Using Conductivity Measurements To Determine the Identities and

Laboratory Experiment pubs.acs.org/jchemeduc

Using Conductivity Measurements To Determine the Identities and Concentrations of Unknown Acids: An Inquiry Laboratory Experiment K. Christopher Smith* and Ariana Garza Department of Chemistry, University of Texas-Pan American, 1201 West University Drive, Edinburg, Texas 78539-2999, United States S Supporting Information *

ABSTRACT: This paper describes a student designed experiment using titrations involving conductivity measurements to identify unknown acids as being either HCl or H2SO4, and to determine the concentrations of the acids, thereby improving the utility of standard acid−base titrations. Using an inquiry context, students gain experience with titrations, conductivity, procedural design, and analysis of results. The results of the experiment indicate that it is robust enough for use with advanced high school or college general chemistry students.

KEYWORDS: High School/Introductory Chemistry, First-Year Undergraduate/General, Laboratory Instruction, Inquiry-Based/Discovery Learning, Acids/Bases, Conductivity, Titration/Volumetric Analysis

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This experiment is characterized as an open inquiry experiment.4 Students are not provided with instructions on the procedure or the analysis of results, and it is designed for students who have had experience with standard titration experiments. As such, this experiment is suitable for advanced high school or college general chemistry students. In addition, it is possible that students have no previous experience with conductivity measurements, so students are directed to an information resource on conductivity measurements in the experimental handout (see Supporting Information). Student learning objectives for this laboratory experiment include giving students experience designing their own experiments and conducting their own unscripted data analysis. Other learning objectives are to give students hands-on experience with chemical instrumentation and measurements involving conductivity probes, and to have them engage in the graphical analysis of data.

ost general chemistry courses include experiments involving titrations where students determine the concentration of an unknown acid by titration with standardized sodium hydroxide (NaOH). In the usual titration, students record the volume of NaOH required to neutralize a chosen volume of unknown acid, and the neutralization end point is determined by an indicator or instrument.1 Students relate the stoichiometric amounts of hydroxide (OH−) and hydronium (H+) ions to determine the concentration of the unknown acid. Such titrations do not allow for the identification of the unknown acid and students would not be able to distinguish between, for example, 0.30 M hydrochloric acid (HCl) and 0.15 M sulfuric acid (H2SO4). For students to determine the concentration of the unknown acid, they must be given either the identity (HCl, H2SO4, etc.) or the proticity (monoprotic, diprotic, etc.) of the unknown acid. This experiment is designed so that students can use conductivity measurements to identify unknown acids as being either HCl or H2SO4, and to determine the concentrations of the unknown acids. The conductivity of a solution depends on several factors including solute concentration and temperature.1 Conductometric titrations have also been applied to acid−base systems.2,3 In this experiment, students are required to design a procedure using titrations with standardized NaOH, conductivity measurements, and conductivity data provided to them to determine the identity and concentration of two unknown acids. © XXXX American Chemical Society and Division of Chemical Education, Inc.

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EXPERIMENTAL OVERVIEW Students use titrations with standardized NaOH and the conductivity data in Table 1 to identify their unknown acids as either HCl or H2SO4, based on the salt produced in the titration being either NaCl (from HCl) or Na2SO4 (from H2SO4). The students are also required to determine the concentration of each of their unknown acids. The conductivity data in Table 1 were collected between 22.0 and 22.9 °C using

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DOI: 10.1021/ed500905q J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Laboratory Experiment

Table 1. Concentrations and Conductivities of Various Salts Sodium chloride (NaCl)

Linear

y = 162200x + 716.1

(R2 = 0.996)

(3)

Sodium sulfate (Na2SO4)

Concentration (M × 10−3)

Conductivity (μS/cm)

Concentration (M × 10−3)

Conductivity (μS/cm)

99.40 79.52 59.64 38.77 19.38 9.692 4.846

11083 9017 6938 4604 2231 1125 504

100.2 80.15 60.11 39.07 19.54 9.769 4.884

16496 13799 10876 7463 4086 2125 1053

Polynomial

y = − 399032x 2 + 202650x + 163.27

(R2 = 0.9999)

(4)

