universal tracer monitored titrations

Published: November 09, 2011

r 2011 American Chemical Society 9217 dx.doi.org/10.1021/ac2025656 |Anal. Chem. 2011, 83, 9217–9220

LETTER

pubs.acs.org/ac

Universal Tracer Monitored TitrationsMichael D. DeGrandpre,*,† Todd R. Martz,‡ Robert D. Hart,† David M. Elison,† Alice Zhang,† andAnna 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

The titration apparatus has evolved over its ∼250 yearhistory,1�3 but the basic principles and the advantages

titrations offer have not changed. A titration utilizes the stoichio-metric reaction of a titrant with an analyte. It proceeds byquantitative addition of titrant to a known amount of sample untilan end point is reached. Because the amount of titrant and sampleare measurable to within 0.3% using volume, or 0.1% using mass,3

titrations have precision and accuracy that are difficult to achievewith most other chemical and instrumental methods. Formerstudents may reflect upon the tedium of adding titrant from avolumetric buret while carefully recording the position of themeniscus until the end point is reached; however, most moderntitration systems are fully automated with precision pumps andsophisticated end point detection.With this modernization, applica-tions 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 situanalyzer for the measurement of seawater alkalinity led us to therealization that a tracer could be added to the titrant or sample toquantify the amount of titrant added,7 eliminating the need formeasurement of volume or mass. In ref 7, we hypothesized that atracer monitored titration (TMT) could be used for all typesof titrations, e.g., oxidation�reduction, complexometric, preci-pitation, etc. and that a wide range of tracers could be used. Thetracer could be any quantifiable chemical species (e.g., an ion, anabsorbing or fluorescent indicator or even a light scatteringparticle) and could be inert or participate in the reaction. Forexample, a tracer could be either a nonreactive chromophore oran indicator that is used to track the consumption of the analyte.If the tracer is an indicator, all forms of the indicator must absorblight so that total indicator concentration can be quantified at anypoint in the titration. Many indicators have this characteristic,

e.g., they change colors when reduced or complexed.3 If thetracer is inert, the equilibrium position of the titration must bedetermined by an alternative method. For example, an inertcolored tracer can be used in an acid�base titration with a glasspH electrode to monitor pH as the titration proceeds.

The TMT methodology can be understood by derivationfrom the simple titration mole (or mass) balance and is presen-ted here in a more general form than that shown in ref 7. At anypoint in a conventional titration, the mole balance is represen-ted by

½analyte�S �VS

Vmix�Q � ½titrant�T

VT

Vmix

¼ ½analyte�mix �Q � ½titrant�mix ð1ÞwhereQ is the reaction stoichiometry (mols analyte/mol titrant),[analyte]S is the analyte concentration in the sample, [titrant]T isthe concentration of the titrant being added, VS and VT are thesample and titrant volumes (or masses, not mentioned here-after), respectively, and the subscript “mix” denotes the equilib-rium concentrations in the sample�titrant mixture. The totalvolume is Vmix = VT + VS.

The volume ratios in eq 1 are the dilution factors of the titrant(fT) or sample (fS)

fT ¼ VT

Vmixand fS ¼ VS

Vmixð2Þ

In a conventional titration, the dilution factors are determinedwith measured volumes. In the TMT, dilution factors are

Received: September 27, 2011Accepted: November 9, 2011

ABSTRACT: Titrations, while primarily known as the chemical rite ofpassage for fledgling science students, are still widely used for chemicalanalysis. With its many years of existence and improvement, the methodwould seem an unlikely candidate for innovation, yet it is desirable, in thisage of autonomous sensing where analyzers may be sent into space or tothe bottom of the ocean, to have a simplified titrimetric method that doesnot rely upon volumetric or gravimetric measurement of sample andtitrant. In previous work on the measurement of seawater alkalinity, wefound that use of a tracer in the titrant eliminates the need to mea-sure mass or volume. Here, we show the versatility of the method for diversetypes of titrations and tracers. The results suggest that tracers may beemployed in all types of titrations, opening the door for greatly simplifiedlaboratory and field-based chemical analysis.

9218 dx.doi.org/10.1021/ac2025656 |Anal. Chem. 2011, 83, 9217–9220

Analytical Chemistry LETTER

independently determined using a tracer,

f ¼ VVmix

¼ ½tracer�mix½tracer�1

ð3Þ

where V is VT or VS, [tracer]mix is the tracer concentration inthe mixture, and [tracer]I is the initial tracer concentration inthe titrant or sample. The two dilution factors are related byfT + fS = 1.

