Determining the Transference Number of H+(aq) by a Modified

Laboratory Experiment pubs.acs.org/jchemeduc

Determining the Transference Number of H+(aq) by a Modified Moving Boundary Method: A Directed Study for the Undergraduate Physical Chemistry Laboratory Rajeev B. Dabke,* Zewdu Gebeyehu, and Jonathan Padelford Department of Chemistry, Columbus State University, Columbus, Georgia 31907, United States S Supporting Information *

ABSTRACT: A directed study for the undergraduate physical chemistry laboratory for determining the transference number of H+(aq) using a modified moving boundary method is presented. The laboratory study combines Faraday’s laws of electrolysis with mole ratios and the perfect gas equation. The volume of hydrogen gas produced at the cathode is monitored and the perfect gas equation is applied to determine the amount of H2(g) produced. The transference number of H+(aq) is then determined from the volume of HCl(aq) swept by the boundary, the molarity of HCl(aq), and the amount of H2(g) produced. The cell is directly powered by 9 V batteries and involves no electronic circuit or a milliammeter. Preparation of the electrochemical cell, experimental procedure, and results of the experiment are presented.

KEYWORDS: Upper-Division Undergraduate, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Electrochemistry, Electrolytic/Galvanic Cells/Potentials

T

indicates the absence of H+(aq). Measuring the volume of acid swept by the boundary per unit time and the current facilitates the determination of the transference number of H+(aq) from eq 1.6

ransference number (or transport number) is one way of expressing conductivity and mobility of ions1 and determining the junction potential in an electrochemical cell.2,3 The theory of transference number and the methods for measuring it are known to physical chemists and electrochemists.1−6 Various reports on determining the transference number of ions as a laboratory experiment and the pedagogical values of these experiments have appeared in this Journal7−20 over several decades. These reports include the moving boundary method,8,11,15−19 the Hittorf method,7,13,14,20 and the electromotive force method.10 In particular, the moving boundary method8,11,15−19,21 has been at the forefront for the determination of transference numbers of ions. The volume of electrolyte swept by the boundary may be measured with more accuracy than the change in concentration of an ion in the Hittorf method.21 Transference number can be defined as a fraction of total current carried by each ion present in solution. The moving boundary apparatus consists of a graduated pipet filled with the desired electrolyte and the electrodes are positioned at the upper and lower end of the pipet serving as a capillary. A direct current is passed through the electrodes. For determining the transference number of H+(aq), the capillary is filled with aqueous hydrochloric acid of known concentration and methyl orange as a visual indicator. Passage of direct current prompts migration of H+(aq) toward the negative electrode (cathode). As H+(aq) ions are swept away from the anode, a moving boundary is formed. The red coloration above the boundary indicates the presence of H+(aq). The lower yellow coloration © 2012 American Chemical Society and Division of Chemical Education, Inc.

t+ =

z+clAF I Δt

(1)

where t+ is the transference number, z+ represents charge on the H+ ion (i.e., +1), c is molar concentration of H+(aq), F is the Faraday constant (i.e., 96485.3 C mol−1), I is current in ampere, and Δt is time in seconds, respectively. In a capillary, the moving boundary sweeps a volume (L or dm3) of HCl(aq) in the form of a cylindrical shape of height l dm and the crosssectional area of A dm2. Hence, the term lA in eq 1 represents the volume of HCl(aq) swept by the moving boundary. Dimensional analysis of eq 1 indicates that transference number is a dimensionless quantity. As indicated in eq 1, transference number can be determined from the rate of migration of the boundary at a known current. The current tends to gradually decrease during movement of the boundary.11,17 Nevertheless, in view of applying eq 1, it is critically important to maintain a constant direct current during the experiment. This stringent condition demands a constant manual adjustment of the current11,16,18,19 or construction of a constant current supply.15,22 In this paper, we present a modified moving boundary apparatus. The apparatus directly runs on 9 V batteries and Published: September 26, 2012 1600

dx.doi.org/10.1021/ed200786a | J. Chem. Educ. 2012, 89, 1600−1603

Journal of Chemical Education

Laboratory Experiment

cathode. In a separate experiment a milliammeter is included in the circuit. During the progress of this experiment, the current gradually decreases. This resulted in a gradually decelerating migration of the boundary and production of H2(g). However, Faraday’s laws of electrolysis confirm the quantitative relation between the amount of H2(g) produced at the cathode and the charge passing through the electrochemical cell, irrespective of both the speed of the movement of the boundary or the speed of the production of H2(g). Relatively simple circuitry, colorful change in the capillary, and the application of Faraday’s laws of electrolysis combined with the mole ratios and the perfect gas equation make this experiment suitable for a directed study in undergraduate physical chemistry laboratory. A student developed and tested this experiment as a fourth-year research project in our physical chemistry laboratory.