As can be seen, the conductivity data fit equally well to either function for NaCl, but fit best to the polynomial function for Na2SO4. During a titration of either HCl or H2SO4 with NaOH, the conductivity of the neutralized salt solution at the end point (NaCl from HCl or Na2SO4 from H2SO4) can be used to identify the acid. Theoretically, when 25.00 mL of an unknown acid (either HCl or H2SO4) is titrated to the colorimetric end point with 60.00 mL of 0.100 M NaOH, 0.00600 mol of OH− ions have been neutralized in the titration. This corresponds to 0.00600 mol of H+ having been present in the unknown acid. If the unknown acid was HCl, the 0.00600 mol of H+ ions would correspond to 0.00600 mol of HCl, which corresponds to 0.00600 mol of sodium chloride (NaCl) at the end point. With an end point volume of 85.00 mL, the concentration of NaCl would be 0.0706 M. This would yield a conductivity of 8110 μS/cm using the polynomial function (eq 2) for NaCl presented earlier. Using similar reasoning (and accounting for the different stoichiometric factors between H+ ions and H2SO4), if the unknown acid was H2SO4, then the Na2SO4 present at the end point would yield a conductivity of 6820 μS/ cm. By comparing the end point conductivity calculated using eqs 2 and 4 to the experimental measurement of the conductivity of the neutralized solution, one can conclude which salt (NaCl or Na2SO4) is present in the solution. This information would allow for the determination of the identity and concentration of the unknown acid.

a Vernier conductivity probe (Vernier Software & Technology, Beaverton, OR) with a high range of 0 to 20 000 μS/cm and a resolution of 10 μS/cm.5 The conductivity probe was calibrated before each measurement. In general chemistry laboratory experiments, the concentrations of acids used are typically low, on the order of 0.1 M. As such, salt concentrations of 0.1 M and lower are presented in Table 1. The conductivity of a salt solution reaches a maximum at a higher concentration, typically greater than 2 M, and then begins to decrease.6 Plots of the data presented in Table 1 are shown in Figure 1.

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EXPERIMENTAL PROCEDURES This experiment was carried out by seven students in a chemistry elective course designed for preservice chemistry teachers. There was one conductivity probe in the laboratory, and students worked individually. The first student finished in 1 h and 5 min, while the last student finished in 2 h and 15 min. One week prior to conducting the experiment, the students were given a handout containing the conductivity data in Table 1 and information on the experimental theory (see Supporting Information). Students were instructed to design an experimental procedure that would use acid/base titration and conductivity to determine the identity and concentration of an unknown acid. On the day of the experiment, students reviewed their experimental procedures with the instructor. The instructor reviewed the procedures primarily for safety concerns. Several of the students’ procedures required them to have their own conductivity probe for the duration of the experiment. After being informed by the instructor that there was just one conductivity probe per lab, these students adjusted their procedures accordingly. The majority of the students developed experimental procedures that involved titration of a measured volume of the unknown acid with standardized NaOH followed by determination of the conductivity with the probe. One student’s procedure called for the dilution of a chosen volume of the unknown acid before titration with standardized sodium hydroxide solution, because this student remembered that

Figure 1. Plot of conductivity versus concentration for sodium chloride and sodium sulfate.

The data shown in Table 1 were fit to a linear function and a polynomial function. The data were fit to a linear function because they appear approximately linear when plotted and students were perhaps likely to use a linear function in their analysis. The data were plotted to a polynomial function because at increasing concentrations the conductivity of a solution begins to decrease and appear to fit to a polynomial function.6 The data shown in Table 1 can be fit to either a linear or a polynomial function as shown. For NaCl: Linear

y = 112280x + 79.293

Polynomial

(R2 = 0.999)

(1)

y = − 135704x 2 + 125928x − 105.77

(R2 = 0.9999)

(2)

For Na2SO4: B




Table 2. Experimental Conductivities, Calculated Conductivities, Concentrations, and Percent Error for Student Neutralized Unknown Acid Solutions Neutralized Unknown Acid Solution

Experimental Conductivity (μS/cm)

Calculated Conductivity if the Unknown Acid Was HCl (aq)

Calculated Conductivity if the Unknown Acid Was H2SO4(aq)

Calculated Concentration of the Unknown Acid (M)

Percent Error (%)

A A A A B B B C C C

6747 7880 7891 7847 7002 6701 6682 6924 6960 6871

7490 8630 9100 8960 6710 6410 5920 7990 7850 7590

6320 7250 7630 7520 5680 5440 5040 6720 6610 6400

0.185 0.154 0.200 0.184 0.134 0.122 0.103 0.114 0.107 0.0963

6.6 22.2 1.0 7.1 3.9 5.4 20.2 4.6 1.8 11.7

Table 3. Experimental Conductivities, Calculated Conductivities, Concentrations, and Percent Error for Author Neutralized Unknown Acid Solutions Neutralized Unknown Acid Solution

Experimental Conductivity (μS/cm)

Calculated Conductivity if the Unknown Acid Was HCl (aq)

Calculated Conductivity if the Unknown Acid Was H2SO4(aq)

Calculated Concentration of the Unknown Acid (M)

Percent Error (%)

