tem conducted in the presence of 2 X lo-’ monomole of DEAEM in excess of silt shows (Curve 3) an easily identified end point, coinciding with the equivalence point. The above examples demonstrate that the accuracy of the “polyelectrolyte indicator” method even at considerable dilutions is within the limits of & l % . The precision of the method also appears to be fairly high; hundreds of titrations were carried out, and the precision of the determinations was always within the limits of the precision of the volumetric methods employed in the preparation of the acids and the bases. The amount of polyamine added is not critical. An addition of excess of polyamine-e.g.,’twice as much as the acidmakes the titration curve almost horizontal for its entire length, till the break at the end point. An addition of a very small amount of polyamine-e.g., tenth of the concentration of the acid-causes the titration curve to resemble an ordinary titration curve till the approach of the end point, when the curve rises rapidly, flattens out for a minute interval, and then again yields the characteristic break. Very great excess of the polyamine-e.g., ten times the amount of the acidmay affect the accuracy, as in such a case some per cents of the acid may remain on the: polyamine even after complete phase separation. We have found it convenient to use polyamine so as to have a monomolar concentration of about 50z of the acid . A separation of two acids with low pK’s, such as the first two protons in phosphoric acid (pK1 = 2.1, pKz = 7.2)
cannot be carried out with the aid of DEAEM, as pHppt has to be between 4 and 5 to satisfy Equation 22. It has, however, been found that poly(2-vinylpyridine) has properties similar to those of DEAEM, while precipitating at pH = 4.8 (6).Titration of 0.01M phosphoric acid without PVP (Curve 1) and in the presence of PVP (Curve 2) is shown in Figure 9. I t can be seen that the end point obtained by the precipitation of PVP is close to the conventional potentiometric end point. At greater dilutions, however, PVP does not yield such good results; it appears that PVP, unlike DEAEM, retains some protons on its precipitate (6), so that Equations 17 and 19 cannot be applied rigorously. It is probable, however, that a number of polyamines may be found covering a wide range of pHppt and at the same time as suitable as DEAEM for the accurate visual determination of dilute acids in potentiometric titrations. ACKNOWLEDGMENT
The authors thank Prof. A. Katchalsky, Head of the Polymer Dept. of the Weizmann Institute of Science, under whose direction this investigation was carried out, Dr. I. Miller of the Polymer Department of the Weizmann Institute of Science for the samples of poly(vinylpyridine), and S. Marian of the Plastics Department of the Weizmann Institute of Science for help in the preparation of poly(DEAEM). RECEIVED for review August 2, 1966. Accepted October 7, 1966.
Automatic Chelometric Titratioln of Metal Ions Using a Silver-( Die!thylenetrinitrilo)pentaacetic Acid El ectrode Eugene D. Olsen and Frank S. Adamo Chemistry Department, University of South Florida, Tampa, Fla. 33620 Metal cations can be determined by automatic potentiom et r ic tit r at io n with (diet hy I e net r initr iIo)pe nt a acetic acid (DTPA) using a silver indicator electrode if a trace of silver(1) is added before the titration. The electrode functions $as a pM electrode, giving symmetrical titration curves. Using an automatic-recording, continuous increment-addition titrator, amounts of magnesium, calcium, and barium down to 104M were titrated with better than 1% accuracy and precision, with the accuracy and precision improving at higher concentrations. Mixtures of magnesium and calcium were titrated for total metal ion content, and zinc was determined by back titration with magnesium nitrate after adding excess DTPA. Some advantages of the electrode system over mercury-EDTA or silverEDTA electrodes are cited.
-
THEAUTOMATION of potentiometric EDTA titrations has been a difficult task, The mercury-EDTA electrode is extremely valuable for manual potentiometric titrations ( I , 2), but it is difficult to use in automatic titrations because of its slow response in basic solution (2-4). Recently a number of authors C. N. Reilley and R. W. Schmid, ANAL.CHEM., 30, 947 (1958). C. N. Reilley, R. W. Schmid, and D. W. Lamson, Ibid.,p. 953. J. S. Fritz and B. B. Girralda, Ibid.,36, 737 (1964). G. Guerin, J. Desbarres, and B. Tremillon, J . Electroanal. Chern., 1,226 (1959/1960).
