In the Classroom
A Lemon Cell Battery for High-Power Applications Kenneth R. Muske,* Christopher W. Nigh, and Randy D. Weinstein Department of Chemical Engineering, Villanova University, Villanova, PA 19085-1681; *
[email protected] The lemon cell, or lemon juice battery, has been widely used as an electrical power source for classroom demonstrations and laboratory exercises that range from elementary school to undergraduate general chemistry courses. A number of examples can be found in the educational literature including Souder (1) and Letcher and Sonemann (2) who both use a lemon cell to power a digital clock, Kelter et al. (3) who use an orange juice battery to power an analog clock, and Swartling and Morgan (4) who discuss lemon cell power for a calculator, clock, and various LED devices. Goodisman (5) presents a brief overview of other published examples of similar demonstrations. Each of these applications, however, uses the lemon cell to provide electrical energy for low-power devices. In this article, we discuss the development of a safe, small, inexpensive, reliable, and easily constructed lemon juice cell as a replacement for commercial batteries in higher-power applications. Our specific interest is the use of the lemon cell battery to run an electric dc motor. However, other highpower applications such as radios, portable cassette or CD players, and battery-powered toys are equally appropriate for demonstration and laboratory purposes. Application The target application for the lemon cell described in this article is the power source for the 9-V electric dc motor provided in LEGO Mindstorm kits. First-year engineering students in the introductory engineering course use components from this kit to construct a model car as part of the course design project and competition. Each student group must design and construct a LEGO car and a lemon cell power source that are capable of completing a series of tasks. At the end of the semester, a competition takes place between the student groups that includes a timed run through a fixed race course, a load pull, and an aesthetics competition. Instructors from each of the engineering disciplines in the college supervise two lecture and two laboratory sessions in this course. These sessions serve two purposes. The first is
to introduce each discipline to the incoming engineering students and the second is to present the interdisciplinary science and engineering concepts required to design and construct their car. Among other topics, the chemical engineering department presents the chemical and engineering principles behind the design and construction of the lemon cell battery, the electrical engineering department presents the operating principles governing the electric dc motor, and the mechanical engineering department presents the principles behind transforming the mechanical energy supplied by the motor into locomotive force to propel the car. Lemon Cell Battery Design We consider a galvanic cell constructed from one magnesium metallic strip and one copper metallic strip placed in commercial lemon juice. This lemon cell battery operates by oxidation of the magnesium anode in the lemon juice to form magnesium ions, the flow of electrons created on the magnesium strip through the circuit to the copper strip, and the reduction of hydrogen ions from the acid in the lemon juice at the copper cathode to form molecular hydrogen gas. The driving force for this cell is the difference between the magnesium electrode potential at the anode and the hydrogen electrode potential at the cathode. An excellent description of the chemistry and governing equations for this process has been presented by Kelter et al. (3) and is not replicated here. The student groups are given the materials shown in Table 1 to construct their lemon cell battery. The lemon cell is constructed by placing a copper strip on one side of a cuvet and placing a magnesium strip on the other side. The strips are secured within the cell by bending one end of each strip over the top lip of the cuvet. Cells may be connected in series by contacting the bent portion of the magnesium strip of one cell with the bent portion of the copper strip of another cell. This connection is secured using an alligator clip. The cells are activated by filling with lemon juice. The table salt is used to increase the conductivity of the lemon juice in
Table 1. Materials Given to the Student Groups Material
Quantity
Source
Lemon juice (2.5 pH)
15 oz
Supermarket
Noniodized table salt
unlimited
Supermarket
Magnesium ribbon
6 ft, 3-mm wide, 0.15-mm thick
Alpha Aesar
Copper sheet
1 ft, 1-in. wide, 0.1-in. thick
McMaster-Carr
Polystyrene UV–vis cuvets
20, 4.5-mm square
Fisher Scientific
12-Gauge copper wire
2 ft
McMaster-Carr
Alligator clips
20
Digikey
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In the Classroom
Figure 2. Example of a student car on the race course. The student group also constructed the bridge shown in the picture to span the gap in the course.
torque of the motor. Further discussion of the behavior and governing equations for dc electric motors can be found in introductory electrical engineering texts such as (6) and (7). In addition to the battery configuration, the student groups can also adjust the gear ratio used to drive the wheels. These two design parameters must complement each other to maximize performance. Figure 1. (A) A schematic of a six-cell 9-V lemon cell battery. (B) Six lemon juice cuvet cells connected in series to form a 9-V battery.
