting is the possibility of determining the stoichiometry of the overall titration and the stability constants of mixed complexes from the mole ratio R of strong base to chelating agent after measuring the slope of the linear segment preceding the equivalence point [11]. For this purpose, the reacting strength of the strong base must be known with the best possible accuracy. It is known that strong base solutions are generally contaminated by carbonate, and in consequence their reacting strength depends on the end-point pH of the individual titration in which they are used [8]. The effective titre can be conveniently determined by pH-stat titration of a primary standard acid [7,8] at the intended operating pH of the pH-stat chelatometric titration. By this means, the 0.1000 M solution of sodium hydroxide low in carbonate used in the
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experiments described here was seen to increase only negligibly its contamination as an effect of the necessary manipulations. In preliminary experiments, solutions at the usual level of carbonate contamination (about 2%) were used without appreciable inconvenience. 3.4. Selected titration systems When discussing the theory of pH-stat complexometric titrations [11], summarised in Section 3.1, we took those of copper(II) and magnesium(II) with EDTA as examples representative of the main features of the technique. Owing to their diverse properties, these systems are also very suitable for introducing the experimental application of the pH-stat technique, while confirming the theoretical deductions. In addition, we report here the results of investigations on two other cations of great analytical relevance, calcium(II) and zinc(II). For comparison with other well-established techniques, we have considered only volumetric methods based on chelatometric reactions. Indeed, the most common instrumental determination technique of metals in solution, atomic absorption spectrometry, measures concentration in a much lower range and with limited precision, with the inconvenience of requiring a specific lamp for every element. Direct potentiometry also requires a specific electrode for each determinand cation and has only moderate precision. When higher precision determinations are required, the choice is usually chelatometric titration (even in preference to gravimetry, which is too time consuming). Visual titrations are performed after adding a suitable indicator. The procedures can be automated and their precision improved by using photometric titrators. Therefore, in order to state whether the new technique offers any advantage in an automated analytical laboratory, we have compared pH-stat titrations of each investigated metal cation with corresponding indicated photometric titrations. However, it must be stressed that a photometric titration can hardly be considered an accurate reference method. Indeed, the shape of the titration curve (let it be absorbance A, or transmittance T, against titrant volume V), and by consequence the procedure for locating the equivalence volume, are strongly dependent on the values of the conditional stability constants of the com-
plexes involved (cation-EDTA and cation-indicator). In practice, the location of the equivalence point may become rather subjective, although less than in visual titrations. With computerised photometric titrators, the accuracy depends on the algorithm chosen. An alternative automatable technique, the potentiometric titration, is convenient only if an electrode selective for the analyte cation is available (procedures involving the use of electrodes responding to an auxiliary cation, e.g. mercury(II), are not of current use in the analytical laboratory). Even in this instance, it can suffer some limitation due to the relatively high lower response limit of the sensor. All titrations were performed using primary standard solutions of cations. In order to favour a direct comparison among all series of titrations, the results were expressed by calculating the titre CY of the EDTA solution (Table 1). 3.5. Copper The chelatometric titration of copper(II) can be performed either in acidic solution at pH not exceeding 5, above which precipitation occurs, or at pH near to 8 [12,13]. We have tested the determination of Cu(II) in the acid pH range from pH 5 to 3, where the chelate is still strong enough (log KCuY ≥ 8.3) [16] to form quantitatively even in the proximity of the equivalence point and assign the titration a good intrinsic [17] precision. Typical pH-stat titrations plots of 2.4×10−3 M copper(II) (48.64 mol in approximately 20 cm3 of supporting solution) at various pH values are represented in Fig. 2A. The buffers were, respectively, 2 × 10−3 M chloroacetate at pH 3 and 2 × 10−3 M acetate at pH 4 and 5. It is known that the chelation of Cu(II) is moderately slow. The speed increases with increasing pH. At pH 3, reaching stationary conditions required at least 45 s as shown in Fig. 1; with increasing pH, 30–15 s became sufficient. With additions of primary titrant aliquots corresponding to approximately 1/10 of the equivalence volume (48 l), titrations lasted not more than 12–15 min and yielded satisfactory results. Some experiments performed by halving the aliquot volume (24 l) yielded identical results, with an only moderate improvement in the statistical evaluation of the linear parameters and the drawback of longer duration.
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Fig. 2. (A) Titration plots of volume of auxiliary titrant (0.1000 M NaOH) against volume of primary titrant (0.1002 M EDTA) for pH-stat titrations of 48.64 mol of copper(II) in approximately 20 ml of supporting solution at pH—(䊉): 5.00 (2×10−3 M acetate buffer); (䉱): 4.00 (2 × 10−3 M acetate); (䊏): 3.00 (2 × 10−3 M chloroacetate). Aliquots of 48 l of 0.1 M EDTA were added at intervals of 1 min (at pH 3) or 30 s (at pH ≥ 4). Equilibration time 2 s; control band 2 pH units. (B) Deviations (residuals) of the experimental auxiliary titrant volumes from the interpolated linear segments for the titration at pH 5. Empty symbols after the equivalence point.
The shape of the plots agrees well with the theoretical expectations (see [11], Fig. 2). With decreasing pH, the slope of the linear segment at V < Ve decreases, being increasingly affected by the formation of protonated chelate (CuHY− ). In contrast, the slope of the segment at V > Ve , which is null at pH 4 and 5, becomes slightly positive at pH 5, as a result of the partial reaction of the base with the excess of H2 Y2− to produce H3 Y− . The linearity of the two segments composing the titration plots was always satisfactory. The standard deviation of the linear parameters was generally <1 l for the intercept and 0.002 for the slope (which for
V < Ve changed from about 1.5 at pH 3 to nearly 2 at pH 5). Fig. 2B represents the deviations (residuals) of the experimental volumes of auxiliary titrant from the interpolated linear segments for the plot at pH 5. In titrations at pH 4 and 5, the residuals were generally <1 l and did not show any trend. At pH 3, the residuals of the first segment showed some deviation from linearity (a convexity), which however was not significantly influential on the straight-line parameters. Only at this pH a single point very near to the equivalence volume showed a systematic deviation due to nonquantitative reaction, and was omitted from least-square linearisation. The results, expressed as the titre of the EDTA solution (mean of five titrations), are summarised in Table 1. For sake of completeness, pH-stat titrations at pH 2 and 8 were also attempted. In a 0.01 M hydrochloric acid, the combined effect of slower reaction and higher buffering power prevented titrations being carried out in a reasonable time with acceptable accuracy and precision. The tedious procedure necessary to keep copper(II) dissolved at pH 8 in ammonia buffer without increasing too much the buffering power made titration at this pH rather impractical. Photometric titrations for comparison were made in 0.1 M acetate buffer at initial pH 5.0 using PAN (1-(2-pyridylazo)-2-naphthol) as the indicator at the wavelengths of the absorption peaks both of the free indicator (460 nm) and of its complex with copper (545 nm). The end point was located, according to the customary criteria [9], just after the beginning of the very sharp transmittance change. The results are reported in the last column of Table 1. The results of pH-stat titrations at pH 4 and 5 agree with their theoretical value as well as the photometric one. Only at pH 3 is a systematic error, small but significant, present. It does not depend on imperfect linearity (partial extrapolation does not change the result), nor on the nature of the buffer (similar results were obtained in phthalate buffer). The error corresponds to a consumption of EDTA by copper below the stoichiometric 1:1 ratio. It could be caused by the reaction being slower than apparent from the direct titration plot (Fig. 1); however, longer (2 min) intervals between additions did not change the result. It is also compatible with the hypothesis of appreciable formation of binuclear complexes; however, this is little probable at a low concentration of the metal
