LETTER pubs.acs.org/ac
Universal Tracer Monitored Titrations Michael D. DeGrandpre,*,† Todd R. Martz,‡ Robert D. Hart,† David M. Elison,† Alice Zhang,† and Anna G. Bahnson† † ‡
Department of Chemistry and Biochemistry, The University of Montana, Missoula, Montana 59812, United States Scripps Institution of Oceanography, La Jolla, California 92093, United States ABSTRACT: Titrations, while primarily known as the chemical rite of passage for fledgling science students, are still widely used for chemical analysis. With its many years of existence and improvement, the method would seem an unlikely candidate for innovation, yet it is desirable, in this age of autonomous sensing where analyzers may be sent into space or to the bottom of the ocean, to have a simplified titrimetric method that does not rely upon volumetric or gravimetric measurement of sample and titrant. In previous work on the measurement of seawater alkalinity, we found that use of a tracer in the titrant eliminates the need to measure mass or volume. Here, we show the versatility of the method for diverse types of titrations and tracers. The results suggest that tracers may be employed in all types of titrations, opening the door for greatly simplified laboratory and field-based chemical analysis.
he titration apparatus has evolved over its ∼250 year history,13 but the basic principles and the advantages titrations offer have not changed. A titration utilizes the stoichiometric reaction of a titrant with an analyte. It proceeds by quantitative addition of titrant to a known amount of sample until an end point is reached. Because the amount of titrant and sample are measurable to within 0.3% using volume, or 0.1% using mass,3 titrations have precision and accuracy that are difficult to achieve with most other chemical and instrumental methods. Former students may reflect upon the tedium of adding titrant from a volumetric buret while carefully recording the position of the meniscus until the end point is reached; however, most modern titration systems are fully automated with precision pumps and sophisticated end point detection. With this modernization, applications have proliferated across technical and professional disciplines.4 Our previous work using indicators for measurement of CO2 and pH5,6 and our desire to develop an autonomous in situ analyzer for the measurement of seawater alkalinity led us to the realization that a tracer could be added to the titrant or sample to quantify the amount of titrant added,7 eliminating the need for measurement of volume or mass. In ref 7, we hypothesized that a tracer monitored titration (TMT) could be used for all types of titrations, e.g., oxidationreduction, complexometric, precipitation, etc. and that a wide range of tracers could be used. The tracer could be any quantifiable chemical species (e.g., an ion, an absorbing or fluorescent indicator or even a light scattering particle) and could be inert or participate in the reaction. For example, a tracer could be either a nonreactive chromophore or an indicator that is used to track the consumption of the analyte. If the tracer is an indicator, all forms of the indicator must absorb light so that total indicator concentration can be quantified at any point in the titration. Many indicators have this characteristic,
T
r 2011 American Chemical Society
e.g., they change colors when reduced or complexed.3 If the tracer is inert, the equilibrium position of the titration must be determined by an alternative method. For example, an inert colored tracer can be used in an acidbase titration with a glass pH electrode to monitor pH as the titration proceeds. The TMT methodology can be understood by derivation from the simple titration mole (or mass) balance and is presented here in a more general form than that shown in ref 7. At any point in a conventional titration, the mole balance is represented by VS VT Q ½titrantT Vmix Vmix ¼ ½analytemix Q ½titrantmix
½analyteS
ð1Þ
where Q is the reaction stoichiometry (mols analyte/mol titrant), [analyte]S is the analyte concentration in the sample, [titrant]T is the concentration of the titrant being added, VS and VT are the sample and titrant volumes (or masses, not mentioned hereafter), respectively, and the subscript “mix” denotes the equilibrium concentrations in the sampletitrant mixture. The total volume is Vmix = VT + VS. The volume ratios in eq 1 are the dilution factors of the titrant (fT) or sample (fS) fT ¼
VT Vmix
and
fS ¼
VS Vmix
ð2Þ
In a conventional titration, the dilution factors are determined with measured volumes. In the TMT, dilution factors are Received: September 27, 2011 Accepted: November 9, 2011 Published: November 09, 2011 9217
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LETTER
Scheme 1. Strong AcidStrong Base Titration Reaction
Scheme 3. Complexation Titration Reaction: The Competitive Complexation Reaction of Ethylenediaminetetraacetic Acid (EDTA) and Calmagite (CalMag) for Detection of Calcium12
Scheme 2. Redox Titration Reaction: The L-Ascorbic Acid (Vitamin C, C6H8O6) Oxidation3
independently determined using a tracer, f ¼
V ½tracermix ¼ Vmix ½tracer1
ð3Þ
where V is VT or VS, [tracer]mix is the tracer concentration in the mixture, and [tracer]I is the initial tracer concentration in the titrant or sample. The two dilution factors are related by fT + fS = 1. In most titrations, titrant is added until an end point (ep) is reached, as indicated by, for example, a change in the color of an indicator. The ep corresponds approximately to the equivalence point where eq 1 is equal to zero. In a conventional titration, eq 1 is solved for [analyte]S and the corresponding amount of titrant added at the end point, VT(ep), is used along with the known titrant concentration and VS to determine the analyte concentration: ½analyteS ¼ Q ½titrantT