does not involve a milliammeter, rheostat, or an electronic circuit to regulate the current. The term IΔt in eq 1 is a product of the current (amp) and the time (s) and it represents the charge (coulombs) passed through the electrochemical cell. The charge passed through the cell quantitatively accounts for the volume of HCl(aq) swept by the moving boundary. A 2 mL graduated pipet serves as a capillary and measures the volume of HCl(aq) swept by the boundary. The volume of H2(g) is measured and the perfect gas equation is used to determine the amount of H2(g). Equation 2 shows the reduction of H+(aq) to H2(g) at the cathode. 2H+(aq) + 2e− → H 2(g)

(2)

Faraday’s laws of electrolysis and eq 2 point out that two Faradays of charge delivers 1 mol of H2(g). The quantity of charge (IΔt) passing through the electrochemical cell is calculated from these relations and eq 1 is used to determine the transference number of H+(aq). The apparatus used in the present experiment is comprised of a cadmium anode and a platinum cathode (Figure 1). As the power supply is started, a boundary is started at the anode and moves in the upward direction. The H2(g) is evolved at the

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PEDAGOGICAL OBJECTIVES The pedagogical objectives of this experiment are (i) to apply the perfect gas equation to determine the amount of a gas produced at the electrode, (ii) to apply the mole relationships to quantify the electric charge passed through an electrochemical cell, (iii) to apply Faraday’s laws of electrolysis, and (iv) to determine the transference number of H+(aq).

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EXPERIMENTAL SETUP The moving boundary cell (Figure 1) is made of a PTFE (polytetrafluoroethylene) beaker and two pipets. The cadmium electrode is positioned at the base of the 2 mL graduated pipet that serves as a capillary. A 20 mL portion of HCl(aq) of known concentration with indicator is placed in the cell which is powered by three 9 V batteries connected in series. An upward moving boundary is formed in the capillary. An inverted glass pipet (5 mL capacity) is used to measure the volume of hydrogen gas produced at the cathode. The volume of HCl(aq) swept by the moving boundary and the volume of the H2(g) produced at the platinum electrode are recorded. The average height of the electrolyte column in the gas measuring pipet is measured to determine the contribution of the hydrostatic pressure. A complete description of experimental procedures, instructions for the staff and students, stepby-step calculations, and a postlaboratory exercise are included in the Supporting Information.

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HAZARDS Safety glasses must be worn while performing the experiment and instructors must examine and approve the electrode connections before students begin the experiment. Hydrogen gas is flammable and a fume hood or a workstation with a proper exhaust system must be used for a large size class. Hydrochloric acid causes burns, is harmful if inhaled, and must be prepared in a fume hood. Cadmium metal serving as an anode slowly dissolves in the acid. Cadmium metal is harmful if swallowed and chronic inhalation of cadmium compounds has been associated with lung and prostate cancer. Labeled waste containers must be used to collect the waste chemicals.

Figure 1. Schematic diagram of the transference number cell: (a) three 9 V batteries connected in series, (b) platinum wire electrode, (c) hydrogen gas bubbles produced at the platinum electrode, (d) ) 5 mL glass pipet holding HCl(aq), (e) HCl(aq) level, (f) three magnetic stir bars, (g) Parafilm seal, (h) the height of the aqueous electrolyte column, (i) HCl(aq) electrolyte, (j) boundary formed in the capillary, (k) yellow coloration of methyl orange indicating the absence of H+(aq) ions, (l) cadmium metal electrode housed in the capillary, (m) switch, and (n) water jacket. Note: A large magnetic stir bar is taped to the pipet, serving as a docking station for the small magnetic stir bar housed inside the pipet. The small magnetic stir bar is moved in the up and down direction through the pipet to dislodge the hydrogen gas bubbles adhering to the inner surface of the pipet. The small magnetic stir bar is guided by the manual movement of another large magnetic stir bar. Dashed arrow shows the movement of the large magnetic stir bar.