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cation and at a pH where protonated forms of the ligand prevail, and is not reported in the literature. The real cause could be some experimental artifact depending on pH, but it was not further investigated. In practice, titrations can be made at pH 3 if extreme accuracy is not required (however, the high precision obtained suggests that a “blank” correction is possible). 3.6. Zinc Titration of Zn(II) with EDTA according to traditional procedures is feasible in basic media up to pH 12, and in acidic media at pH 4–6 [12–14]. The higher buffering power required to keep zinc dissolved makes pH-stat titration at basic pH impractical. On the other hand, the specific properties of the technique prompted us to test the pH-stat titration at a more acidic pH. The investigated range was thus pH 3–6. The pH-stat titrations plots of 2.0 × 10−3 M zinc(II) (49.57 mol in approximately 25 cm3 of supporting solution) at pH between 3 and 6 are shown in Fig. 3A. The solution was buffered with 2 × 10−3 M chloroacetate at pH 3, 2 × 10−3 M acetate at pH 4 and 5, 7 × 10−3 M hexamethylene tetramine at pH 6. The response was acceptably fast at low pH, much faster at pH 4, where 15 s was sufficient for its completion after each addition. The linearity of the two segments of titration plot was satisfactory (Fig. 3B). Even at pH 3, where log KZnY is as low as 6.0 [16], only points very near to the equivalence (in Fig. 3A, a single point at 480 l) showed barely appreciable deviations from quantitativity and had to be omitted from the least-squares fitting. Formation of protonated chelate (ZnHY− ) strongly affects the slope at V < Ve at pH 3, much less at pH 4. By contrast, the effect of the reaction of the base with the excess of H2 Y2− to produce H3 Y− becomes very evident at pH 6. The results, summarised in Table 1, show that the best results are obtained at pH 4–6. At pH 3, a small but significant error, similar to that found in copper titrations at the same pH, was present. Otherwise, they agree both with the theoretical value and with that resulting from photometric titrations. These were made at pH 10.0 in ammonia buffer with Eriochrome Black T (EBT) as the indicator at 620 nm (free indicator) and 550 nm (complex with zinc) and showed
Fig. 3. (A) Titration plots for pH-stat titrations of 49.57 mol of zinc(II) in 25 ml of supporting solution at pH—(䊉): 6.00 (7 × 10−3 M hexamethylene tetramine buffer); (䉲): 5.00 (2 × 10−3 M acetate); (䊏): 4.00 (2 × 10−3 M acetate); (䉱): 3.00 (2 × 10−3 M chloroacetate). Other experimental parameters as in Fig. 2. (B) Residuals of the plot at pH 6.
a sudden slope change, which was taken as the end point. 3.7. Magnesium In discussing the theory of complexometric pH-stat titration [11], magnesium was taken as an example of a cation giving a moderately stable chelate, with a titration pH range restricted to basic values. It is usu ally titrated at pH 10, where log KMgY is 8.2. By contrast, pH-stat titrations are expected to be still feasible at significantly lower pH values, where the stability of the EDTA chelate is so small as to prevent traditional titrations, particularly with a visual end point. A wide pH range (pH 6–10) was explored in order to investigate the experimental feasibility limits with not strictly quantitative reactions. In Fig. 4A, titrations of
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Fig. 4. (A) Titration plots for pH-stat titrations of 50.78 mol of magnesium(II) in 20 ml of supporting solution (0.1 M sodium perchlorate) at pH—(䊉): 10.00 (2 × 10−3 M ammonia buffer); (䉱): 9.00 (2 × 10−3 M ammonia); (䊏): 8.00 (5 × 10−3 M triethanolamine); (䉲): 7.00 (5×10−3 M triethanolamine); (䉬): 6.00 (5×10−3 M hexamethylene tetramine). 48 l of 0.1 M EDTA were added at intervals of 1 min (at pH 6 and 7) or 30 s (at higher pH). Other experimental parameters as in Fig. 2. (B) Residuals of the plot at pH 8.
2.5 × 10−3 M magnesium(II) (50.78 mol in approximately 20 cm3 of supporting solution) are represented. The buffer was 5 × 10−3 M hexamethylene tetramine at pH 6, 5 × 10−3 M triethanolamine at pH 7 and 8, 2 × 10−3 M ammonia at pH 9 and 10. The reaction was quantitative starting from pH 8 (log KMgY = 6.4), where even the experimental points nearest to equivalence did not show appreciable deviations from the linear trend (Fig. 4B). At pH 7 (log KMgY = 5.3), only the points lying at about (1.0± 0.1)Ve deviated significantly and had to be neglected in the linear fitting. The slope of the linear segment corresponding to an excess of titrand cation was found to be practically independent of pH, showing that mag-
nesium does not significantly take part in side reactions involving proton exchange [11] in the experimental pH range. Beyond the equivalence point, the slope increases steadily with increasing pH. At pH 10, the slope change at the equivalence is only moderate, because the excess of H2 Y2− reacting with the base produces an appreciable fraction of H4 Y together with H3 Y2− . At pH 6 (log KMgY = 3.9), the linear range of the two segments was too restricted to allow reliable interpolation of the equivalence volume. The photometric titrations were made at pH 10.0 in ammonia buffer with EBT as the indicator at 620 nm (free indicator) and 560 nm (complex with magnesium). The end point was taken at the point of maximum slope of the sigmoidal titration curve. The results of both methods (Table 1) agree with the theoretical value. However, the photometric titrations show a larger uncertainty. The experiments confirm that, in agreement with theoretical expectations [11], pH-stat titrations of magnesium have their optimum operating range around pH 8–9. At pH 10, the optimum value of traditional titrations, the slope change begins to be critically small. By contrast, a lower pH can be used, if necessary [10], although not much under 7. 3.8. Calcium The chelatometric determination of calcium is usually performed at pH 9–12 in ammonia buffer. In visual titrations, the best precision is usually obtained at pH 9–10 by using magnesium as auxiliary cation and EBT as the indicator. The plots in Fig. 5 represent pH-stat titrations of 51.55 mol of calcium in 25 cm3 of supporting solution containing 5 × 10−3 M hexamethylene tetramine (pH 6), 1.0 × 10−2 M triethanolamine (pH 7 and 8), or 2 × 10−3 M ammonia (pH 9 and 10). At pH 6, the points within about ±5% of the equivalence volume showed significant deviations due to nonquantitative reaction and were omitted from the calculations. The results are summarised in Table 1. It is seen that for calcium, like magnesium, the higher limit of the available pH range is conditioned by the acid–base properties of the chelating agent. By contrast, the higher stability of the chelate of calcium with respect to magnesium allows a lower pH to be used. Fig. 5A and Table 1 show that pH 6 (with
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slope segment of the titration plot preceding the equivalence depends on proton-exchange side reactions in which the titrated cation is involved. If only formation of the protonated chelate occurs as such a side reaction, its stability constant can be determined from the slope of that segment, expressed as the mole ratio R = n(NaOH)/n(EDTA) [11]: KMHY =
Fig. 5. (A) Titration plots for pH-stat titrations of 51.55 mol of calcium(II) in 25 ml of supporting solution (0.1 M sodium perchlorate) at pH—(䊉): 10.00 (2 × 10−3 M ammonia buffer); (䉱): 9.00 (5 × 10−3 M ammonia); (䊏): 8.00 (1.0 × 10−2 M triethanolamine); (䉲): 7.00 (1.0 × 10−2 M triethanolamine); (䉬): 6.00 (5 × 10−3 M hexamethylene tetramine). Aliquots of 48 l of 0.1 M EDTA were added at intervals of 1 min. Other experimental parameters as in Fig. 2. (B) Residuals of the plot at pH 10. log KCaY = 5.9) is still available for sufficiently precise titrations. Independent of pH, pH-stat titrations of calcium seem slightly more precise than photometric ones (last column of Table 1). These were made at pH 10.0 in 0.1 M ammonia buffer with EBT as the indicator at 620 or 550 nm; the end point was obtained by extrapolating the sloping branch of the absorbance or transmittance.