VT ðepÞ VS
ð4Þ
In the TMT, the corresponding dilution factor at the end point, fT(ep), determined with eq 3, is used ½analyteS ¼
Q ½titrantT 1=fT ðepÞ 1
ð5Þ
Equation 5 shows that no measurement of volume is required. If the tracer is in the titrant, it can be added very accurately using volumetric or gravimetric methods. However, in cases where it is advantageous to add the tracer to the sample or where an indicator must be added to the sample, the change in volume must be insignificant relative to the total volume or must be accounted for in the dilution factor calculation (see Materials and Methods). While there have been many variations on the general theme, all titrations have measured titrant and sample volumes, mass, or flow rate. Coulometric titrations use charge to quantify titrant, but sample volume or mass must be measured.3,8 Other titration schemes have used continuous pumping, but flow rate must be carefully controlled, essentially making it a volumetric measurement.911 With the TMT, the burden of performance is placed on the tracer measurement method rather than volumetric and gravimetric measurements. Some instrumental methods, such as spectrophotometry and conductimetry, have precision and accuracy comparable to measurement of mass and volume. In the first application of the TMT, precision of (0.1% was obtained using a pH indicator tracer and a simple dualwavelength colorimeter.7 Here, we evaluate 3 additional titration schemes with different tracers: (Scheme 1) a strong acidstrong base titration using an inert dye tracer added to the titrant with pH electrode detection of the end point; (Scheme 2) an oxidation reduction titration of vitamin C with conductometric detection of an inert tracer (NaCl) and an indicator end point; (Scheme 3) a
complexation titration of calcium with an indicator added to the sample that acts as both tracer and end point detector. Our goal in the experimental design was not to fully optimize each titration method but to determine the validity of the hypotheses outlined above. As shown below, the TMT has great versatility and shows promise for application in a wide range of titration-based analyses.
’ MATERIALS AND METHODS Scheme 1. Brilliant blue dye (supermarket blue food coloring) was used as a pH independent, i.e., inert, tracer added to the NaOH titrant. Absorbance was measured using a fiber-optic dip probe with a 4 cm path length connected to a simple colorimeter (Brinkman PC910). The wavelength was set to 640 nm with a bandpass filter. The dip probe was immersed in the sample titrant solution during the titration. The pH was measured using a Ross combination electrode connected to a benchtop pH meter. Titrant was prepared by adding a dye stock solution to unstandardized 0.01 M NaOH titrant. Titrations were carried out by adding increments of titrant with a precision pipet ((1%) to 15.4, 41.3, and 65.0 mL sample volumes of ∼0.01 M HCl, mixed with a magnetic stirrer. The pipet was used so that conventional and TMT-based titrations could be directly compared. After each pipet addition, electrode pH and dip probe absorbance were recorded. Absorbance and pH data were recorded until the pH inflection point was passed. Beer’s law (A = εbc) was used to determine the dye concentration during the titration where A is absorbance, ε is the dye molar absorptivity, b is the optical path length, and c is the dye concentration. An effective molar absorptivity was calculated as follows: 200 μL of dye stock was pipetted into 1 L of deionized (DI) water; absorbance was measured at room temperature using the dip probe, which registered an absorbance of 0.627, and effective molar absorptivity was calculated. While molar absorptivities are temperature and matrix dependent, the sensitivity to these environmental variables was not examined. The molar absorptivity was used during a titration to calculate dye concentration and dilution factors after each addition of titrant (eq 3). First derivative plots of d(pH)/d(mL-titrant) or d(pH)/d(fT) were used to determine the volume of titrant or fT at the end point, respectively. The peak maximum corresponds to the end point. Scheme 2. Iodine oxidizes ascorbic acid, forming dehydroascorbic acid (C6H6O6). Triiodide (I3) titrant (∼0.0075 M) was prepared by dissolving ∼0.0025 M potassium iodate (KIO3) in excess acidified (0.15 M H2SO4) potassium iodide (∼0.06 M, KI) solution.3 L-ascorbic acid concentrations ranged from 0.7 to 1.4 μM. Ten drops (∼0.3 mL) of starch solution were added to ∼100 mL of sample immediately before the titration. Specific conductance was selected as the tracer detection method. Although the inherent conductivity of the titrant could be used as the tracer, the conductivity was increased so that reacting ions did not significantly alter the ionic composition during the titration. To do this, solid NaCl tracer was added to the titrant to increase the total cation (H+ and Na+) concentration to ∼1.8 M. The specific 9218
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Table 1. Molar Absorptivities of the Complexed (C) and Free (F) Forms of Calmagitea at their Absorbance Maxima (537 and 610 nm)
a
εC537
18, 181
εC610 εF537
1, 764 12, 518
εF610
20, 305
From ref 12. Units are M-1 cm-1.
