In the Laboratory
W
Comparing the Titrations of Mixed-Acid Solutions Using Dropwise and Constant-Flow Techniques Paul Charlesworth,* Matthew J. Seguin, and David J. Chesney Department of Chemistry, Michigan Technological University, Houghton, MI 49931-1295; *
[email protected] Background Titration of a mixture of phosphoric acid and hydrochloric acid (3, 14–17) is complicated by the fact that even though phosphoric acid is a weak acid, the K1 (7.11 × 10᎑3; ref 18) is sufficiently large that it cannot be differentiated from the proton of the strong acid HCl in a typical titration. The second dissociation of phosphoric acid, K2 (6.32 × 10᎑8; ref 18), is also large enough that its endpoint appears as a significant inflection in a titration plot of pH as a function of titrant volume. Phosphoric acid’s third dissociation, K3 (7.08 × 10᎑13; ref 18), is weak enough that it does not appear as a rapid increase in pH, so the titration is usually concluded after the second equivalence point has been reached. During a mixed-acid titration, the first noticeable end point (Veq1, H3PO4 → H2PO4− completed) corresponds to the volume of NaOH required to neutralize both the first proton of H3PO4 and the strong proton dissociation of HCl. The volume difference between Veq1 and the second noticeable endpoint (Veq2, H2PO4− → HPO42− completed) is defined as (∆V ). The volume difference, ∆V, corresponds to the quantity of titrant required to neutralize the second proton on H3PO4. Multiplication of the volume, ∆V, by the titrant molarity gives the number of moles of H3PO4 in the sample. Subtracting ∆V from Veq1 gives the volume of titrant that is used to find the number of moles of HCl in a similar fashion (Figure 1). Traditionally, mixed-acid analyses are performed with a buret–pH meter system, where the student delivers small in-
crements, dropwise at times, from a buret and records pH as a function of the titrant volume. The data are entered into a spreadsheet and a pH versus volume plot constructed prior to evaluation. The first derivative (dpH兾dV ) can be taken to determine the exact inflection points Veq1 and Veq2. These volumes are subsequently used to determine the quantity of each acid in the sample. This process can typically take a student up to 2 hours to collect the data from three trials and up to 2 or more additional hours to evaluate, depending on the student’s ability and the quantity of data points recorded. Performing these titrations using a Mariotte bottle and a pH electrode connected to either a pH meter linked to a strip chart recorder or directly to a computer interface can significantly reduce data collection and analysis time while maintaining good accuracy. Evaluating Errors Associated with a Constant-Flow Titration A Mariotte bottle was constructed and used in conjunction with a pH meter linked to a strip chart recorder for evaluating the error associated with constant-flow titrations. Details for construction and use of the apparatus can be found in the Supplemental Material.W The Mariotte bottle’s flow rate was determined by measuring the time to fill a 10.00-mL volumetric flask. This process was repeated three times and the results averaged. The chart speed was determined by first setting the recorder to a speed of 15 cm min᎑1 and marking a starting line on the paper. Simultaneously, the chart drive and a stopwatch were started and the paper allowed to feed for about 45 seconds 12
Veq1
∆V
Veq2
∆V
10
H3PO4
HCl 8
pH
This article describes a series of experiments that compare the accuracy of titrations performed using constant-flow techniques with those from the more traditional dropwise techniques. The individual experiments have been adapted to increase student interest (1, 2) in the undergraduate classroom by combining techniques from published automated titrations (3–10) with those from published data collection devices (5, 10–13). While the individual components have been investigated at a research level, we are unaware of studies that make a direct comparison between the techniques and study their incorporation into the undergraduate classroom. Based on accuracy, student skill level, quantity of time allotted, and available resources, results suggest that constantflow techniques are the most practical for students to use. Furthermore, this article presents solutions to technical problems that can affect the quality of data collected with constant-flow techniques (see the Supplemental MaterialW). Although this article is a comparison of dropwise and continuous titration methods, it is expected that instructors will select one of the techniques as a single student experiment rather than reproducing the whole comparison.
6
4
2
0
2
4
6
8
10
12
14
16
18
Titrant Volume / mL Figure 1. Titration curve showing how each acid concentration is identified. Each ∆V represents the complete titration of one proton from phosphoric acid.