(1) (2) (3) (4)
have used modified mercury electrodes for automatic titrations, all analyses being based on titration to a preselected end point potential using various types of anticipation circuits (5-8). All such titrations require prior knowledge of the end point conditions, and unless the preselected end point potential is set very precisely, the titrations can be very inaccurate (8). Very recently Blaedel and Laessig published a series of papers describing continuous EDTA titrations under a variety of conditions (9-12). While their equipment is elaborate and likewise requires preselection of the end point potential, their equipment rigidly controls the end point conditions and is to be recommended wherever a large number of titrations are to be carried out on a routine basis. The automatic recording of potentiometric titration curves has certain advantages over titrating to a preselected end point (5) M. C. Gardels and J. C. Cornwell, ANAL.CHEM., 38,774 (1966).
(6) J. Haslam, D. C. M. Squirrell, and I. G. Blackwell, Analyst., 85, 27 (1960). (7) W. Hessler, Bergakademie 17, 478 (1965); CA, 64, 1351d (1966). (8) R. C. Schonebaum and E. Breekland, Talanfa,11, 659 (1964). (9) W. J. Blaedel and R. H. Laessig, ANAL.CHEM., 37, 332 (1965). (10) Ibid.,p. 1255. (11) Ibid.,p. 1650. (12) Ibid., 38, 186 (1966). VOL. 39, NO. 1, JANUARY 1967
81
potential. Detailed knowledge of the sample composition and end point conditions is not required prior to titration, and the equivalence point potential of the indicator electrode need not be extremely reproducible for high accuracy. Further, complete titration curves permit some qualitative and semiquantitative deductions regarding unknown samples to be made from the shapes of the curves and magnitude of the potentials. In addition, the equipment can be much simpler, and the permanent record of the titration curve permits reevaluations to be made a t a later date. However, titrators which add titrant continuously at a constant flow rate require a titration reaction and indicator electrode response which are practically instantaneous, and usually these conditions are not fulfilled, especially near the equivalence point (13). The continuous addition of titrant in increments permits more latitude in equilibration rates, as reported earlier ( I d ) , but nonetheless the electrode response must be reasonably rapid to make such titrations practical. Recently a silver-EDTA electrode which responded more rapidly than the mercury electrode was reported by Strafelda (15, 16), and Fritz and Garralda (3), for the manual potentiometric titration of metal ions. The potential of a silverEDTA electrode usually depends on the negative logarithm of the EDTA concentration [“electrode of the second type” (17)], giving decidedly asymmetric titration curves which complicate the problem of automatic titrations. This paper introduces the silver-DTPA electrode as an “electrode of the third type” [or pM electrode, where pM = -log(M) and M is a metal ion], giving nearly symmetrical titration curves. Used in conjunction with a slightly modified version of a recently developed automatic recording continuous increment-addition titrator ( 1 4 , the system is illustrated with automatic titrations of various alkaline earths and zinc. EXPERIMENTAL
Apparatus. The apparatus used for automatic delivery of titrant solutions was the same as that described previously (14), with two minor modifications and one addition. A thick-walled polyethylene tubing 3/4 inch-0.d. by 18 inches long was used as the buret in place of the glass Hempel distilling column, to minimize the contact of chelating agent titrant with glass. The siphon pipet was omitted, with the drops emerging from the capillary flow restrictor serving as the increment additions. A series of capillary flow restrictors was prepared by heating 5-inch lengths of about 1/4-mm i.d. capillary tubing in a flame and pulling them out 1 to 1.5 inches. Some of the capillaries were broken in the center, and further segments broken off until drops of about 0.02 ml emerged from the pointed end. On the unbroken capillaries used in most of this work, the drop size was about 0.08 ml. The volume of the drops was determined each day by collecting and weighing several 10-drop fractions of DPTA titrant, and the weight per drop was converted to volume per drop by weighing two to three portions of a known volume of the titrant. Regardless of the drop size chosen for a titration, only those capillaries giving approximately two to three drops per minute with an approximately 30-inch hydrostatic head were used. A Heath Model EUW-301 potentiometric recording electrometer with a chart speed of 0.5 inch per min. was used. The electrometer range switch was set at 200 mv (13) L. Meites and H. C. Thomas, “Advanced Anal. Chem.,” p. 66. McGraw Hill, New York, 1958. (14) E, D. Olsen, J. Chem. Educ., 43, 310 (1966). (15) F. Strafelda, Collection Czech. Chem. Commun., 30, 2320 (1965). (16) Ibid., 28, 3345 (1963). (17) R. W. Schmid, Chrwist-Analyst, 51, 56 (1962).