In most titrations, titrant is added until an end point (ep) isreached, as indicated by, for example, a change in the color of anindicator. The ep corresponds approximately to the equivalencepoint where eq 1 is equal to zero. In a conventional titration,eq 1 is solved for [analyte]S and the corresponding amount oftitrant added at the end point, VT(ep), is used along with theknown titrant concentration and VS to determine the analyteconcentration:

½analyte�S ¼ Q � ½titrant�T � VTðepÞVS

ð4Þ

In the TMT, the corresponding dilution factor at the end point,fT(ep), determined with eq 3, is used

½analyte�S ¼ Q � ½titrant�T1=fTðepÞ � 1

ð5Þ

Equation 5 shows that no measurement of volume is required. Ifthe tracer is in the titrant, it can be added very accurately usingvolumetric or gravimetric methods. However, in cases where it isadvantageous to add the tracer to the sample or where an indicatormust be added to the sample, the change in volume must beinsignificant relative to the total volume or must be accounted forin the dilution factor calculation (see Materials and Methods).

While there have been many variations on the general theme, alltitrations have measured titrant and sample volumes, mass, or flowrate. Coulometric titrations use charge to quantify titrant, but samplevolume or mass must be measured.3,8 Other titration schemes haveused continuous pumping, but flow ratemust be carefully controlled,essentially making it a volumetric measurement.9�11With the TMT,the burden of performance is placed on the tracer measurementmethod rather than volumetric and gravimetricmeasurements. Someinstrumental methods, such as spectrophotometry and conductime-try, have precision and accuracy comparable tomeasurement ofmassand volume. In the first application of the TMT, precision of(0.1%was obtained using a pH indicator tracer and a simple dual-wavelength colorimeter.7 Here, we evaluate 3 additional titrationschemes with different tracers: (Scheme 1) a strong acid�strongbase titration using an inert dye tracer added to the titrant with pHelectrode detection of the end point; (Scheme 2) an oxidation�reduction titration of vitamin Cwith conductometric detection of aninert tracer (NaCl) and an indicator end point; (Scheme 3) a

complexation titration of calcium with an indicator added to thesample that acts as both tracer and endpoint detector.Our goal in theexperimental design was not to fully optimize each titration methodbut to determine the validity of the hypotheses outlined above. Asshown below, the TMT has great versatility and shows promise forapplication 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 theNaOH titrant. Absorbance was measured using a fiber-optic dipprobe with a 4 cm path length connected to a simple colorimeter(Brinkman PC910). The wavelength was set to 640 nm with abandpass filter. The dip probe was immersed in the sample�titrant solution during the titration. The pH was measured usinga Ross combination electrode connected to a benchtop pHmeter. Titrant was prepared by adding a dye stock solution tounstandardized 0.01MNaOH titrant. Titrations were carried outby adding increments of titrant with a precision pipet ((1%) to15.4, 41.3, and 65.0 mL sample volumes of∼0.01 M HCl, mixedwith a magnetic stirrer. The pipet was used so that conventionaland TMT-based titrations could be directly compared. After eachpipet addition, electrode pH and dip probe absorbance wererecorded. Absorbance and pH data were recorded until the pHinflection point was passed.

Beer’s law (A = εbc) was used to determine the dye concentra-tion during the titration where A is absorbance, ε is the dye molarabsorptivity, b is the optical path length, and c is the dyeconcentration. An effective molar absorptivity was calculated asfollows: 200 μL of dye stock was pipetted into 1 L of deionized(DI) water; absorbance was measured at room temperature usingthe dip probe, which registered an absorbance of 0.627, andeffective molar absorptivity was calculated. While molar absorp-tivities are temperature and matrix dependent, the sensitivity tothese environmental variables was not examined. The molarabsorptivity was used during a titration to calculate dye concen-tration 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 dehydroas-corbic acid (C6H6O6). Triiodide (I3