3.9. The determination of equilibrium constants of protonated complexes It has been theoretically deduced [11] and experimentally confirmed (Sections 3.5 and 3.6) that the
2−R (R − 1)[H+ ]
(2)
For determining accurately KMHY , accurate measurement of the equilibrium concentration of the hydronium ion and careful control of the ionic strength are essential. An internal calibration of the electrochemical measuring cell in the supporting solution should be made before each titration [7,8]. In our experiments, the cell was calibrated externally with usual pH standards, and only the repeatability of the operating value of pH during a single experiment was carefully controlled, the exact value being of low relevance for titration accuracy (see Section 3.1). Therefore, their results can be used only for a mere preliminary check of the theoretical expectations. The titrations most suitable for this purpose are those of copper at pH 3.00, where the side-reaction effect is larger. R was 1.4651 ± 0.0007 (n = 5), yielding KCuHY = 1.150 × 10−3 , log KCuHY = 3.061. This value compares well with the one given in the literature, log KCuHY = 3.0 at 25 ◦ C, µ = 0.1 [16,18]. The very small standard deviation of R shows that KMHY can be determined with precision possibly much better than with traditional methods and with accuracy limited only by that of the pH measurement. Even the value R = 1.8922±0.0006 obtained at pH 4.00, yielding KCuHY = 1.208 × 10−3 , log KCuHY = 3.082, is acceptable, particularly considering that the effect on R amounts to only 10% of the limit value 2.
4. Conclusions The experiments here described fulfil satisfactorily the theoretical expectations [11] about the analytical suitability of pH-stat chelometric titrations as well as about the shape of the titration plots. Accuracy and precision are very good. The experimental parameters are easily adjusted to fit the properties of the titration system. The duration of a single titration is acceptable.
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In comparison, photometric titrations can reach comparable precision only at the cost of longer duration; indeed, in our experiments, they required smaller additions in the proximity of the equivalence both when the end point was interpolated (with sigmoidal titration plots) or extrapolated (to identify a discontinuity). The most serious limit for practical applications of pH-stat titrations with EDTA is the requirement that the titrated solution has a moderate buffering power. The moderately basic maximum operating pH (not much higher than 10) is largely counterbalanced by the possibility of exploiting reactions that are not strictly quantitative, i.e. with the smaller conditional stability constants of the chelate complex prevailing at lower pH. A clear advantage of the pH-stat procedure with regularly timed discontinuous addition of primary titrant is that the direct titration plot of the auxiliary titrant volume against time generally gives immediate evidence of slowly occurring reaction and of reaching equilibrium. Such a direct control is difficult or impossible, for instance, with indicated photometric titrations. Even the suitability of pH-stat procedures for the determination of some stability constants has been confirmed. Both applications seem to deserve larger consideration in the analytical and research laboratory. Acknowledgements The work was carried out with the financial support of CNR. The co-operation of Alberto Doimo in the
preparation of the computer program for timed discrete additions is gratefully acknowledged. References [1] C.F. Jacobsen, J. Léonis, Compt. Rend. Trav. Lab. Carlsberg sér. Chim. 27 (1951) 333. [2] C.F. Jacobsen, J. Léonis, K. Linderstrøm-Lang, M. Ottesen, Methods Biochem. Anal. 4 (1957) 171. [3] G.G. Guilbault, Enzymatic Methods of Analysis, Pergamon Press, Oxford, 1970. [4] M. Kopanica, V. Stara, in: G. Svehla (Ed.), Wilson and Wilson’s Comprehensive Analytical Chemistry, vol. XVIII, Elsevier, Amsterdam, 1983, p. 124, p. 174. [5] S. Pantel, Anal. Chim. Acta 199 (1987) 1. [6] H.V. Malmstad, E.H. Piepmeier, Anal. Chem. 37 (1965) 34. [7] C. Maccà, L. Soldà, Electroanalysis 14 (2002) 57. [8] C. Maccà, L. Soldà, Electroanalysis 14 (2002) 63. [9] K. Mooibroek, Phototitrations: A Guide to Methods, Mettler Instrumente A.G., Greifensee, CH, 1978. [10] F. Di Gregorio, R. Sisto, J. Dairy Res. 47 (1980) 417–419. [11] C. Maccà, Anal. Chim. Acta 456 (2002) 313. [12] G. Schwarzenbach, H. Flasckha, Complexometric Titrations, 2nd ed., Methuen, London, 1969. [13] R. Pribil, Applied Complexometry, Pergamon Press, Oxford, 1982. [14] T.S. West, Complexometry with EDTA and Related Reagents, BDH, Poole, 1969. [15] Anonymous, Complexometric Assay Methods with Titriplex, Merk, Darmstadt. [16] A. Ringbom, Complexation in Analytical Chemistry, Interscience, New York, 1963. [17] C. Maccà, Analyst 108 (1983) 395. [18] A.E. Martell, R.M. Smith, Critical stability constants, in: Amino Acids, vol. 1, Plenum Press, New York, 1974.
