In the Laboratory
Potentiometric Measurement of Transition Ranges and Titration Errors for Acid/Base Indicators Paul A. Flowers Department of Physical Science, University of North Carolina at Pembroke, Pembroke, NC 28372-1510
Potentiometric titrations based on neutralization, precipitation, and redox reactions are standard fare in sophomore analytical chemistry laboratories. In the case of neutralization reactions, such experiments are typically concerned with either the determination of an acidic or basic analyte or its identification via molar mass and pK data derived from the measured titration curves. A 1987 survey showed that potentiometric neutralization titrations of this type were included in the laboratory curricula of 82% of all responding institutions (1). Several reports in this Journal have described extensions of and variations on this theme, including computer-assisted data acquisition (2), alternative data analysis schemes (3), and applications to the analysis of household cleaners (4) and cola beverages (5). Further in this regard, the typical sophomore analytical chemistry classroom devotes a substantial amount of lecture time to acid/base equilibrium theory (1) as it relates to indicator transition ranges and subsequent titration errors. In an effort to provide students a laboratory experience supporting their classroom discussions on this important topic, I have developed an experiment involving potentiometric measurement of transition ranges and titration errors for common acid/base indicators. Similar in nature to the classroom demonstration described by Nathan (6), this procedure entails the potentiometric titration of a millimolar HCl solution containing an indicator with comparably dilute NaOH. The pH and visually assessed color of the reaction solution are monitored as a function of added titrant volume, and the resultant data are plotted to permit determination of the indicator’s transition range and associated titration error. A related experiment evaluating endpoint precisions and errors for several indicators in the standardization of HCl against Tris has been described (7), though the procedure employed only chemical endpoint detection. By simultaneously monitoring solution pH, the experiment reported here permits estimation of indicator transition ranges and, further, affords students additional experiences in potentiometric measurements and graphical data analysis. Student response is typically quite positive, and the measured quantities correlate reasonably well to literature values as described below. Experimental Procedure Standard HCl and NaOH (ca. 0.1 M) prepared for a previous experiment are diluted 100-fold with boiled distilled water to yield roughly 0.001 M solutions. These concentrations are suitable for observing the transition ranges of the chosen indicators: bromocresol green (BG), bromothymol blue (BB), and phenolphthalein (PT). After calibrating a pH meter with standard buffer solutions, a convenient volume of the acid sample (e.g., 10–15 mL for a 25-mL buret) and a few drops of BG so-
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lution are subjected to the usual potentiometric titration procedure, but including careful measurement of the titrant volume and solution pH corresponding to the first noticeable change in solution color (V1 and pH1) and the first appearance of the “completely” basic indicator color (V2 and pH2). These color changes are best distinguished by comparison to color-standard solutions prepared by adding a few drops of BG solution to separate flasks containing the acid sample and base titrant. The procedure is then repeated using BB and PT indicators. Data Analysis The pH/volume data are plotted for each of the three different titrations. On each plot, the potentiometrically determined endpoint is determined in the usual fashion, and the observed indicator transition range, pH 1 to pH2, is noted. By accepting the potentiometric endpoint as the equivalence point, Veq, two titration errors may then be defined as follows: E1 ≡ V1 – Veq (for titration to first noticeable color change)
(1)
E2 ≡ V2 – Veq (for titration to complete color change)
(2)
Though the data are not shown here, I have occasionally required students to generate theoretical titration curves based on the known concentrations of their acid and base solutions, and to estimate titration errors using these curves and literature values for the indicator transition ranges. Results and Discussion One typical student’s data obtained using PT indicator solution are shown in Figure 1. The measured transition range, 8.0–9.1, is labeled “A” in Figure 1, and the corresponding titration errors of roughly +0.8 and +3.0 mL are labeled “B” (first color change) and “C” (complete color change), respectively. Cumulative student data for one class are summarized in Table 1 along with literature values for the indicator transition ranges. Given the highly subjective nature of color perception and the small size of the data set, the agreement between measured and literature values may certainly be viewed as satisfactory. A rigorous statistical analysis of these data is not possible, as the employed procedure did not involve replicate measurements and the pooled data set thus has zero degrees of freedom. I omitted replicate analyses in order to reduce laboratory time and permit the examination of several indicators by each student, though the procedure may, of course, be modified to include replications if statistical analysis of the data is desired. Likewise, minor variations on the experimental procedure would permit examination of other indicators, weak or polyfunctional acids and bases, or titrations based on
Journal of Chemical Education • Vol. 74 No. 7 July 1997
In the Laboratory
Table 1. Potentiometrically Measured Transition Ranges and Relative Titration Errors for Three Indicators Indicatora
Transition Range (Literature)b (mL)
Average Transition Range (Measured)c (mL)
Average Minimal Relative Titration Errorc (%)
BG
3.8 – 5.4
3.9 – 5.6
{7.5
BB
6.0 – 7.6
5.7 – 7.3
+1.6
PT
8.0 – 9.6
7.8 – 9.0
+3.0
a
Figure 1. Plot of pH vs. titrant volume for titration of ca. 0.001 M HCl with ca. 0.001 M NaOH using phenolphthalein as indicator. Shown on the plot are the transition range (A) and errors for titration to the first color change (B) and to a complete color change (C).
other reaction classes (e.g., redox). Student response to this experiment is generally quite favorable, and its results often generate a good deal of discussion on equilibrium topics and other related issues. In addition to demonstrating what constitutes an “appropriate” indicator for a given titration, students also gain an appreciation of the importance of certain procedural details, for example, titrating to a green versus a blue BG endpoint. Further, this experiment can provide an excellent segue to the traditional laboratory involving photometric determination of an acid/base hydrolysis constant. Realizing that an indicator’s transition range must encompass its pK value, students may use their potentiometric data to select appropriate pH values for preparation of three separate indicator solutions of appropriate speciation (i.e., containing the acid form only, the base form only, and a mixture of both).
BG = bromocresol green; BB = bromothymol blue; PT = phenolphthalein. b From Harris, D.C. Quantitative Chemical Analysis; W. H. Freeman: New York, 1995; p 296. c N = 7, minimal relative titration error ≡ E/ Veq × 100%, where E is the lesser of E1 and E2 (see eqs 1 and 2 of text).
Acknowledgment I wish to acknowledge my graduate mentor, the late Gleb Mamantov, for years of dedicated support and encouragement. Literature Cited 1. Locke, D. C.; Grossman, W. E. L. Anal. Chem. 1987, 59, 829A– 835A. 2. Lynch, J. A.; Narramore, J. D. J. Chem. Educ. 1990, 67, 533– 535. 3. Castillo, S.; Carlos, A.; Jaramillo, A. J. Chem. Educ. 1989, 66, 341. 4. Lieu, V. T.; Kalbus, G. E. J. Chem. Educ. 1988, 65, 184–185. 5. Murphy, J. J. Chem. Educ. 1983, 60, 420–421. 6. Nathan, L. C. J. Chem. Educ. 1973, 50, 262. 7. Harvey, D. T. J. Chem. Educ. 1991, 68, 329–331.
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