�) titrant (∼0.0075 M) wasprepared by dissolving ∼0.0025 M potassium iodate (KIO3) inexcess acidified (0.15 M H2SO4) potassium iodide (∼0.06 M,KI) solution.3 L-ascorbic acid concentrations ranged from 0.7 to1.4 μM. Ten drops (∼0.3 mL) of starch solution were added to∼100 mL of sample immediately before the titration. Specificconductance was selected as the tracer detection method. Althoughthe inherent conductivity of the titrant could be used as the tracer,the conductivity was increased so that reacting ions did notsignificantly alter the ionic composition during the titration. Todo this, solid NaCl tracer was added to the titrant to increase thetotal cation (H+ and Na+) concentration to ∼1.8 M. The specific

Scheme 1. Strong Acid�Strong Base Titration Reaction

Scheme 2. Redox Titration Reaction: The L-Ascorbic Acid(Vitamin C, C6H8O6) Oxidation3

Scheme 3. Complexation Titration Reaction: The Competi-tive Complexation Reaction of EthylenediaminetetraaceticAcid (EDTA) and Calmagite (CalMag) for Detection ofCalcium12



conductivity was measured at room temperature using a YSI 600multiparameter sonde calibrated with six NaCl/H2SO4 solutionsover the range expected in the sample�titrantmixture (0.25�0.60M).The slightly nonlinear calibration was fit with a second orderpolynomial. Sonde instrument calibrations did not show anysignificant change over a period of 1 month. Samples for analysiswere made from ascorbic acid dissolved in DI water. Titrationswere conducted by adding titrant with a volumetric buret untilthe blue starch end point was reached. As in Scheme 1, sampleand titrant volumes were recorded to allow comparison betweenthe conventional and TMT methods. Nonvolumetric titrationsof sample were also performed by adding titrant dropwise to∼100mL samples with a Pasteur pipet. To test themethod with areal sample, vitamin C tablets were prepared by dissolving thetablet in 100 mL of DI water and titrated by additions with aburet. The vitamin C concentration listed on the product labelwas used for comparison to the titration results.

Scheme 3. Calmagite indicator solution (5.248 � 10�4 M)was made by dissolving indicator in NH4Cl/NH4OH bufferdiluted to a final volume with DI water. Calcium standardsolutions (2.5�5.0� 10�3 M) were made from a stock solutionof CaCl2 dihydrate in DI water. EDTA titrant (8.395� 10�3 M)

was made by dissolving the disodium salt of EDTA in DI water.Spectrophotometric titrations were performed using a UV�visspectrophotometer (Agilent Model 8453) with titrant addeddirectly into a stirred 1 cm cuvette. The sample, along withseveral drops of buffer/indicator solution in accordance with thetraditional method,12 was placed in the cuvette. The initialdilution factor due to the buffer/indicator solution was calculatedusing eq 3. To make direct comparisons with the conventionaltitration, the titrant was added using an automated buret system.Absorbance was measured after each titrant addition. Totalcalmagite concentration was calculated at 537 and 610 nm usingthe molar absorptivities values approximated from Figure 3 in ref12 and are shown in Table 1.

’RESULTS AND DISCUSSION

Scheme1.Conventional and TMT acid�base titration curvesare very similar (Figure 1). In the conventional approach,titration curves of three different sample volumes for the sameanalyte concentration appear at different positions along thex-axis (Figure 1A). In the TMT, the position of each titrationcurve is identical showing that the TMT is independent of thesample volume used (Figure 1B). More sample requires propor-tionally more titrant, resulting in the same dilution factors at theend point for the same analyte concentration. The derivative ofthe titration curve was used to more accurately define the end point(Figure 1C). The precision and accuracy are not statisticallydifferent for both methods (Figure 2). Although there is a largeuncertainty in this comparison because of the few samplesanalyzed, these results show that an inert dye tracer can be used

Table 1. Molar Absorptivities of the Complexed (C) and Free(F) Forms of Calmagitea at their Absorbance Maxima (537and 610 nm)

εC537 18, 181

εC610 1, 764

εF537 12, 518

εF610 20, 305a From ref 12. Units are M-1 cm-1.

Figure 1. Conventional (A) and TMT (B) titrations of a strong acidwith a strong base (Scheme 1) of three different volumes of strong acidsample (∼15, 41, and 65 mL). The dilution factor was calculated usingeq 3 by monitoring the concentration of an inert dye (brilliant blue).The derivative of the titration data (C) was used to determine the endpoint (shown only for the TMT data).