order to reduce the internal resistance of the cell. A schematic of a series of six cells connected in this manner to form a 9V battery is shown in Figure 1A and a picture of an actual 9V lemon cell battery constructed from six cuvets is shown in Figure 1B. We use a cuvet because its compact size allows a number of cells to be connected together to produce the desired voltage and current with a small footprint and light weight. The cuvets can also be reused. The space and weight requirements for the lemon cells are an important consideration because the battery must be contained within the car. An example of a student car and lemon cell battery is shown in Figure 2. Although each cell is relatively small, it is capable of producing a fairly consistent supply of electrical energy over the ten to fifteen minute time frame required to complete the race course and load pull. The cells are also easy to rebuild and several student groups have rebuilt their cells between the race course and load pull competitions. Each student group experiments with the number and location of cells, the salt concentration in the lemon juice, and the dilution of the lemon juice. The goal is to maximize the performance of their car. Increasing the number of cells connected in series will increase the voltage supplied by the battery. Increasing the voltage supplied to a dc electric motor will increase its maximum rotational speed. Increasing the number of cells connected in parallel will increase the current supplied by the battery. Increasing the current supplied to a dc electric motor will increase the maximum applied 636
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Hazards Although lemon juice and salt are used in the construction of the cells, there are safety issues that must be considered when experimenting with and applying the battery. Hydrogen is generated as a result of the production of electrical energy. It is important that the working area is well ventilated and that all electrical connections are made before the addition of lemon juice to the cuvets to prevent the possibility of an electric spark causing ignition of the hydrogen gas. The electric motor position should also be designed away from and below the lemon cells to avoid contact with the hydrogen. The cells will foam owing to the generation of hydrogen gas. Although this foaming is unlikely to cause splashing of the lemon juice onto an experimenter, eye protection is recommended when working with the lemon cells. The lemon juice–salt solution is also corrosive and must be cleaned off any surfaces or electrical components that it comes in contact with. We have experienced the failure of several electric motors owing to the extended contact with this solution when they were not cleaned after use by the students. This caution also applies to the wire and alligator clips. Lemon Cell Battery Performance Analysis The emphasis of this development is the adaptation of the lemon juice cell for high power application. The major limitation of this simple cell is the absence of a salt bridge resulting in the reduction of hydrogen ions at the magnesium anode that supplies no current to the circuit and corrodes the magnesium strip. A second limitation is the internal resistance in the cell that can significantly reduce the closed circuit cell potential. Because of the current demand on the
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In the Classroom
cells, internal resistance results in a significant reduction of the power supplied by the cells. Reducing the rate of hydrogen generation at the magnesium anode and the corrosion of the magnesium anode can be accomplished by reducing the acidity of the lemon juice by diluting it with water. Although a weaker acid will reduce the corrosion rate, it will also negatively affect the hydrogen ions available for reduction and the internal resistance. The internal resistance of the cell arises from limitations to ionic diffusion both in solution and at the metal surfaces. The surface limitations are not easily addressed without modifying the form of the anode and cathode, which will not be explored here. The solution limitation, however, is easily addressed by increasing the conductivity of the lemon juice with the addition of table salt. We choose table salt because it is safe, effective, inexpensive, and easily obtainable. Increasing the ionic strength of the solution will increase its conductivity, but there is a limit to this benefit because the metal surface is not affected and its contribution will eventually dominate the internal resistance of the cell. Increasing ionic strength can also reduce the hydrogen ion activity, which will reduce the cell potential. The Nernst equation provides some insight into this effect E = E⬚ −
γ Mg 2+ Mg 2 + PH2 RT log 2 nF γ 2 + H+
Figure 3. Internal resistance of the lemon cell as a function of salt concentration at a series of lemon juice dilutions.
(1)
H
where E is the equilibrium cell potential, E ⬚ is the equilibrium cell potential at standard conditions minus the overpotential at the copper cathode, γ’s are the activity coefficients, and PH2 is the hydrogen gas pressure. In the analysis which follows, it is assumed that the hydrogen gas is at standard conditions. Physical chemistry texts such as Atkins (8) provide a detailed discussion of electrochemical cells and the application of the Nernst equation. As shown in eq 1, decreasing hydrogen ion activity by increasing ionic strength or hydrogen ion concentration by dilution with water will reduce the equilibrium cell potential. In order to explore the effect of dilution and salt addition, a series of experiments at different dilutions and salt concentrations was carried out. The internal resistance is determined using R int =
(Voc − Vload)
(2)
I
where Rint is the internal resistance, Voc is the open-circuit voltage of the cell, Vload is the voltage drop across the load, and I is the current. The open-circuit voltage is measured using a volt meter connected to the two terminals of the lemon cell (magnesium strip and copper strip). The voltage drop across the load is also measured by a volt meter. The load in these experiments is a 91-Ω resistor used to complete the circuit. The current is measured using a second meter in series with the resistor and also computed by the relationship I = Vload 兾91. There was essentially no difference between the current determined by these two methods. A 91-Ω resistor was used for these experiments because it was the closest match to the internal resistance of the lemon cell that was available. We wished to determine the inwww.JCE.DivCHED.org
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Figure 4. Open-circuit voltage of the lemon cell as a function of salt concentration at a series of lemon juice dilutions.