82
ANALYTICAL CHEMISTRY
for most titrations, with the exceptions of a 100-mv setting for 10-4M barium and magnesium, and 500 mv for 1 0 - 3 ~ or greater calcium solutions. A fiber-tip, saturated calomel reference electrode was used with a silver-billet indicator electrode (Coleman No. 3-571). The silver electrode was cleaned periodically by light buffing with a polishing cloth, followed by thorough washing with soap and water and rinsing with distilled water, To record the addition of each drop to the titration beaker, a simple drop counter was devised which impressed a voltage pulse on the recorder chart each time a drop fell from the capillary flow restrictor. The counter consisted of two platinum wires, separated by about inch, mounted horizontally and parallel to each other, and positioned immediately below the capillary flow restrictor. As each drop fell it would momentarily make contact between the two platinum wires, thereby inserting a 1.5-v size “D” flashlight battery across the electrometer input terminals. The size of the voltage pulse recorded could be adjusted by changing the amount of separation between the two platinum wires, thereby changing the resistance in the flashlight battery circuit. To prevent the retention of any droplets on the platinum wires, the ‘/?-inch tip on each wire was bent downward 90”. Any liquid adhering to the platinum wires indicated they were dirty, and they were conveniently cleaned by heating in a flame. Approximately 1.5-inch lengths of thin platinum wire were used, with electrical connections made to insulated copper wire by simply twisting and taping. Solutions. The metal ion stock solutions (0.1M) were prepared from their reagent grade nitrates, diluted 10-fold before use, and standardized by titration with EDTA as described elsewhere ( 2 , 18). A 0.1M stock solution of DTPA [(diethylenetrinitrilo)pentaacetic acid] was prepared by dissolving 39.5 grams of DTPA reagent powder in about 1 liter of water, with the addition of sodium hydroxide pellets to p H 8.5. The stock solution was diluted two- or 10-fold, to 0.05M or O.OlM, respectively, before using in titrations, and was standardized by direct titration of standard magnesium using Eriochrome Black T indicator. A 0.015M stock solution of silver nitrate was prepared by dissolving 0.25 gram of AgN03 in about 100 ml of water. This solution was diluted 10-fold before use. Borate buffer (0.5M)was prepared by dissolving 61.8 grams of boric acid reagent and 20 grams of reagent sodium hydroxide pellets in 2 liters of water. p H should be 9.0 to 9.5. Phenolate buffer at p H 10, prepared as described in (3), was usable in place of the borate buffer, but resulting titration curves were inferior because of an asymmetrical leveling beyond the end point, for reasons which are not known. Determination of Silver-DTPA Stability Constant. Using the method of Schmid and Reilley (19), 100 ml of a solution lO-3M in silver-DTPA, lO-3M in DTPA, and 0.10M in KN03, was titrated with 1.OM NaOH or 1.OM H N 0 3 in a constant temperature bath at 25.0 f 0.1 O C. Glass and silver billet indicator electrodes were used with saturated calomel reference electrodes, and the p H was measured to +0.01 p H unit with a Heath Model EUW-301 electrometer, and the potential to ~ t 0 . 2mv with a Sargent Model DR digital pH meter. The acid dissociation constants of DTPA reported by Durham and Ryskiewich (20) were used. Direct Titration of Metal Ions. Samples containing 0.05 to 0.10 mmole of metal ions were adjusted to about p H 9 with 10 ml of 0.5M borate buffer, and diluted to approximately 100 ml. One drop (0.05 ml) of 0.0015M AgN03 was added, and the solutions titrated with 0.01MDTPA, using an approximately 0.08-ml drop size from the automatic buret. (18) E. D. Olsen, ANAL.CHEM.,36, 246 (1964). (19) R. M7. Schmid and C. N. Reilley, J. Am. Chem. Soc., 78,5513 (1956). (20) E. J. Durham and D. P. Ryskiewich, Zbid., 80,4812 (1958).