A A B B C C

7707 7942 6721 6699 6956 6984

9080 9070 6540 6560 7880 7890

7620 7610 5540 5560 6630 6640

0.198 0.197 0.128 0.129 0.109 0.109

0 0.5 0.8 0 0 0

conductivity measurements at all. These procedures do not make use of the conductivity data in Table 1 and would not yield results relevant to identifying the unknown acid. These types of procedures highlight the importance of students understanding that the experimental data they planned to collect should be related to the conductivity data in Table 1.

previous titration experiments performed in general chemistry called for dilution of the acid before titrating. Three unknown acid solutions were prepared for the experiment and labeled as “A”, “B”, and “C”. Each student was assigned one or two of the unknown acids such that each unknown acid would be analyzed by at least three students. The students were provided with standardized 0.100 M NaOH to use in their titrations. The temperature during the experiment ranged from 19.5 to 20.1 °C, whereas the conductivity data in Table 1 were collected between 22.0 and 22.9 °C. Students were prompted to consider these temperature differences when conducting their experiments and analyzing their data. This experiment was also carried out as a “dry run” with 35 students in the second semester of a two-semester university freshman level general chemistry course sequence. These students designed their own procedures but did not conduct the experiment. These general chemistry students developed a greater range of experimental procedures compared to the preservice chemistry teacher students, but all of the experimental procedures were not appropriate. Nine of the general chemistry students’ procedures involved titration of a measured volume of the unknown acid with standardized NaOH while determining conductivity with the probe during the entire titration, whereas eight of the students’ procedures involved titration of a measured volume of the unknown acid with standardized NaOH followed by determination of the conductivity with the probe. Both of these procedures were appropriate and would yield relevant results. In contrast, 13 of the general chemistry students’ procedures involved titration of a measured volume of the unknown acid with standardized NaOH followed by determination of the conductivity of a fresh sample of the unknown acid itself, while five of the students’ procedures involved titration of a measured volume of the unknown acid with standardized NaOH with no

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HAZARDS The acids (HCl and H2SO4) and base (NaOH) used in this experiment are in low concentration, but are still corrosive to skin and eyes as well as irritating to the respiratory tract upon inhalation. These compounds should be used in a well ventilated area with eyewash and shower facilities. In addition to full coverage clothing and shoes, chemical splash goggles should be worn at all times. Nitrile or polyethylene gloves should be worn to protect from splash contact. If contact occurs, the affected area should be washed with plenty of tepid water for at least 20 min for acids and 30 min for base. Seek medical advice if needed.

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RESULTS AND DISCUSSION The actual identity and concentration of the unknown acids were as follows: “A” was 0.198 M H2SO4, “B” was 0.129 M HCl, and “C” was 0.109 M H2SO4. The experimental conductivities measured by students for the various neutralized unknown acid solutions and the conductivities calculated using eqs 2 and 4 are shown in Table 2. The resulting concentrations of the unknown acids as well as the percent error associated with each concentration are also shown. The data shown in Table 2 allows the determination of the identity of each unknown acid as HCl or H2SO4. The experimental error in the student data is generally acceptable for use with advanced high school and college general chemistry students. Students used graduated cylinders to C




volume of the sample of acid before the titration. In addition, in analyzing the authors’ titration data to identify the unknown acid as being either HCl or H2SO4, most students were unsure where to begin until it occurred to them to treat the titration data first as if it corresponded to HCl then as if it corresponded to H2SO4, then compare the calculated conductivities with the experimental conductivity data. Students generally reported this laboratory experiment was engaging and allowed them to be creative in designing their experimental procedures. As with any titration, it was somewhat tedious for them stop their titrations exactly at the end point. Students also indicated that this experiment was suitable for advanced high school or college general chemistry students, but not introductory high school chemistry students. There were two main procedures reported by the students which were appropriate to accomplish the objectives in this laboratory experiment. One procedure, involving titrating a sample of the acid and recording the conductivity of the solution at the end point, is advantageous in that one conductivity probe can be used for all the students in the laboratory. One disadvantage to this procedure though, is that students must stop their titrations exactly at the end point. The other procedure, involving titrating a sample of the acid while recording the conductivity of the solution throughout the entire titration, is advantageous in that conductivity titrations have clearly defined end points for titrations of both strong and weak acids,2 they would not require students to stop the titration exactly at the end point, and they would not require indicators. One disadvantage to this procedure, though, is that each student or group of students would require a conductivity probe. In addition, as an alternative to working through the curve fitting equations to identify the acids as described previously, students can use software such as the Vernier Logger Pro software (Vernier Software & Technology, Beaverton, OR). This software allows students to plot the salt concentration and conductivity data in Table 1 and fit a curve to the data, and then use the cursor to hover over any point on the curve and read off the concentration and corresponding conductivity. As such, once students calculate the concentration of NaCl or Na2SO4 that would be present in their solution at the end point, if the unknown acid was HCl or H2SO4, respectively, they can then read the corresponding conductivities directly from their plots of the salt concentration and conductivity data in Table 1 to identify their unknown acid as being either HCl or H2SO4.