JChemEd.chem.wisc.edu • Vol. 80 No. 11 November 2003 • Journal of Chemical Education
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In the Laboratory Table 1. Results from Different Techniques Showing the Propagated Error (e) Technique
Trials
Average HCl mmol ± e
Average H3PO4 mmol ± e
HCl Std Dev
H3PO4 Std Dev
Dropwise
4
0.456 ± 0.043
0.756 ± 0.043
0.019
0.019
Constant-flow, strip chart
10
0.456 ± 0.088
0.767 ± 0.079
0.021
0.058
Vernier
10
0.455 ± 0.031
0.760 ± 0.054
0.013
0.063
before measuring the distance traveled by the pen and computing a ratio in cm sec᎑1. This process was repeated three times and the results averaged. The amount of acid in millimoles was calculated from the distance traveled on the strip chart recorder using eq 1 amount acid (mmol) = distance (cm) ×
1
(
)
chart speed cm s −1
(
)
× flow rate a mL s −1
(
(1)
)
× titrant strength mmol mL−1
A computer interface capable of collecting pH as a function of time can be used in conjunction with the Mariotte bottle. Performing the experiment with a computer interface dramatically decreases experimental uncertainty. This is because the only calibration step involving a standard deviation is the flow-rate calibration. In the computer-based experiments, an Orion Combination pH electrode was connected directly to a computer interface linked to the computer by a serial cable. The Mariotte bottle was prepared and the flow rate calibrated as described previously. No further calibration procedures were required with the computer interface because the software accompanying each interface can routinely plot pH as a function of time. The titrant volume was calculated by multiplying the flow rate by the time taken to reach the endpoint. A 2.5-L stock solution of NaOH was prepared and standardized against dried, analytical-grade potassium hydrogen phthalate. A 2.5-L stock mixed-acid solution, ∼0.02 M HCl and ∼0.03 M H3PO4, was also prepared. The same mixedacid sample and titrant was used for both the dropwise and the constant-flow error analysis.
Dropwise Determination An Orion Combination pH electrode was used in conjunction with a pH meter (Fisher Scientific Model #915) and standardized against 1.0 M buffer solutions. A 50.00-mL aliquot of mixed acid was volumetrically delivered into a 400mL beaker. The pH probe was submerged and an initial pH was recorded. Sodium hydroxide was added, dropwise near the equivalence points, and the pH was recorded as a function of titrant volume. The data were used to produce a d pH兾dV versus volume curve to find Veq1 and Veq2. These volumes were used to calculate amount (moles) of each acid in the sample. 1312
Constant-Flow Determination An Orion Combination pH electrode was connected to either a pH meter (Fisher Scientific Model #915) linked to a strip chart recorder or directly to a computer interface, and standardized against 1.0 M buffer solutions. A 25.00-mL aliquot of the mixed-acid sample was volumetrically delivered to a 150-mL beaker along with a magnetic spin bar. The Mariotte bottle was filled with standardized NaOH (volumetrically diluted by 50%), calibrated, and prepared as described in the Supplemental Material.W Simultaneously the stopcock was opened and the data collection was started. The pH curves were used to find Veq1 and Veq2. These volumes were used to calculate moles of each acid in the sample. The volumes obtained using the dropwise technique were considered to be the actual value and all other values were compared to those (Table 1). Constant-flow techniques produced results that were comparable to those obtained by the traditional dropwise technique regardless of whether a strip chart or Vernier system was used for data collection. The standard deviations listed for the computer interfaces were not a function of precision, but of the measurements made during the calibration steps and of the volume required to reach the equivalence point, which could fluctuate via small changes in spin rate or pipetting errors. Hazards These experiments utilize 0.02 M HCl and 0.03 M H3PO4, solid weak organic acids, and 0.1 M NaOH, that are irritating to the eyes and mucous membranes. Safety glasses should be worn at all times while in the lab. Avoid prolonged exposure to vapors. Goggles and gloves should be worn while preparing solutions from concentrated reagents. A lubricant such as glycerol should be used when inserting the glass tube into the rubber stopper when preparing the Mariotte bottles. Student Experiments The lab documentation, found in the Supplemental Material,W presents experiments suitable for two different levels of chemistry. The Equivalent Mass of an Unknown Acid is intended for use in the general chemistry lab and the MixedAcid Analysis procedure is intended for use in a quantitative analysis chemistry course. The experiments have different expectation levels in terms of structure, experimental setup, precision, and lab report. Quantitative analysis students, for example, were required to assemble their own Mariotte bottle, adjust the hy-
Journal of Chemical Education • Vol. 80 No. 11 November 2003 • JChemEd.chem.wisc.edu
In the Laboratory