Table I. Reproducibillity of Drop Size from Titrant Delivery System Weight of 10 drops, grams Capillary C Capillary B Capillary A 0.7970 0.7951 0.7971 0.7961 0.7963 0.7964 0.7972 Av 0.1965
0,2463 0.2467 0,2464 0.2463 0.2471 0.2467
Re1 std dev
Av 0.2466 Re1 std dev
0.09%
0.12%
0.1181 0.1182 0.1183 0.1179 0.1180 0.1181
Av 0.1181 Re1 std dev 0.12% NUMBER OF TITRANT DROPS ADDED
For titration of 0.01- to 0.05-mmole samples, an approximately 0.02-ml drop size was used, so that at least 50 drops were required to the ‘end point. For titration of 0.25- to 0.50-mmole samples, 0.135MDTPA was used, and one drop of 0.015M A g N 0 3 was used. In all studies the silver (indicator) ion concentration was kept low, and no blank corrections were made. Back-Titration of Zinc. T o a sample containing 0.05 to 0.10 mmole of zinc, an accurately measured volume of 0.05M DTPA was added which was approximately twice the amount needed to react with the zinc ion. Ten milliliters of 0.5M borate buffer was add’ed, and the solution was diluted to approximately 100 ml. After adding one drop of 0.0015M AgN08, the solution was titrated with 0.01M Mg(N03)*, using an approximately 0.08-ml drop size from the automatic buret. RESULTS
Reproducibility of Drop Size. The analytical accuracy of this apparatus hinges or1 constancy and reproducibility of the drop size. Table I illustrates the reproducibility of drop size using three different capillary flow restrictors. Capillaries B and C were pointed on the end, while capillary A had its constriction in the center. Drops were automatically counted on the recorder chart while being collected. Removing the platinum drop-counter wires did not significantly change the size of the drops collected. Flow rates in all cases were such that about two to three drops emerged per minute, giving a range in flow rates of from about 0.2 to 0.02 ml/min for the three capillaries in Table I. With this apparatus, the flow rate was constant to about + 1 to 2 ( I d ) ,which as Table I shows, is sufficiently constant to ensure excellent reproducibility of drop size. Although the drop size was constant over the course of a day, it should be checked each day, since capillary characteristics sometimes changed slightly from day to day. Silver-DTPA Stability Constant. The log of the silverDTPA stability constant was calculated to be 8.61, with a standard deviation of 0.04, using potentials over the p H range of 8 to 10. Potentials were reproducible within 1 mv over the entire pH range, and the reversibility was demonstrated by alternately increasing and decreasing the pH with NaOH and “ 0 3 , respectively. Direct Titration of Ba, Ca, and Mg. Figure 1, showing the automatically recorded titration curve for the titration of 5 X 10-4M barium with 0.01M DTPA, illustrates the type of titration curve obtained. The polarity is such that the potential becomes more negative as the titration proceeds. Each time a drop falls from the capillary flow restrictor a voltage pulse from the flashlight battery causes an easily discernible pulse on the chart paper, enabling the number of drops to the
Figure 1. Automatically recorded titration of 5 X 10-4M barium(I1) with 0.01M DTPA