pH-stat techniques in titrimetric analysis IV. pH-stat monitoring of chelatometric titrations Carlo Maccà a,∗ , Lidia Soldà a , Mirella Zancato b a
Department of Inorganic, Metallorganic and Analytical Chemistry, University of Padua, Via Marzolo 1, I-35131 Padova, Italy b Department of Pharmaceutical Sciences, University of Padua, Via Marzolo 5, I-35131 Padova, Italy Received 11 April 2002; accepted 18 July 2002
Abstract The theory of pH-stat chelatometric titrations recently developed [Anal. Chim. Acta 456 (2002) 313] is experimentally substantiated here. The titrations of four representative doubly charged cations having different behaviour (copper, zinc, calcium, magnesium) are taken as examples. Copper is titratable between pH 3 and 5, zinc between 3 and 6, calcium between 6 and 10, and magnesium between 7 and 10. The shapes of the titration plots agree well with the theory, accounting for simultaneous equilibria involving proton exchange. The technique yields accurate and precise results, which compare favourably with those of other instrumental techniques, in particular photometric titrations. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Titrimetric analysis; Chelatometric titrations; pH-stat titrations; Calcium(II); Copper(II); Magnesium(II); Zinc(II)
1. Introduction Automatic pH-metric titrators frequently include the pH-stat or “Stat” operating function. In this mode, the titrator measures the pH of a test solution and simultaneously counteracts any spontaneous or induced variation (either an increase or a decrease) of this quantity with respect to a pre-selected operating control value by adding the appropriate amount of a suitable reagent (a strong acid or a strong base, respectively). The pH-stat technique [1] is widely used in the chemical and biochemical laboratory when it is necessary to keep under strict control that most important experimental parameter for instance in the course of organic reactions or of biological processes, and in ∗ Corresponding author. Tel.: +39-0498275205; fax: +39-0498275161. E-mail address: [email protected] (C. Macc`a).
studies of reaction rates or of enzyme kinetics [2,3]. Moreover, the measurement of the reactant’s delivery rate provides a direct means for determining reaction rates and performing kinetic analyses [4,5]. In contrast, the use of the pH-stat technique for monitoring volumetric titrations has been very seldom investigated, and is quite unknown in current practice in the analytical laboratory. This paper is part of a series intended to study in more depth the theoretical and practical aspects of this technique in volumetric analysis. The theory and applications of pH-stat monitoring of acid–base titrations [6], respectively, are the object of two recent papers [7,8]. In chelatometric titrations, the use of pH-stat is currently suggested for the mere purpose of keeping the pH at an optimal value, when concentrated buffers could alter the reaction course [9]. At our knowledge, only a single procedure using the pH-stat technique for detecting the titration end point (determination of calcium and magnesium in
0003-2670/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 3 - 2 6 7 0 ( 0 2 ) 0 0 6 9 1 - 8
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skim milk) has so far been described [10]. In the third paper of this series [11], the fundamentals of pH-stat chelatometric titrations have been developed, and the criteria for optimising the experimental conditions have been discussed. Accordingly, such titrations are expected to attain good accuracy and high precision. The purpose of the present work is to substantiate those favourable anticipations by implementing experimental procedures for some representative determinations.
electrode with encapsulated Ag/AgCl reference electrode in 3 M KCl and sleeve junction (Ingold, Urdorf, Switzerland, type 405.60.88.E) was measured with a resolution of 0.1 mV or 0.01 pH. The Stat program allowed choosing either mV or pH as the controlled operational parameter. The measured solution was contained in a 20– 90 cm3 jacketed cell Metrohm (Herisau, Switzerland) type 6.1418.220 and stirred with a PTFE-coated magnetic bar. It was thermostated at 25.0 ± 0.1 ◦ C and fluxed with carbon dioxide-free nitrogen.
2. Experimental
2.1.2. Photometric titrations Photometric titrations were monitored with a Metrohm 662 Photometer equipped with a light-guide measuring cell. The photometric probe could be accommodated in the titration cell through the cover. The stepless wavelength setting is 400–700 nm with a 10 nm resolution. The analogue output is 0–1 V with a 1 mV resolution. The MicroTT 2050 programmable potentiometric titrator was used for adding the titrant EDTA solution and for recording the titration plot by taking the voltage signal from the photometer’s output.
2.1. Apparatus 2.1.1. pH-stat titrations The apparatus required must allow the simultaneous addition of two reactants: the primary titrant (the chelating agent), by stepwise addition of equal, small volume increments, or by continuous addition at a constant volume rate, and the auxiliary titrant (a strong base) under pH-stat control. Single instruments automatically performing all the required operations are not currently available. However, a partly automatic apparatus can easily be assembled by combining a potentiometric (pH-metric) titrator having the pH-stat function with a system for controlled delivery of the primary titrant. The experiments with stepwise delivery of primary titrant here reported were performed with a syringe burette Microbur 2030 (Crison, Barcelona) fitted with a 1 cm3 syringe 1001 TLL (Hamilton, Bonaduz, Switzerland). The resolution of delivered volumes is, 4×10−4 and 1×10−3 cm3 , respectively; accuracy was determined to be better than resolution. The burette was driven by a PC through the proprietary “Bureta” program, modified to repeat additions of constant volume aliquots at fixed time intervals. Experiments with continuous delivery of the primary titrant were performed with the apparatus described in [8]. For delivering the auxiliary titrant under pH-stat control, a microprocessor-controlled programmable potentiometric titrator Crison MicroTT 2050 was used. It was equipped with a Crison Microbur 2030 syringe burette fitted with a 2.5 cm3 1002 TLL syringe (Hamilton) and was connected to an Epson LX-400 printer. The signal from a combination glass
2.2. Reagents All chemicals of analytical grade or better were used as received. The 0.1 or 0.01 M standard solution of metal cations were prepared from high purity metals (Cu), oxides (MgO, ZnO) or salts (CaCO3 ) with the usual procedures [12–15]. The 0.1 M solutions of primary titrant were prepared by weighing analytical grade disodium ethylendinitrilotetraacetate (Na2 H2 Y, EDTA) after desiccation at 80 ◦ C. A 0.1000 M solution of sodium hydroxide low in carbonate (sodium carbonate <0.2%) BDH cat. 191503E was used as the auxiliary titrant. All solutions were prepared with ultrapure water produced with a Milli-Q Plus apparatus (Millipore, Bedford, MA). 2.3. Procedure 2.3.1. pH-stat titrations The measuring electrochemical cell was calibrated separately with pH standards at 4.00 and 7.00. The
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titration cell was filled with 20 cm3 of 0.1 M sodium perchlorate solution containing a suitable buffer at low concentration (generally (1–2) × 10−3 M) and a volume of standard solution of the metal cation containing approximately 50 mol of cation was added. A preliminary adjustment of the solution pH to a value slightly more acidic than the operating value was made either by addition of some drops of diluted acid or (if the standard solution of cation was too acidic) by a preliminary end-point titration with strong base. The exact operating pH value was reached by temporarily activating the Stat function. Finally, the Stat operation and the record of the titration plot were simultaneously started and, after a known time delay (30 or 60 s which allowed to control the stability of pH), the primary titrant addition was begun. Constant volume (24–48 l) stepwise additions at fixed time intervals (30 s–2 min), or continuous additions (minimum rate 0.05 cm3 min−1 ) were carried on until the added primary titrant was 1.5–2 times the equivalence volume (usually corresponding to 0.5 cm3 ). The numerical titration report (displaying time, measured pH or mV, auxiliary titrant volume, single volume increments, temperature) was printed during operation at 10 s intervals. The graphical report (auxiliary titrant volume versus time) was printed after ending the titration. The true titration plot was recalculated by using as the abscissa the primary titrant volume VY and as the ordinate the volume of auxiliary titrant VOH required to reach stationary conditions (pH constant in time at the operating value within the resolution of the pH-stat system, i.e. 0.01 units). The equivalence volume of the primary titrant, Ve , was determined by least-square analysis as the abscissa of the intersection between two straight-line segments. Data was treated with SigmaPlot scientific graphing software (Jandel Scientific, Erkrath, Germany). 2.3.2. Photometric titrations Photometric titrations were performed on a measured volume of standard solution of the analyte cation diluted with 25 ml of buffer at the required pH and containing a suitable indicator. The programmable titrator was operated in the “inflection point” titration mode with constant volume additions. This mode allowed printing and plotting the complete titration record. The input signal was taken from the photometric probe, op-