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RESULTS AND DISCUSSION The pressure of gas collected in the empty space in the pipet is corrected for the vapor pressure of water and for the hydrostatic pressure of the electrolyte column.23,24 Table 1 provides data on five independent trials of determination of transference number of H+(aq). Battery current is stopped and 1601




Table 1. Experimental Data and Results for Determination of Transference Number of H+(aq) Trial Numbera

Molarity of HCl(aq)/M

Barometer Pressure/mm Hg

Volume of H2(g) Produced/mL

Volume of HCl(aq) swept by boundary/mL

Average Height of the Electrolyte Column/cm

Transference Numberb

1 2 3 4 5

0.105 0.107 0.100 0.100 0.100

758.2 758.2 753.2 753.2 753.2

0.50 0.50 0.20 0.20 0.20

0.31 0.31 0.13 0.13 0.13

7.0 10.8 12.0 11.0 10.5

0.82 0.84 0.83 0.82 0.82

The temperature was 22.0 °C. The density and vapor pressure of water at this temperature are 998 kg m−3 and 19.8 mm of Hg (or 0.0261 atm), respectively.23 bTransference number from the average of five trials =0.83 (standard deviation ±0.01) a

the migration of the boundary through 0.80 mL volume. The temperature of HCl(aq) is measured before and after each trial and no measurable change in the temperature is noticed. The hydrogen gas produced in the experiment is treated as a “perfect” gas for calculations.

the electrolyte is changed after each trial. The average transference number of H+(aq) is determined to be 0.83 (standard deviation ±0.01). In a separate experiment, the volume of H2(g) produced at the cathode is monitored as a function of the volume of HCl(aq) swept by the moving boundary. The volume of H2(g) produced linearly changed with the volume of HCl(aq) swept by the moving boundary. The data for two different concentrations of HCl(aq) are plotted (Figure 2). This linear

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CONCLUSION The agreement between the transference number value within experimental results and that between experimental results and the literature data1,3 (Table 2) underlines the efficacy of the Table 2. Summary of Experimental Results and Literature Data for Transference Number of H+(aq) by Moving Boundary Method Source Experimental Average of 5 Trials HCl (0.102 M HCl average concentration) at 22.0 °C from Table1 Figure 2: 0.100 M HCl at 22.0 °C Figure 2: 0.195 M HCl at 22.0 °C Literature 0.10 M HCl at 25 °C 0.20 M HCl at 25 °C

Figure 2. Plot of volume of H2(g) produced at cathode versus volume of HCl(aq) swept by the moving boundary. The electrolyte temperature was 22.0 °C; barometric pressure was 756.5 mmHg. Average height of the electrolyte column was 12.1 and 10.5 cm for 0.100 and 0.195 M HCl, respectively. The density and vapor pressure of water at 22.0 °C temperature are 998 kg m−3 and 19.8 mm of Hg, respectively.23 The derivation justifying these plots is discussed in the Supporting Information.

a

Transference Number Value 0.83 0.83 0.84 0.8314a 0.8337a

Refs 1, 3.

modified moving boundary experiment. The transference number of H+(aq) does not significantly depend on the concentration of HCl(aq) in 0.10 to 0.20 M range1,3 and our data support this observation. Equation 1 contains concentration c in units of mol/L, which is slightly temperature dependent through the density of water. This relation indicates the transference number is slightly dependent on temperature. Application of the perfect gas equation and Faraday’s laws of electrolysis encompass the undergraduate physical chemistry pedagogy and address the objectives of the study.

dependence confirmed the quantitative relation between the amount of the products generated at the cathode and the volume swept by the moving boundary. The slope of the plot for 0.100 M HCl(aq) is 1.53 (R2 = 0.998). The slope signifies 1.53 mL of H2(g) produced at the cathode accounts for a unit volume (i.e., 1.0 mL) of HCl(aq) swept by the moving boundary. The transference number for 0.100 M HCl is determined to be 0.83. The experiment is repeated for the higher concentration of HCl(aq) and slope of the plot for 0.195 M HCl(aq) is higher than that for 0.100 M HCl by a factor of 1.92 (Figure 2). This is nearly the value 1.95 expected from the concentrations. The transference number of H+(aq) for 0.195 M HCl is 0.84. The significant figures in the transference number determined from our experimental data are limited by the digits in the measured volume of H2(g). In a separate experiment, we monitored the current flowing through the circuit during the progress of the experiment. The initial current is 6 mA and gradually dropped to about 1 mA during

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ASSOCIATED CONTENT

S Supporting Information *

A complete description of experimental procedures; instructions for the staff and students; step-by-step calculations; and a post-laboratory exercise. 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. 1602



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ACKNOWLEDGMENTS Jonathan Padelford was the fourth-year undergraduate student testing the experiment. We thank James O. Schreck and the reviewers of the manuscript for their helpful comments and suggestions.

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REFERENCES

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Determining the Transference Number of H+(aq) by a Modified

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