measure their chosen volumes of unknown acids. Measuring the volume acid more precisely could improve results. As was previously mentioned, there was a difference in temperature between the student experiment and the determination of the conductivity data presented in Table 1. The experimental results shown in Table 3 are from two trials performed by the authors. These titrations were carried out between 23.0 and 23.4 °C, and the volumes of the unknown acids were measured using volumetric pipets. As expected, the data generated by the authors (Table 3) shows better agreement with the known values than that generated by the students (Table 2). This underscores the importance of accurately determining titration end points and controlling experimental procedures and conditions. In determining the identity and concentration of their unknown acids, the preservice chemistry teacher students did not follow the calculations outlined earlier. They tended to compare their experimental conductivity value to the conductivity values in Table 1 and select the salt with the closest matching conductivity. The students would then base the identity of their unknown acid and their unknown acid concentration on the values for the salt shown in Table 1. This indicates that students might require some guidance in carrying out their calculations. The 35 general chemistry students who were involved in the “dry run” of this laboratory experiment were given titration data (unknown acid and NaOH volumes, NaOH concentration, and conductivity values) from different trials of the authors’ titrations in Table 3. The general chemistry students were asked to use the titration data to identify the unknown acid as being either HCl or H2SO4, and to determine the concentration of the acid. As a guiding prompt, the students were asked to first calculate the conductivity at the end point of a hypothetical titration involving HCl and NaOH and another hypothetical titration involving H2SO4 and NaOH. The students were instructed to explore linear and polynomial fits to the data in Table 1, and to use information from their plots to calculate the conductivities at the end points of the titrations (see Supporting Information). In calculating the end point of the hypothetical titration involving HCl and NaOH, 21 of the general chemistry students used the polynomial function, while 14 students used the linear function. In calculating the end point of the hypothetical titration involving H2SO4 and NaOH, 29 of the general chemistry students used the polynomial function, while 6 students used the linear function. In analyzing the authors’ titration data to identify the unknown acid as being either HCl or H2SO4, and to determine the concentration of the acid, 19 of the general chemistry students used the polynomial functions, 2 students used the linear functions, and 14 students’ work was not clear enough to determine which functions they used. Thirty-two of the general chemistry students correctly identified the unknown acid as being either HCl or H2SO4 based on their analysis of the authors’ titration data, and three students did not correctly identify the acid. In contrast, 18 of the general chemistry students correctly calculated the concentration of the unknown acid, while 17 students did not correctly calculate the concentration of the unknown acid. Most of the students who did not correctly calculate the concentration of the unknown acid made the mistake of dividing the number of moles of acid by the total volume at the end point of the titration instead of dividing the number of moles of acid by the

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CONCLUSION

This experiment provides students with an opportunity to engage in inquiry learning where they are responsible for designing their own procedure and determining how to analyze their data. It is an interesting, challenging, and novel experiment in that it allows them to use titrations involving simple conductivity measurements to identify unknown acids as being either HCl or H2SO4, and to determine the concentrations of the unknown acids. The principles in this experiment can be applied to a variety of acids, bases, and salts, once the salt product of the neutralization reaction of the acid and the base is known, and conductivity and concentration data of the salt are collected. D



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ASSOCIATED CONTENT

* Supporting Information S

Experimental handout for students and notes for the instructor. This material is available via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the students in the general chemistry courses for participating in the experiment. REFERENCES

(1) Farris, S.; Mora, L.; Capretti, G.; Piergiovanni, L. Charge Density Quantification of Polyelectrolyte Polysaccharides by Conductimetric Titration: An Analytical Chemistry Experiment. J. Chem. Educ. 2012, 89, 121−124. (2) Smith, K. C.; Edionwe, E.; Michel, B. Conductimetric Titrations: A Predict-Observe-Explain Activity for General Chemistry. J. Chem. Educ. 2010, 87, 1217−1221. (3) Nyasulu, F.; Stevanov, K.; Barlag, R. Exploring Fundamental Concepts in Aqueous Solution Conductivity: A General Chemistry laboratory Exercise. J. Chem. Educ. 2010, 87, 1364−1366. (4) Buck, L. B.; Bretz, S. L.; Towns, M. H. Characterizing the Level of Inquiry in the Undergraduate Laboratory. J. Coll. Sci. Teach. 2008, 38, 52−58. (5) Vernier. Conductivity Probe. http://www.vernier.com/products/ sensors/con-bta/ (accessed November 2014). (6) Levine, I. N. Physical Chemistry, 5th ed.; McGraw-Hill: New York, NY, 2002.

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Using Conductivity Measurements To Determine the Identities and

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