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erated either in the absorbance or transmittance mode. Very small (10 l) additions were made, and a strict stability criterion (signal drifting less than 1 mV in 10 s) was chosen, in order to reach the best precision and accuracy even when the signal change at the end point was abrupt or the complexation reaction was slow. 3. Results and discussion 3.1. The pH-stat titration plot and the choice of operating pH In pH-stat chelatometric titrations of metal cations, the addition of primary titrant (EDTA or another suitable chelating agent) is accompanied by the addition of the auxiliary titrant (a strong base solution) at a rate suitable to maintain the pH constant at a pre-selected value by neutralising the acidity delivered by EDTA. The titration plot shows the added volume of strong base, VOH , against the volume of EDTA, VY . When the chelation of the titrand cation is complete, the delivery of acidity by EDTA does stop or change rate, depending on the operating pH. Therefore, in the correspondence of the equivalence point the titration plot’s slope also changes. If the conditions are suitable, it is expected that the change of slope is easily appreciable. The dependence of the titration plot’s shape on the nature of the reactants and on pH has been discussed in detail [11]. Two main aspects of the titration plot do condition the feasibility of a titration: the extent of slope change and its sharpness. The extent of slope change depends on the difference between the net number of protons delivered by EDTA before and after the equivalence point. Its sharpness, in turn, depends on the quantitativity of the chelation reaction. Both are strongly influenced by pH [11]. According to the primary reaction: Mm+ + H2 Y2− → MYm−4 + 2H+
(1)
the slope of the titration plot before the equivalence point ideally corresponds to 2 mol of strong base per mole of EDTA. However, competing reactions involving proton exchange, whose extent depends on pH, can decrease this ratio [11]. The slope after the equivalence point, ideally null after the completion of
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reaction (1), is dictated by the degree of protonation of the unreacted ligand at the operating pH. At pH increasing over about 5, the prevailing form is HY3− ; at still higher pH it is Y4− . Therefore, a finite and increasing amount of base is consumed to deprotonate the excess titrant, H2 Y2− ; the relative amount gradually approaches the maximum value of 2 mol of auxiliary titrant per mole of primary titrant in excess. In consequence, the change of slope at the equivalence point vanishes at a pH is larger than about 11.5 [11]. In turn, the quantitativity of the chelation reaction depends on the conditional stability constant of the chelate complex KMY in the reaction medium. This quantity is heavily conditioned by the dependence of the degree of protonation of EDTA anion on pH [16]. Competing ligands decreasing the free-cation fraction of the unreacted metal may also have an appreciable effect. The overall trend is towards a decrease of KMY on decreasing pH. As the reaction becomes less and less quantitative, the slope change occurs in a larger and larger interval around the equivalence point, thus impairing the sharpness of the equivalence point. For every analyte cation, a compromise value of pH for the two contrasting effects must be found. This optimum value can be accurately forecast if the stability constant of the chelate complex and the equilibrium constants of the competing reactions are known with sufficient accuracy [11]. It must be noted that pH does not need to be known with the greatest accuracy, as long as it lies in the wanted range and is kept rigorously constant during each single titration. For quantitative determinations, calibration of the measuring cell with usual pH standards is quite acceptable. 3.2. Choice of the instrumental and other experimental parameters The experimental parameters to be set at the beginning of each titration are either of chemical or of instrumental nature. The chemical parameters are operating pH and buffer power of the supporting solution. The instrumental ones are addition rate, equilibration time and control band [8]. The choice of pH is dictated by the criteria discussed in Section 3.1. The buffering power of the measured solution regulates the sensitivity of the pH-static response, i.e. the deviation of pH from the operat-
ing value caused by unbalanced titrants ratio. In the absence of any buffer, EDTA addition, particularly when discontinuous, could cause sudden and large pH changes, hindering the pH-static control. A too high buffering power would instead cover the titrant’s action. Both effects cause large random errors [8]. With synthetic samples, optimum conditions are realised by adding a suitable buffer pair. The approach to the choice of the instrumental parameters is similar to the one discussed in detail for acid–base pH-stat titrations [8]; in the present instance, however, it is much more dependent on the nature of the chemical system involved. Indeed, an important peculiarity of chelation reactions is that they are more or less appreciably slow, at variance with neutralisation, which is generally fast. When the reaction is fast, the practical ratedetermining stage can be, alternatively, the mixing of reactants, the electrode response, or the ability of the pH-stat device to keep pace with the acidity change. This last is mostly conditioned by the instrumental parameters set. By acid–base titrations, it was quite generally possible to operate with continuous, although moderately slow, addition of titrand (which in acid–base titrations operationally takes the place of the primary titrant). In contrast, preliminary experiments did show that complexometric reactions with continuous additions, although yielding apparently satisfactory linear segmented plots, were frequently affected by appreciable systematic errors. These were removed by operating with constant additions at fixed time intervals. With this procedure, the plot of auxiliary titrant volume against time together with the numerical record of both quantities and pH (see Section 2.3) allowed to verify point by point the time necessary to reach equilibrium conditions (Fig. 1). The size of the added aliquots (1/20 to 1/10 of the equivalence volume), and thus their number, was chosen to satisfy the somewhat contrasting requirement of efficient pH-stat control, good least-squares evaluation of data and reasonable total titration time. The time between two subsequent additions, set after the results of a preliminary titration, was just long enough to allow the reaction to reach equilibrium after each addition (Fig. 1). The size of additions also has a role in dictating the instrumental parameters specific of the pH-stat operational mode, i.e. equilibration time and control band
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Fig. 1A shows a typical graphical titration record (volume of auxiliary titrant against time) for an appreciably slow reaction (copper(II) at pH 3). Fig. 1B shows the corresponding pattern of pH as recorded in the numerical titration report (see Section 2.3). Stepwise additions of EDTA were made at 1 min intervals; pH was measured at 2 s intervals and recorded every 10 s. The patterns of both plots of pH and NaOH volume against time show that 30–45 s were required to reach stationary conditions after each addition of primary titrant. After the equivalence point, the measured solution is no any more under pH-stat control, because the excess EDTA behaves as a weak base (it hydrolyses by about 30%) and slowly increases the solution pH [11]. 3.3. The auxiliary titrant
Fig. 1. (A) Recorded plot of the volume of auxiliary titrant (0.1000 M NaOH) against time for a pH-stat titration at pH 3.00 of 48.64 mol of copper(II) in approximately 20 ml of supporting solution (0.1 M sodium perchlorate containing 2 × 10−3 M formate buffer). Aliquots of 48 l of 0.1 M of EDTA were added at 1 min intervals. Equilibration time 2 s; control band 2 pH units. (B) The corresponding plot of measured pH against time.