ternal resistance at maximum power that is obtained when the supply and load impedances are balanced. A discussion of these equations can be found in introductory physics or electrical engineering texts. The average of two experimental trials for the internal resistance of the lemon cell at four different lemon juice dilutions and a variety of salt concentrations are shown in Figure 3. The internal resistance decreases significantly with the addition of a small quantity of salt and then remains essentially constant after the concentration reaches 0.5 M. The open-circuit voltage, however, continues to decrease with the addition of salt ranging from an average of 1.78 V with no salt to 1.52 V at a salt concentration of 1 M and then 1.46 V at a salt concentration of 5 M. The open-circuit voltage as a function of salt concentration at the four different lemon juice dilutions is shown in Figure 4. Although there is some variation in the experimental voltage measurements, two trends are present in these data. The first is that the average open-circuit cell potential for the four lemon juice dilutions decreases as the salt concentration increases. As the ionic strength of the solution is increased by increasing the salt concentration, the result is a decrease in the hydrogen ion activity coefficient with a corresponding decrease in the cell potential as predicted by the
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In the Classroom Table 2. Lemon Juice pH as a Function of Dilution Volume % Lemon Juice
pH
100
2.52
075
2.54
050
2.57
025
2.62
Figure 5. Power as a function of time at a series of lemon juice dilutions.
Nernst equation. This decrease in activity can be explained by the long-range interactions between oppositely charged ions in solution. The chemical potential of an ion is lowered by electrostatic interactions with neighboring ions of opposite charge. As the ionic strength of the solution increases, these interactions also increase, which further reduce the chemical potential and, consequently, the activity coefficient. This simple system provides a good experimental illustration of this effect on the activity coefficient that can be described mathematically using the extended Debye–Huckel equation as discussed by Harris (9). More accurate mathematical models for high ionic strength systems, which unfortunately are also significantly more complicated, are summarized by Zemaitis et al. (10). The second trend evident in Figure 4 is that the opencircuit cell potential appears to decrease as the lemon juice concentration increases for most salt concentrations. This observation is contrary to what would be predicted by the Nernst equation if the hydrogen ion concentration was inversely proportional to the dilution and the activity coefficient was independent of dilution. Because citric acid is a weak triprotic organic acid and commercial lemon juice contains a number of other compounds, the hydrogen ion concentration and activity are not straightforward linear functions of dilution. As shown in Table 2, the pH of lemon juice solutions does increase slightly as a function of dilution. However, effects from the other factors in the Nernst equation are present in the electrochemical cell. The power supplied by the lemon cell is maximized at a salt concentration somewhere between 0.1 M, where the average internal resistance is 122 Ω and the average open-circuit voltage is 1.64 V, and a 0.5 M salt concentration, where the average internal resistance is 94 Ω and the average opencircuit voltage is 1.56 V. The power delivered by the lemon cell as a function of time for four different lemon juice dilutions with a salt concentration of 0.5 M are shown in Figure 5. The effect of dilution on the supplied power is clearly seen in this figure where each of the diluted lemon juice solution cells provides more power than the undiluted lemon juice cell. The 75% lemon juice solution produces the highest energy delivery over the twenty minute experiment at 7.5 W s. There appears to be little difference between the 50% solution at 7.0 W s and the 25% solution at 6.9 W s over twenty 638
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minutes. The undiluted lemon juice produced only 5.9 W s of energy. The energy produced by each of these cells was determined by approximating the area under the curve produced by the power versus time experimental data in Figure 5. It is clear that diluting the lemon juice slightly and adding a small quantity of salt significantly increases the energy provided by the cell. An additional advantage of dilution and salt addition is a reduction in the foaming of the cell. This reduction allows the cuvet to be filled to a higher level without spillage and also reduces the possibility of the conductive foam forming a short circuit between cells connected in parallel. Acknowledgments The contributions of the College of Engineering faculty members involved in the creation of the Introduction to Engineering course, design project, and student group competition are gratefully acknowledged. We would like to particularly acknowledge the helpful advice provided by James Peyton Jones of the Electrical and Computer Engineering Department. Literature Cited 1. Souder, L. G. School Shop. 1983, 43, 24. 2. Letcher, T. M.; Sonemann, A. W. J. Chem. Educ. 1992, 69, 157–158. 3. Kelter, P. B.; Carr, J. D.; Johnson, T.; Castro-Acuna, C. M. J. Chem. Educ. 1996, 73, 1123–1127. 4. Swartling, D. J.; Morgan, C. J. Chem. Educ. 1998, 75, 181– 182. 5. Goodisman, J. J. Chem. Educ. 2001, 78, 516–518. 6. Bobrow, L. S. Fundamentals of Electrical Engineering, 2nd ed.; Oxford University Press: New York, 1996. 7. Rizzoni, G. Principles and Applications of Electrical Engineering, 3rd ed.; McGraw-Hill: New York, 2000. 8. Atkins, P. W. Physical Chemistry, 4th ed.; Freeman: New York, 1990. 9. Harris, D. Exploring Chemical Analysis, 3rd ed.; Freeman: New York, 2005. 10. Zemaitis, J. F.; Clark, D. M.; Rafal, M.; Scrivner, N. C. Handbook of Aqueous Electrolyte Thermodynamics; Wiley: New York, 1986.
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