Figure 2. Comparison of precision and accuracy for conventional (green) and TMT (purple) methods. The number of samples analyzed for each scheme is printed in the top panel, and the actual probabilities (two-tailed p) are also given in the top (F-test) and bottom (t test) panels. There was insufficient evidence to reject the null hypotheses (i.e., precision or accuracy are not different) at the 0.05 significance level for all comparisons except accuracy for titration schemes 2b and 3. The “real sample” in titration scheme 2b was a vitamin tablet with a known vitamin C content. In titration scheme 2c, titrant was added with a nonvolumetric pipet. No corresponding conventional analysis was possible in this case (NA).
Figure 1. Conventional (A) and TMT (B) titrations of a strong acid with a strong base (Scheme 1) of three different volumes of strong acid sample (∼15, 41, and 65 mL). The dilution factor was calculated using eq 3 by monitoring the concentration of an inert dye (brilliant blue). The derivative of the titration data (C) was used to determine the end point (shown only for the TMT data).
conductivity was measured at room temperature using a YSI 600 multiparameter sonde calibrated with six NaCl/H2SO4 solutions over the range expected in the sampletitrant mixture (0.250.60 M). The slightly nonlinear calibration was fit with a second order polynomial. Sonde instrument calibrations did not show any significant change over a period of 1 month. Samples for analysis were made from ascorbic acid dissolved in DI water. Titrations were conducted by adding titrant with a volumetric buret until the blue starch end point was reached. As in Scheme 1, sample and titrant volumes were recorded to allow comparison between the conventional and TMT methods. Nonvolumetric titrations of sample were also performed by adding titrant dropwise to ∼100 mL samples with a Pasteur pipet. To test the method with a real sample, vitamin C tablets were prepared by dissolving the tablet in 100 mL of DI water and titrated by additions with a buret. The vitamin C concentration listed on the product label was used for comparison to the titration results. Scheme 3. Calmagite indicator solution (5.248 104 M) was made by dissolving indicator in NH4Cl/NH4OH buffer diluted to a final volume with DI water. Calcium standard solutions (2.55.0 103 M) were made from a stock solution of CaCl2 dihydrate in DI water. EDTA titrant (8.395 103 M)
was made by dissolving the disodium salt of EDTA in DI water. Spectrophotometric titrations were performed using a UVvis spectrophotometer (Agilent Model 8453) with titrant added directly into a stirred 1 cm cuvette. The sample, along with several drops of buffer/indicator solution in accordance with the traditional method,12 was placed in the cuvette. The initial dilution factor due to the buffer/indicator solution was calculated using eq 3. To make direct comparisons with the conventional titration, the titrant was added using an automated buret system. Absorbance was measured after each titrant addition. Total calmagite concentration was calculated at 537 and 610 nm using the molar absorptivities values approximated from Figure 3 in ref 12 and are shown in Table 1.
’ RESULTS AND DISCUSSION Scheme 1. Conventional and TMT acidbase titration curves are very similar (Figure 1). In the conventional approach, titration curves of three different sample volumes for the same analyte concentration appear at different positions along the x-axis (Figure 1A). In the TMT, the position of each titration curve is identical showing that the TMT is independent of the sample volume used (Figure 1B). More sample requires proportionally more titrant, resulting in the same dilution factors at the end point for the same analyte concentration. The derivative of the titration curve was used to more accurately define the end point (Figure 1C). The precision and accuracy are not statistically different for both methods (Figure 2). Although there is a large uncertainty in this comparison because of the few samples analyzed, these results show that an inert dye tracer can be used 9219
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Figure 3. Conventional (red, top axis) and TMT (blue, bottom axis) spectrophotometric EDTA complexation titrations of the same Ca sample. Uncomplexed (Ca-free) calmagite absorbance at 610 nm, A (610 nm), stops increasing at the end point when the EDTA has complexed all of the Ca and dilution by the titrant begins to dominate the signal. Best-fit lines for the data on either side of the titration inflection point were used to obtain a more accurate end point.