[8]. The equilibration time is the time after which in the Stat mode the meter is made to accept the measured signal as stable and ideally corresponding to the equilibrium emf of the measuring cell when stationary conditions are reached. Given the fast response of the physical measuring system, an equilibration time of 2 s was sufficient. The choice of the control band [8] is possibly less critical than in acid–base titrations, because the reaction and, consequently, the delivery of acidity, are moderately slow and do not require fast compensation of large pH changes if the size of added primary titrant aliquots is small. The purposely added pH buffer (see above) helped to damp pH from swinging.
For determining the metal cation contained in the sample solution, it is not necessary to know accurately the titre of the auxiliary titrant solution. Indeed, the titre of the strong base only decides on the experimental slopes (cm3 /cm3 ) of the two segments composing the titration plot without altering the abscissa of their intersection, i.e. the equivalence volume of the primary titrant. In principle, if the reacting strength of the secondary titrant is accurately determined [7,8] and the real path of the overall reaction (cation+chelating agent+base) with its exact stoichiometry [11] is known, the amount of analyte can also be determined from the end-point volume of the auxiliary titrant. Much more interesting is the possibility of determining the stoichiometry of the overall titration and the stability constants of mixed complexes from the mole ratio R of strong base to chelating agent after measuring the slope of the linear segment preceding the equivalence point [11]. For this purpose, the reacting strength of the strong base must be known with the best possible accuracy. It is known that strong base solutions are generally contaminated by carbonate, and in consequence their reacting strength depends on the end-point pH of the individual titration in which they are used [8]. The effective titre can be conveniently determined by pH-stat titration of a primary standard acid [7,8] at the intended operating pH of the pH-stat chelatometric titration. By this means, the 0.1000 M solution of sodium hydroxide low in carbonate used in the
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experiments described here was seen to increase only negligibly its contamination as an effect of the necessary manipulations. In preliminary experiments, solutions at the usual level of carbonate contamination (about 2%) were used without appreciable inconvenience. 3.4. Selected titration systems When discussing the theory of pH-stat complexometric titrations [11], summarised in Section 3.1, we took those of copper(II) and magnesium(II) with EDTA as examples representative of the main features of the technique. Owing to their diverse properties, these systems are also very suitable for introducing the experimental application of the pH-stat technique, while confirming the theoretical deductions. In addition, we report here the results of investigations on two other cations of great analytical relevance, calcium(II) and zinc(II). For comparison with other well-established techniques, we have considered only volumetric methods based on chelatometric reactions. Indeed, the most common instrumental determination technique of metals in solution, atomic absorption spectrometry, measures concentration in a much lower range and with limited precision, with the inconvenience of requiring a specific lamp for every element. Direct potentiometry also requires a specific electrode for each determinand cation and has only moderate precision. When higher precision determinations are required, the choice is usually chelatometric titration (even in preference to gravimetry, which is too time consuming). Visual titrations are performed after adding a suitable indicator. The procedures can be automated and their precision improved by using photometric titrators. Therefore, in order to state whether the new technique offers any advantage in an automated analytical laboratory, we have compared pH-stat titrations of each investigated metal cation with corresponding indicated photometric titrations. However, it must be stressed that a photometric titration can hardly be considered an accurate reference method. Indeed, the shape of the titration curve (let it be absorbance A, or transmittance T, against titrant volume V), and by consequence the procedure for locating the equivalence volume, are strongly dependent on the values of the conditional stability constants of the com-
plexes involved (cation-EDTA and cation-indicator). In practice, the location of the equivalence point may become rather subjective, although less than in visual titrations. With computerised photometric titrators, the accuracy depends on the algorithm chosen. An alternative automatable technique, the potentiometric titration, is convenient only if an electrode selective for the analyte cation is available (procedures involving the use of electrodes responding to an auxiliary cation, e.g. mercury(II), are not of current use in the analytical laboratory). Even in this instance, it can suffer some limitation due to the relatively high lower response limit of the sensor. All titrations were performed using primary standard solutions of cations. In order to favour a direct comparison among all series of titrations, the results were expressed by calculating the titre CY of the EDTA solution (Table 1). 3.5. Copper The chelatometric titration of copper(II) can be performed either in acidic solution at pH not exceeding 5, above which precipitation occurs, or at pH near to 8 [12,13]. We have tested the determination of Cu(II) in the acid pH range from pH 5 to 3, where the chelate is still strong enough (log KCuY ≥ 8.3) [16] to form quantitatively even in the proximity of the equivalence point and assign the titration a good intrinsic [17] precision. Typical pH-stat titrations plots of 2.4×10−3 M copper(II) (48.64 mol in approximately 20 cm3 of supporting solution) at various pH values are represented in Fig. 2A. The buffers were, respectively, 2 × 10−3 M chloroacetate at pH 3 and 2 × 10−3 M acetate at pH 4 and 5. It is known that the chelation of Cu(II) is moderately slow. The speed increases with increasing pH. At pH 3, reaching stationary conditions required at least 45 s as shown in Fig. 1; with increasing pH, 30–15 s became sufficient. With additions of primary titrant aliquots corresponding to approximately 1/10 of the equivalence volume (48 l), titrations lasted not more than 12–15 min and yielded satisfactory results. Some experiments performed by halving the aliquot volume (24 l) yielded identical results, with an only moderate improvement in the statistical evaluation of the linear parameters and the drawback of longer duration.
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Fig. 2. (A) Titration plots of volume of auxiliary titrant (0.1000 M NaOH) against volume of primary titrant (0.1002 M EDTA) for pH-stat titrations of 48.64 mol of copper(II) in approximately 20 ml of supporting solution at pH—(䊉): 5.00 (2×10−3 M acetate buffer); (䉱): 4.00 (2 × 10−3 M acetate); (䊏): 3.00 (2 × 10−3 M chloroacetate). Aliquots of 48 l of 0.1 M EDTA were added at intervals of 1 min (at pH 3) or 30 s (at pH ≥ 4). Equilibration time 2 s; control band 2 pH units. (B) Deviations (residuals) of the experimental auxiliary titrant volumes from the interpolated linear segments for the titration at pH 5. Empty symbols after the equivalence point.