end point to be easily counted. Determination of the number of drops and partial drops to an equivalence point is facilitated by the fact that the volume of each drop is constant and the titration curve is quite symmetrical in the end point region. Thus, the drop giving the largest equilibrium potential change will be the drop containing the equivalence point, and the fraction of that drop used to just reach the equivalence point can be calculated quickly from the equilibrium potential changes of the increment immediately preceding and the increment immediately following the equivalence point drop, as outlined previously (14). Thus, in Figure 1, the end point is calculated to be 77.46 f 0.02 drops. Titration curves for magnesium and calcium likewise gave symmetrical titration curves, whereas the use of EDTA instead of DTPA gave pronounced asymmetrical curves, in agreement with findings of Fritz and Garralda (3). Nonsymmetrical titration curves greatly complicate accurate end point determinations, because the point of steepest slope is more difficult to ascertain, and in addition, the inflection point is not always the equivalence point ( I O , 21). The titration curve for barium (Figure 1) was chosen to illustrate the alkaline earth titrations, because barium forms the weakest DTPA complex of the alkaline earths [Kstahility 108.6 (22)], and gives the smallest potential changes in the region of the end point of the alkaline earths. In addition, the equilibration time for barium after the addition of each drop of titrant was similiar to that of calcium, but appreciably slower than that of magnesium, which equilibrates very rapidly with this system. With this flow rate and drop size (about 0.25 ml/ min and 0.08 ml/drop, respectively), potentials are close enough to equilibrium in the end point region to give excellent end point accuracy, but a slower flow rate and/or smaller drop size could be used wherever necessary. In contrast, EDTA gave slightly faster equilibration rates with calcium, but much slower equilibration rates with magnesium, precluding the automatic EDTA titration of magnesium with either a silver or a mercury electrode. Schonebaum and Breekland (8)also had difficulty automating the EDTA titration of magnesium. It (21) W. J. Blaedel and V. W. Meloche, “Elementary Quantitative Analysis,” 2nd ed., pp. 276, 754, Harper & Row, New York, 1963. (22) L. G. SillCn and A. E. Martell, “Stability Constants of MetalIon Complexes,” Special Publication No. 17, The Chemical Society, London, 1964. VOL. 39, NO. 1, JANUARY 1967
83
Table 11. Automatic Titration of Various Amounts of Magnesium, Calcium, and Barium Metal ion Mg+
Ca+2
Ba+%
Metal ion, mmoles Taken Found
Error,
z
0.6110 0.1222 0.06110 0.01222 0.5990 0.1198 0.05990 0.01198
0.6098 0.1223 0.06074 0.01232 0.5973 0.1197 0.05980 0.01196
-0.20 $0.08 -0.59 +0.81 -0.28 -0.08 -0.17 -0.20
0.6000 0.1200 0.06OOO 0.01200
0.5998 0.1201 0.05983 0.01210
-0.04 $0.08 -0.28 +0.83
Re1 std dev, %” 0.16b 0.16 0.46 0.87 0. 08b 0.10 0.25 0.56 0. 08b
0.30 0.46 0.86
a Relative standard deviation of three to five determinations, unless otherwise noted. 6 Relative range of two determinations.