draulic head, and calibrate the whole instrument. The general chemistry students, however, were provided with the complete instrument and instructed not to modify the hydraulic head. The precision and extent of the calibration methods required for quantitative analysis courses were also considerably greater than those needed for general chemistry courses. This was primarily because our quantitative analysis laboratories are typically assessed based on accuracy, where general chemistry laboratories are normally assessed based on completeness and effort. Data from seven randomly selected quantitative analysis students are presented in Table 2. Each student performed both the mixed-acid analysis using dropwise addition near the equivalence points and the constant-flow technique using a Mariotte bottle and pH meter linked to a strip chart recorder. The results show the absolute difference (in mmoles for each acid) between the actual value (determined dropwise by the instructor) and the student-determined value for each technique. Most students obtained more accurate results with the constant-flow technique than they did with the dropwise technique. Although it is difficult to draw broad conclusions owing to the small sample size, our data show that the difference is significant for the students in this study, when using a two-tailed t-test at the 95% confidence level. Surveys were administered to evaluate student learning and satisfaction related the dropwise and constant-flow techniques. There was a clear indication that the students preferred the constant-flow technique to the dropwise technique, and that those students using the constant-flow technique exhibited greater conceptual understanding than those using the dropwise technique. A two-tailed t-test showed this is significant at the 95% confidence level. Further details and copies of the surveys and tests may be found in the Supplemental Material.W Conclusion This study shows that performing a constant-flow mixedacid analysis using a Mariotte bottle dramatically decreases data collection and analysis time from over two hours to under one hour, while maintaining a high degree of accuracy. Replacing the pH meter and strip chart recorder with a computer interface reduces setup time and eliminates errors normally associated with strip chart calibration. Furthermore, this study shows that the constant-flow techniques can be successfully implemented into student laboratories at both the general chemistry and the quantitative analysis levels with only minor modification as described in the Supplemental Material.W Students from the quantitative analysis course who performed the mixed-acid analysis using both the dropwise and constant-flow techniques reported that they preferred the constant-flow technique and believed that it helped them to understand key concepts pertinent to this type of titration. Students in the general chemistry course who used the constant-flow technique for unknown acid identification showed a statistically significant increase in post-test score relative to those students who used the dropwise technique. These students also more consistently identified their unknown and did so in one class period compared to the two class periods required by students using the dropwise technique
Table 2. Comparison of the Absolute Difference between the Student’s Experimental Value and Actual Valuea for Each Acid Utilizing the Dropwise and Constant-Flow Techniques Student
Dropwise Technique/ mmol
Constant-Flow Techniqueb/ mmol
HCl
H3PO4
HCl
H3PO4
1
0.026
0.028
0.013
0.054
2
0.024
0.020
0.018
0.036
3
0.018
0.035
0.013
0.012
4
0.037
0.025
0.011
0.067
5
0.026
0.029
0.002
0.016
6
0.013
0.028
0.015
0.026
7
0.018
0.027
0.012
0.048
a
Actual values determined by the dropwise technique performed by the instructor. b
Mariotte bottle and strip chart were used.
W
Supplemental Material
Student procedures for both a general chemistry lab and a quantitative analysis lab, quantitative analysis lab student questionnaire, general chemistry lab quiz, assessment of the labs, instructor guide to the labs, potential error sources, and instructions for constructing a Mariotte bottle are available in this issue of JCE Online. Literature Cited 1. Wise, M.; Groom, F. M. Education 1996, 117, 61–69. 2. Brungardt, J. B.; Zollman, D. J. Res. Sci. Teach. 1995, 32, 855–869. 3. Hopkins, H. P.; Hamilton, D. D. J. Chem. Educ. 1994, 71, 965–966. 4. Lynch, J. A.; Narramore, J. D. J. Chem. Educ. 1990, 67, 533– 535. 5. Ogren, P.; Nelson, S.; Henry, I. J. Chem. Educ. 2001, 78, 353– 355. 6. Bartroli, J.; Alerm, L. Anal. Chim. Acta 1992, 269, 29–34. 7. Headrick, K. L.; Davies, T. K.; Haegele, A. N. J. Chem. Educ. 2000, 77, 389–390. 8. Cazallas, R.; Fernández, L. A.; Etxebarria, N.; Madariaga, J. M. Lab. Robotics Automation 1993, 5, 161–169. 9. Fox, J. N.; Shaner, R. A. J. Chem. Educ. 1990, 67, 163–164. 10. Meyer, E. F. J. Chem. Educ. 1992, 69, A158–A160. 11. Currie, J. O., Jr.; Whiteley, R. V. J. Chem. Educ. 1991, 68, 923–926. 12. Ritter, D.; Johnson, M. J. Chem. Educ. 1997, 74, 120–123. 13. Gipps, J. J. Chem. Educ. 1994, 71, 671–674. 14. Cooper, E. I.; Rath, D. L. Method for Analyzing pH Titration Data. U.S. Patent 5,640,330, 1997. 15. Lieu, V. T.; Kalbus, G. E. J. Chem. Educ. 1988, 65, 184–185. 16. Ni, Y. Anal. Chim. Acta 1998, 367, 145–152. 17. Papanastasiou, G. Z.; Ziogas, I. Talanta 1995, 42, 827–836. 18. Harris, D. C. Quantitative Chemical Analysis, 5th ed.; W. H. Freeman and Co.: New York, 1998; p AP2.
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