The shape of the plots agrees well with the theoretical expectations (see [11], Fig. 2). With decreasing pH, the slope of the linear segment at V < Ve decreases, being increasingly affected by the formation of protonated chelate (CuHY− ). In contrast, the slope of the segment at V > Ve , which is null at pH 4 and 5, becomes slightly positive at pH 5, as a result of the partial reaction of the base with the excess of H2 Y2− to produce H3 Y− . The linearity of the two segments composing the titration plots was always satisfactory. The standard deviation of the linear parameters was generally <1 l for the intercept and 0.002 for the slope (which for
V < Ve changed from about 1.5 at pH 3 to nearly 2 at pH 5). Fig. 2B represents the deviations (residuals) of the experimental volumes of auxiliary titrant from the interpolated linear segments for the plot at pH 5. In titrations at pH 4 and 5, the residuals were generally <1 l and did not show any trend. At pH 3, the residuals of the first segment showed some deviation from linearity (a convexity), which however was not significantly influential on the straight-line parameters. Only at this pH a single point very near to the equivalence volume showed a systematic deviation due to nonquantitative reaction, and was omitted from least-square linearisation. The results, expressed as the titre of the EDTA solution (mean of five titrations), are summarised in Table 1. For sake of completeness, pH-stat titrations at pH 2 and 8 were also attempted. In a 0.01 M hydrochloric acid, the combined effect of slower reaction and higher buffering power prevented titrations being carried out in a reasonable time with acceptable accuracy and precision. The tedious procedure necessary to keep copper(II) dissolved at pH 8 in ammonia buffer without increasing too much the buffering power made titration at this pH rather impractical. Photometric titrations for comparison were made in 0.1 M acetate buffer at initial pH 5.0 using PAN (1-(2-pyridylazo)-2-naphthol) as the indicator at the wavelengths of the absorption peaks both of the free indicator (460 nm) and of its complex with copper (545 nm). The end point was located, according to the customary criteria [9], just after the beginning of the very sharp transmittance change. The results are reported in the last column of Table 1. The results of pH-stat titrations at pH 4 and 5 agree with their theoretical value as well as the photometric one. Only at pH 3 is a systematic error, small but significant, present. It does not depend on imperfect linearity (partial extrapolation does not change the result), nor on the nature of the buffer (similar results were obtained in phthalate buffer). The error corresponds to a consumption of EDTA by copper below the stoichiometric 1:1 ratio. It could be caused by the reaction being slower than apparent from the direct titration plot (Fig. 1); however, longer (2 min) intervals between additions did not change the result. It is also compatible with the hypothesis of appreciable formation of binuclear complexes; however, this is little probable at a low concentration of the metal
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cation and at a pH where protonated forms of the ligand prevail, and is not reported in the literature. The real cause could be some experimental artifact depending on pH, but it was not further investigated. In practice, titrations can be made at pH 3 if extreme accuracy is not required (however, the high precision obtained suggests that a “blank” correction is possible). 3.6. Zinc Titration of Zn(II) with EDTA according to traditional procedures is feasible in basic media up to pH 12, and in acidic media at pH 4–6 [12–14]. The higher buffering power required to keep zinc dissolved makes pH-stat titration at basic pH impractical. On the other hand, the specific properties of the technique prompted us to test the pH-stat titration at a more acidic pH. The investigated range was thus pH 3–6. The pH-stat titrations plots of 2.0 × 10−3 M zinc(II) (49.57 mol in approximately 25 cm3 of supporting solution) at pH between 3 and 6 are shown in Fig. 3A. The solution was buffered with 2 × 10−3 M chloroacetate at pH 3, 2 × 10−3 M acetate at pH 4 and 5, 7 × 10−3 M hexamethylene tetramine at pH 6. The response was acceptably fast at low pH, much faster at pH 4, where 15 s was sufficient for its completion after each addition. The linearity of the two segments of titration plot was satisfactory (Fig. 3B). Even at pH 3, where log KZnY is as low as 6.0 [16], only points very near to the equivalence (in Fig. 3A, a single point at 480 l) showed barely appreciable deviations from quantitativity and had to be omitted from the least-squares fitting. Formation of protonated chelate (ZnHY− ) strongly affects the slope at V < Ve at pH 3, much less at pH 4. By contrast, the effect of the reaction of the base with the excess of H2 Y2− to produce H3 Y− becomes very evident at pH 6. The results, summarised in Table 1, show that the best results are obtained at pH 4–6. At pH 3, a small but significant error, similar to that found in copper titrations at the same pH, was present. Otherwise, they agree both with the theoretical value and with that resulting from photometric titrations. These were made at pH 10.0 in ammonia buffer with Eriochrome Black T (EBT) as the indicator at 620 nm (free indicator) and 550 nm (complex with zinc) and showed
Fig. 3. (A) Titration plots for pH-stat titrations of 49.57 mol of zinc(II) in 25 ml of supporting solution at pH—(䊉): 6.00 (7 × 10−3 M hexamethylene tetramine buffer); (䉲): 5.00 (2 × 10−3 M acetate); (䊏): 4.00 (2 × 10−3 M acetate); (䉱): 3.00 (2 × 10−3 M chloroacetate). Other experimental parameters as in Fig. 2. (B) Residuals of the plot at pH 6.
a sudden slope change, which was taken as the end point. 3.7. Magnesium In discussing the theory of complexometric pH-stat titration [11], magnesium was taken as an example of a cation giving a moderately stable chelate, with a titration pH range restricted to basic values. It is usu ally titrated at pH 10, where log KMgY is 8.2. By contrast, pH-stat titrations are expected to be still feasible at significantly lower pH values, where the stability of the EDTA chelate is so small as to prevent traditional titrations, particularly with a visual end point. A wide pH range (pH 6–10) was explored in order to investigate the experimental feasibility limits with not strictly quantitative reactions. In Fig. 4A, titrations of
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Fig. 4. (A) Titration plots for pH-stat titrations of 50.78 mol of magnesium(II) in 20 ml of supporting solution (0.1 M sodium perchlorate) at pH—(䊉): 10.00 (2 × 10−3 M ammonia buffer); (䉱): 9.00 (2 × 10−3 M ammonia); (䊏): 8.00 (5 × 10−3 M triethanolamine); (䉲): 7.00 (5×10−3 M triethanolamine); (䉬): 6.00 (5×10−3 M hexamethylene tetramine). 48 l of 0.1 M EDTA were added at intervals of 1 min (at pH 6 and 7) or 30 s (at higher pH). Other experimental parameters as in Fig. 2. (B) Residuals of the plot at pH 8.