with a simple colorimeter to perform acidbase titrations. No attempt was made to perform more replicates or to further optimize the method. In this case, the precision was controlled by the volume increments added around the end point and the few samples analyzed. Accuracy is within the uncertainty of the unstandardized NaOH used in the analysis. Scheme 2. The precision and accuracy are not statistically different for the conventional and TMT methods for analysis of vitamin C standards using the visual (starch) end point (Figure 2, titration scheme 2a). Similar or better performance was obtained when analyzing a real sample (Figure 2, titration scheme 2b) and when the titranttracer mixture was added using a nonvolumetric (Pasteur) pipet (Figure 2, titration scheme 2c). As we had originally hypothesized, high quality titrations can be obtained with the TMT using simple glassware (e.g. beaker and Pasteur pipet) or, as in the first incarnation of the TMT, an inexpensive solenoid pump.7 In this example, the TMT requires a conductivity sensor to detect the tracer. Many precise and accurate conductivity probes are commercially available for this purpose like the YSI probe used here. Regarding interferences, in this titration, the conductivity sensor could be calibrated by simple dilution of the titrant solution because the dilute sample solution did not alter the relative ion concentrations. If higher ion concentrations are present, e.g., in seawater, the conductivity sensor calibration standards should be made accordingly. Some knowledge of the sample matrix would be necessary to customize the conductivity calibration for specific sample types. Scheme 3. The conventional and TMT spectrophotometric complexometric titration curves of calcium (Ca) samples are very similar (Figure 3). The precision is not statistically different for the conventional and TMT methods (Figure 2). However, the accuracy differed for the two methods. The slightly lower TMT accuracy could result from error in the complexing-agent molar absorptivities (see Materials and Methods). In this analysis, the tracer is added to the sample and the dilution factor is based upon the dilution of the tracer/indicator as titrant is added. The indicator concentration is calculated as the sum of the complexed and uncomplexed forms using Beer’s law, and any uncertainty in the molar absorptivities, e.g., caused by changes in solvent or solute composition, will result in a systematic error.7 Importantly, a sample background absorbance within the indicator wavelength range for an indicator-based TMT (e.g., Schemes 1 or 3) would cause an interference as the sample is diluted with titrant.
LETTER
’ CONCLUSIONS These results establish that the TMT methodology eliminates the need for volumetric and gravimetric measurements of titrant and sample for widely different titrations and tracers. In its simplest form, the titrant can be added using nonvolumetric glassware (e.g., eyedropper or beaker) to an unknown amount of sample until the end point is reached (titration scheme 2c). It retains the advantages of classical titrations, that is precise, accurate, and selective analyses can be performed without sample standards if a stable tracer detection method is available, e.g., conductivity or spectrophotometry. The TMT is ideally suited for spectrophotometric methods because the measurement uses the optical characteristics of the tracer (molar absorptivities) and absorbances, which do not depend upon instrument calibration.57 Many water quality and industrial measurements can be made on-site, using hand-held colorimeters with premixed reagents,13 but titrationbased analyses are not currently possible with these devices. It is in this area, where more complex equipment is not suitable, that the TMT may find its widest applications. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT We thank Cory Beatty (UM) for technical assistance and Brian Steele (UM) for discussions. Grants from the U.S. National Science Foundation Division of Ocean Sciences supported this research (OCE-0628569 and OCE-0327763). D.M.E. was supported by an NSF EPSCoR assistantship (EPS-0701906). A.Z. was supported by an NSF REU scholarship (REU-0649306). ’ REFERENCES (1) Szabadvary, F. History of Analytical Chemistry; Pergammon Press: Oxford, 1966. (2) Rosenfeld, L. Four Centuries of Clinical Chemistry; Gordon and Breach Science Publishers: Australia,1999. (3) Harris, D. C. Quantitative Chemical Analysis, 7th ed.; W.H. Freeman and Co.: New York, 2007. (4) See, for example, Mettler Toledo’s website: http://us.mt.com/. Accessed November 2011. (5) DeGrandpre, M. D.; Baehr, M. M.; Hammar, T. R. Anal. Chem. 1999, 71, 1152–1159. (6) Seidel, M. P.; DeGrandpre, M. D.; Dickson, A. G. Mar. Chem. 2008, 109, 18–28. (7) Martz, T. R.; Dickson, A. G.; DeGrandpre, M. D. Anal. Chem. 2006, 78, 1817–1826. (8) Johnson, K. M.; King, A. E.; Sieburth, J. Mar. Chem. 1985, 16, 61–82. (9) Almeida, C. M. N. V.; Lapa, R. A. S.; Lima, J. L. F. C.; Zagatto, E. A. G.; Araujo, M. C. U. Anal. Chim. Acta 2000, 407, 213–223. (10) Powell, F. E.; Fogg, A. G. Analyst 1991, 116, 631–640. (11) Tanaka, H.; Dasgupta, P. K.; Huang, J. Anal. Chem. 2000, 72, 4713–4720. (12) Lindstrom, F.; Diehl, H. Anal. Chem. 1960, 32, 1123–1127. (13) See, for example, Hach’s website: http://www.hach.com/. Accessed November 2011.
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