Figure 2. Comparison of precision and accuracy for conventional(green) and TMT (purple) methods. The number of samples analyzedfor 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 levelfor all comparisons except accuracy for titration schemes 2b and 3. The“real sample” in titration scheme 2b was a vitamin tablet with a knownvitamin C content. In titration scheme 2c, titrant was added with anonvolumetric pipet. No corresponding conventional analysis waspossible in this case (NA).



with a simple colorimeter to perform acid�base titrations. Noattempt was made to perform more replicates or to furtheroptimize themethod. In this case, the precision was controlled bythe volume increments added around the end point and the fewsamples analyzed. Accuracy is within the uncertainty of theunstandardized NaOH used in the analysis.Scheme 2. The precision and accuracy are not statistically

different for the conventional and TMT methods for analysis ofvitamin C standards using the visual (starch) end point (Figure 2,titration scheme 2a). Similar or better performance was obtainedwhen analyzing a real sample (Figure 2, titration scheme 2b) andwhen the titrant�tracer mixture was added using a nonvolu-metric (Pasteur) pipet (Figure 2, titration scheme 2c). As we hadoriginally hypothesized, high quality titrations can be obtainedwith the TMT using simple glassware (e.g. beaker and Pasteurpipet) or, as in the first incarnation of the TMT, an inexpensivesolenoid pump.7 In this example, the TMT requires a conduc-tivity sensor to detect the tracer. Many precise and accurateconductivity probes are commercially available for this purposelike the YSI probe used here. Regarding interferences, in thistitration, the conductivity sensor could be calibrated by simpledilution of the titrant solution because the dilute sample solutiondid not alter the relative ion concentrations. If higher ionconcentrations are present, e.g., in seawater, the conductivitysensor calibration standards should be made accordingly. Someknowledge of the sample matrix would be necessary to customizethe conductivity calibration for specific sample types.Scheme 3. The conventional and TMT spectrophotometric

complexometric titration curves of calcium (Ca) samples are verysimilar (Figure 3). The precision is not statistically different forthe conventional and TMT methods (Figure 2). However, theaccuracy differed for the two methods. The slightly lower TMTaccuracy could result from error in the complexing-agent molarabsorptivities (see Materials and Methods). In this analysis, thetracer is added to the sample and the dilution factor is based uponthe dilution of the tracer/indicator as titrant is added. Theindicator concentration is calculated as the sum of the complexedand uncomplexed forms using Beer’s law, and any uncertainty inthe molar absorptivities, e.g., caused by changes in solvent or solutecomposition, will result in a systematic error.7 Importantly, a samplebackground absorbance within the indicator wavelength range foran indicator-based TMT (e.g., Schemes 1 or 3) would cause aninterference as the sample is diluted with titrant.

’CONCLUSIONS

These results establish that theTMTmethodology eliminates theneed for volumetric and gravimetric measurements of titrant andsample forwidely 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 untilthe end point is reached (titration scheme 2c). It retains theadvantages of classical titrations, that is precise, accurate, andselective analyses can be performed without sample standards if astable tracer detection method is available, e.g., conductivity orspectrophotometry. The TMT is ideally suited for spectrophoto-metric methods because the measurement uses the optical char-acteristics of the tracer (molar absorptivities) and absorbances,which do not depend upon instrument calibration.5�7 Many waterquality and industrial measurements can be made on-site, usinghand-held colorimeters with premixed reagents,13 but titration-based analyses are not currently possible with these devices. It isin this area, where more complex equipment is not suitable, that theTMT may find its widest applications.

’AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

’ACKNOWLEDGMENT

We thank Cory Beatty (UM) for technical assistance andBrian Steele (UM) for discussions. Grants from theU.S. NationalScience Foundation Division of Ocean Sciences supported thisresearch (OCE-0628569 and OCE-0327763). D.M.E. was sup-ported by an NSF EPSCoR assistantship (EPS-0701906). A.Z.was supported by an NSF REU scholarship (REU-0649306).

’REFERENCES

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Figure 3. Conventional (red, top axis) and TMT (blue, bottom axis)spectrophotometric EDTA complexation titrations of the same Casample. Uncomplexed (Ca-free) calmagite absorbance at 610 nm,A (610 nm), stops increasing at the end point when the EDTA hascomplexed all of the Ca and dilution by the titrant begins to dominatethe signal. Best-fit lines for the data on either side of the titrationinflection point were used to obtain a more accurate end point.

universal tracer monitored titrations

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