2.5 × 10−3 M magnesium(II) (50.78 mol in approximately 20 cm3 of supporting solution) are represented. The buffer was 5 × 10−3 M hexamethylene tetramine at pH 6, 5 × 10−3 M triethanolamine at pH 7 and 8, 2 × 10−3 M ammonia at pH 9 and 10. The reaction was quantitative starting from pH 8 (log KMgY = 6.4), where even the experimental points nearest to equivalence did not show appreciable deviations from the linear trend (Fig. 4B). At pH 7 (log KMgY = 5.3), only the points lying at about (1.0± 0.1)Ve deviated significantly and had to be neglected in the linear fitting. The slope of the linear segment corresponding to an excess of titrand cation was found to be practically independent of pH, showing that mag-
nesium does not significantly take part in side reactions involving proton exchange [11] in the experimental pH range. Beyond the equivalence point, the slope increases steadily with increasing pH. At pH 10, the slope change at the equivalence is only moderate, because the excess of H2 Y2− reacting with the base produces an appreciable fraction of H4 Y together with H3 Y2− . At pH 6 (log KMgY = 3.9), the linear range of the two segments was too restricted to allow reliable interpolation of the equivalence volume. The photometric titrations were made at pH 10.0 in ammonia buffer with EBT as the indicator at 620 nm (free indicator) and 560 nm (complex with magnesium). The end point was taken at the point of maximum slope of the sigmoidal titration curve. The results of both methods (Table 1) agree with the theoretical value. However, the photometric titrations show a larger uncertainty. The experiments confirm that, in agreement with theoretical expectations [11], pH-stat titrations of magnesium have their optimum operating range around pH 8–9. At pH 10, the optimum value of traditional titrations, the slope change begins to be critically small. By contrast, a lower pH can be used, if necessary [10], although not much under 7. 3.8. Calcium The chelatometric determination of calcium is usually performed at pH 9–12 in ammonia buffer. In visual titrations, the best precision is usually obtained at pH 9–10 by using magnesium as auxiliary cation and EBT as the indicator. The plots in Fig. 5 represent pH-stat titrations of 51.55 mol of calcium in 25 cm3 of supporting solution containing 5 × 10−3 M hexamethylene tetramine (pH 6), 1.0 × 10−2 M triethanolamine (pH 7 and 8), or 2 × 10−3 M ammonia (pH 9 and 10). At pH 6, the points within about ±5% of the equivalence volume showed significant deviations due to nonquantitative reaction and were omitted from the calculations. The results are summarised in Table 1. It is seen that for calcium, like magnesium, the higher limit of the available pH range is conditioned by the acid–base properties of the chelating agent. By contrast, the higher stability of the chelate of calcium with respect to magnesium allows a lower pH to be used. Fig. 5A and Table 1 show that pH 6 (with
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slope segment of the titration plot preceding the equivalence depends on proton-exchange side reactions in which the titrated cation is involved. If only formation of the protonated chelate occurs as such a side reaction, its stability constant can be determined from the slope of that segment, expressed as the mole ratio R = n(NaOH)/n(EDTA) [11]: KMHY =
Fig. 5. (A) Titration plots for pH-stat titrations of 51.55 mol of calcium(II) in 25 ml of supporting solution (0.1 M sodium perchlorate) at pH—(䊉): 10.00 (2 × 10−3 M ammonia buffer); (䉱): 9.00 (5 × 10−3 M ammonia); (䊏): 8.00 (1.0 × 10−2 M triethanolamine); (䉲): 7.00 (1.0 × 10−2 M triethanolamine); (䉬): 6.00 (5 × 10−3 M hexamethylene tetramine). Aliquots of 48 l of 0.1 M EDTA were added at intervals of 1 min. Other experimental parameters as in Fig. 2. (B) Residuals of the plot at pH 10. log KCaY = 5.9) is still available for sufficiently precise titrations. Independent of pH, pH-stat titrations of calcium seem slightly more precise than photometric ones (last column of Table 1). These were made at pH 10.0 in 0.1 M ammonia buffer with EBT as the indicator at 620 or 550 nm; the end point was obtained by extrapolating the sloping branch of the absorbance or transmittance.
3.9. The determination of equilibrium constants of protonated complexes It has been theoretically deduced [11] and experimentally confirmed (Sections 3.5 and 3.6) that the
2−R (R − 1)[H+ ]
(2)
For determining accurately KMHY , accurate measurement of the equilibrium concentration of the hydronium ion and careful control of the ionic strength are essential. An internal calibration of the electrochemical measuring cell in the supporting solution should be made before each titration [7,8]. In our experiments, the cell was calibrated externally with usual pH standards, and only the repeatability of the operating value of pH during a single experiment was carefully controlled, the exact value being of low relevance for titration accuracy (see Section 3.1). Therefore, their results can be used only for a mere preliminary check of the theoretical expectations. The titrations most suitable for this purpose are those of copper at pH 3.00, where the side-reaction effect is larger. R was 1.4651 ± 0.0007 (n = 5), yielding KCuHY = 1.150 × 10−3 , log KCuHY = 3.061. This value compares well with the one given in the literature, log KCuHY = 3.0 at 25 ◦ C, µ = 0.1 [16,18]. The very small standard deviation of R shows that KMHY can be determined with precision possibly much better than with traditional methods and with accuracy limited only by that of the pH measurement. Even the value R = 1.8922±0.0006 obtained at pH 4.00, yielding KCuHY = 1.208 × 10−3 , log KCuHY = 3.082, is acceptable, particularly considering that the effect on R amounts to only 10% of the limit value 2.
4. Conclusions The experiments here described fulfil satisfactorily the theoretical expectations [11] about the analytical suitability of pH-stat chelometric titrations as well as about the shape of the titration plots. Accuracy and precision are very good. The experimental parameters are easily adjusted to fit the properties of the titration system. The duration of a single titration is acceptable.
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In comparison, photometric titrations can reach comparable precision only at the cost of longer duration; indeed, in our experiments, they required smaller additions in the proximity of the equivalence both when the end point was interpolated (with sigmoidal titration plots) or extrapolated (to identify a discontinuity). The most serious limit for practical applications of pH-stat titrations with EDTA is the requirement that the titrated solution has a moderate buffering power. The moderately basic maximum operating pH (not much higher than 10) is largely counterbalanced by the possibility of exploiting reactions that are not strictly quantitative, i.e. with the smaller conditional stability constants of the chelate complex prevailing at lower pH. A clear advantage of the pH-stat procedure with regularly timed discontinuous addition of primary titrant is that the direct titration plot of the auxiliary titrant volume against time generally gives immediate evidence of slowly occurring reaction and of reaching equilibrium. Such a direct control is difficult or impossible, for instance, with indicated photometric titrations. Even the suitability of pH-stat procedures for the determination of some stability constants has been confirmed. Both applications seem to deserve larger consideration in the analytical and research laboratory. Acknowledgements The work was carried out with the financial support of CNR. The co-operation of Alberto Doimo in the
preparation of the computer program for timed discrete additions is gratefully acknowledged. References [1] C.F. Jacobsen, J. Léonis, Compt. Rend. Trav. Lab. Carlsberg sér. Chim. 27 (1951) 333. [2] C.F. Jacobsen, J. Léonis, K. Linderstrøm-Lang, M. Ottesen, Methods Biochem. Anal. 4 (1957) 171. [3] G.G. Guilbault, Enzymatic Methods of Analysis, Pergamon Press, Oxford, 1970. [4] M. Kopanica, V. Stara, in: G. Svehla (Ed.), Wilson and Wilson’s Comprehensive Analytical Chemistry, vol. XVIII, Elsevier, Amsterdam, 1983, p. 124, p. 174. [5] S. Pantel, Anal. Chim. Acta 199 (1987) 1. [6] H.V. Malmstad, E.H. Piepmeier, Anal. Chem. 37 (1965) 34. [7] C. Maccà, L. Soldà, Electroanalysis 14 (2002) 57. [8] C. Maccà, L. Soldà, Electroanalysis 14 (2002) 63. [9] K. Mooibroek, Phototitrations: A Guide to Methods, Mettler Instrumente A.G., Greifensee, CH, 1978. [10] F. Di Gregorio, R. Sisto, J. Dairy Res. 47 (1980) 417–419. [11] C. Maccà, Anal. Chim. Acta 456 (2002) 313. [12] G. Schwarzenbach, H. Flasckha, Complexometric Titrations, 2nd ed., Methuen, London, 1969. [13] R. Pribil, Applied Complexometry, Pergamon Press, Oxford, 1982. [14] T.S. West, Complexometry with EDTA and Related Reagents, BDH, Poole, 1969. [15] Anonymous, Complexometric Assay Methods with Titriplex, Merk, Darmstadt. [16] A. Ringbom, Complexation in Analytical Chemistry, Interscience, New York, 1963. [17] C. Maccà, Analyst 108 (1983) 395. [18] A.E. Martell, R.M. Smith, Critical stability constants, in: Amino Acids, vol. 1, Plenum Press, New York, 1974.