should be noted that the polarity of the flashlight battery in the drop-counting circuit is such that the counter pulses travel in the direction of the overall potential change, with reversed polarity pulses causing further lags in the overall equilibration rate, which indicates that the recorder response time is a significant part of the total equilibration time. Table I1 summarizes the accuracy and precision obtained in the titration of various amounts of magnesium, calcium, and barium. For amounts down to 0.05 mmole (or 5 X 10-4M), the accuracy and precision was generally better than 0.5 %, and in all cases was better than 1 %, even down to 0.01 mmole (or 10-4M). Ordinary potentiometric titrations are generally limited to about 10-2M for accuracy on the 0.1 error, and lO-3Mfor accuracy on the 1 % error level (23). At the low concentrations in this study the silver-DTPA electrode system gives bigger end point breaks for the alkaline earths than can be obtained with a mercury-EDTA electrode. Reilley and Schmid ( I ) give the end point potential changes that can be expected for titration of lO-3M solutions of the alkaline earths with a mercury-EDTA electrode, and Blaedel and Laessig (12) extend this data down to 10-jMfor calcium, the alkaline earth having the most stable EDTA complex (22). At lOP4M, the calcium end point break with EDTA is in the order of 10 mv ( I 2 ) , and it can be predicted that barium, having a much weaker EDTA complex (22), would give a n even smaller end point break. Using the silver-DTPA electrode, Figure 1 demonstrates that a n excellent end point break of about 80 mv was obtained with 5 X 10-4Mbarium, and a t the lO-*M level the end point breaks ranged from 25 to 30 mv for barium to about 50 mv for calcium. Another advantage of the silver electrode over the mercury electrode is that oxygen does not interfere, whereas with a mercury electrode, deaeration is often necessary, especially in titrations of barium ( I ) .
(23) H.H.Willard, L. L. Merritt, Jr., and J. A. Dean, “Instrumental Methods of Analysis,” 4th ed., p. 564,Van Nostrand, Princeton, N. J., 1965.
84
ANALYTICAL CHEMISTRY
Table 111. Automatic Titration of Mixtures of Calcium and Magnesium Mmoles taken Mmoles found, Error, Re1 dev, std Ca+2
Mg+z
Total
total
0.04792 0.02444 0.07236 0.07249 0.03594 0.03666 0.07260 0.07252 0.02396 0.04888 0.07284 0.07302
z
z
+O. 18
0.03 0.03 0.24
-0.11 $0.25
Titration of Mixtures of Ca and Mg. Mixtures of Ca(I1) and Mg(I1) were made up in moles ratios of 2 : 1,l:1, and 1 :2 Ca/Mg, and the sum of the metal ions were titrated with the results shown in Table 111. The size of the end point breaks and the equilibration rates were intermediate t o those obtained with calcium and magnesium individually, and the curves were symmetrical about the equivalence point. The total calcium plus magnesium concentration level titrated (ca 7 x lO-4M) is below the level of most natural waters, and approaches the levels of softened water ( I 2 ) , and thus this titration system should be directly applicable to the determination of water hardness in natural waters. Back-Titration of Zinc. Concentrations of zinc in the were each back-titrated in order of 10-3Mand 5 X 10-4M triplicate, with relative errors of about 0.3%, and relative standard deviations of 0.3 % or less. Sharp, symmetrical end point breaks and rapid equilibration rates, characteristic of the results obtained in the titration of magnesium, were obtained. DISCUSSION
When EDTA is used for titrations with a silver electrode, asymmetrical titration curves result because the silver-EDTA complex is relatively weak (Katsbility = lo7.3), which allows the silver ion concentration to remain approximately constant until very close to the equivalence point (3). In the case of DTPA titrant, the stability constant for the silver-DTPA complex is more than 20-fold stronger than the silver-EDTA complex, and in the same order as the DTPA complexes of barium and magnesium, permitting the silver electrode to function as a pM indicator electrode in a way analogous to the mercuryEDTA electrode ( I , 2). Only in the case of calcium, which forms a DTPA complex approximately 100-fold stronger than the silver-DTPA complex, is a slight asymmetry in the titration curve noticeable, but the deviation from symmetry is too small to cause significant error. In the case of heavy metal ions which have stability constants higher than calcium, direct titrations are generally impractical at high pH, and indirect titrations using standard magnesium as a titrant will give the symmetrical titration curves characteristic of magnesium, as illustrated in this paper by the back-titration of zinc. The silver-DTPA electrode system should be useable with other types of automatic titrators.
RECEIVED for review June 10, 1966. Accepted November 7, 1966. Paper presented in part a t the Meeting-in-Miniature of the Florida Section of the American Chemical Society, Tampa, Fla., May 1966. Work supported by the National Science Foundation (NSF-GP-3482).
