Demonstration Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX
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Electromotive Force versus Electrical Potential Difference: Approaching (but Not Yet at) Equilibrium Leandro da Silva Rodrigues,† Jones de Andrade,‡ and Luiz H. S. Gasparotto*,† †
Institute of Chemistry, UFRN, Av. Sen. Salgado Filho 3000 Natal, Rio Grande do Norte, Brazil Institute of Chemistry, UFRGS, Av. Bento Gonçalves 9500 Porto Alegre, Rio Grande do Sul, Brazil
‡
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S Supporting Information *
ABSTRACT: One of the most elusive concepts in electrochemistry is that of electromotive force (EMF). Often students, and even instructors, mistakenly take it as “electric potential difference” (EPD) or “voltage difference”. To clarify this issue properly, here we demonstrate an activity that was conducted with readily available and inexpensive resources. We employ the widely known Daniell Cell slightly modified to meet our need of measuring EMF and EPD. The key of the demonstration is to connect to the cell a potentiometer, which is an element that provides a controllable variable resistance. When the slider of the potentiometer is set to the maximum resistance, only negligible charge circulates, which brings the system to a partial equilibrium at which the potential annotated is exactly equivalent to the electromotive force. This is equivalent to opening the circuit of the cell. Upon turning the slider toward lower resistances, charge circulates with the electromotive force no longer measurable because the electrochemical cell is far from a reversible condition. Other aspects such as available work versus energy dissipation, maximum attainable work, and power comparisons are also discussed. KEYWORDS: First-Year Undergraduate/General, Physical Chemistry, Demonstrations, Hands-On Learning/Manipulatives, Electrolytic/Galvanic Cells/Potentials, Thermodynamics
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INTRODUCTION The concept of electromotive force is pivotal in the understanding of reactivity and maximum work in electrochemistry. Since it allows for the determination of other thermodynamic quantities such as reaction free energy, entropy, and activity coefficients,1 it is imperative that the concept of electromotive force be presented free of misconceptions.2,3 It has been noticed that undergraduate students (at times graduate, too) tend to use the terms “electromotive force” and “electric potential” interchangeably.4 This confusion may arise from the fact that both the electromotive force and the electric potential are assessed experimentally via voltmeter, which is an instrument that measures voltage. If at this point the instructor fails to clarify that electromotive force and electric potential are fundamentally distinct, students will perpetuate this misconception. Electric potential is the “amount of energy (or work) per unit of charge required to move that charge from a reference point to another inside the electric field”.1 On the other hand, electromotive force is properly described as “amount of energy (or work) per unit of charge that is reversibly converted by a generator (electric field) into electrical energy by moving a charge from a reference point to another”.5 The generator may be regarded as an “electron pump”. The crucial difference between those two concepts is that “reversibility” here requires © XXXX American Chemical Society and Division of Chemical Education, Inc.
the generator to be at open circuit or no-load conditions. This means that the actual value of electromotive force is obtained only when the generator is at the limit condition of not operating at all or at a state of a partial equilibrium6 with its surroundings (no net change) that is set by forcibly counteracting the spontaneity of the electrochemical reaction. This is not the state of chemical equilibrium that the reaction will eventually reach after enough current has passed through the cell to change the concentrations (activities) of the cell components. Thermodynamic processes are pictured as infinitely slow to ensure equilibrium at every single infinitesimal step. Since that sort of process would take an infinite amount of time to finish, perfectly reversible processes are impossible. A question frequently asked by students is “if values from reversible processes are unachievable, why bother studying them?” The reason is that they provide a frame of reference to determine the efficiency of real processes. For instance, if the reversible work from a certain engine is 100 kJ and one measures an output work of 60 kJ, the efficiency is 60%. Herein, we devised a simple demonstration based on the widely known Daniell cell to demonstrate the difference Received: April 5, 2018 Revised: August 6, 2018
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DOI: 10.1021/acs.jchemed.8b00249 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Demonstration
resistances, it will eventually reach its thermodynamic equilibrium, meaning that the electrochemical cell will no longer produce work, and therefore, ε = 0 V. In contrast, electric potential difference, EPD, is always measurable upon existence of an electric field that appears due to charge separation in the terminals (electrodes). When current flows around a circuit, the relationship between electric potential difference and current is given by Ohm’s law:
between electric potential difference and electromotive force. The key of the demonstration was to connect the copper and zinc electrodes to a potentiometer, which is an element that provides variable resistance that can be controlled. When the slider of the potentiometer is set to the maximum resistance, only negligible charge circulates, which brings the system to a partial equilibrium at which the value annotated is exactly equivalent to the electromotive force. This is equivalent to opening the circuit of the cell. The system is at reversible condition, but not necessarily at thermodynamic equilibrium, for it would require the Gibbs free energy to be zero. Upon turning the slider toward lower resistances, charge circulates with the electromotive force no longer being measurable because the electrochemical cell was far from a reversible condition. The measurable quantity was, in this case, the electric potential difference. Thus, only under reversible conditions does the electric potential difference coincide with that of the electromotive force.
EPD = rI
where EPD is the electric potential, and r and I are the resistance and electric current, respectively. At this point, the distinction between electromotive force, ε, and electric potential difference, EPD, should be clear: only at reversible conditions is the electromotive force, ε, measurable, while potential difference, EPD, requires only the existence an electric field, which may appear in reversible or irreversible processes.
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THEORETICAL BACKGROUND First, it would be helpful to understand from where comes the work of an electrochemical device. We start off by adding a term for electric work in the fundamental equation of thermodynamics: dG = Vdp − SdT + εdZ (constant composition)
Copper sulfate (>99.5%), zinc sulfate (>99.5%), agar (99%), and potassium chloride (99%) were products of Vetec ́ Quimica Fina (Duque de Caxias, Brazil). The multimeter was a MXT DT830B with 0.01 precision. The 500 kΩ linear potentiometer was purchased from Changzhou Kennon Electronics. All solutions were prepared in distilled water. Further materials: crocodile clips, copper wires for connections, U-shaped tube for the salt bridge, copper and zinc sheets as electrodes.
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Procedure
Full procedure and hazards associated with it are provided as Supporting Information.
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RESULTS AND DISCUSSION The first aspect worth investigating is the dependence of the measured EPD on the potentiometer resistance. Figure 1
thus, the origin of the power of an electrochemical device is the change in the entropy S when charge Z is passed isobarically. For instance, a galvanic cell (battery) gets its power from the entropy change caused by the electrochemical reactions that occur inside of it. Given that chemical reactions take place in electrochemical devices, it is logical to include the influence of the composition in the formalism. The Gibbs free energy is then written: ΔG = ΔGo + RT ln Q
EXPERIMENTAL DETAILS
Materials
where ε is the electromotive force and dZ the amount of charge passed in an electrochemical device. The quantity εdZ is the additional electric work. Since the dG is an exact differential, the following Maxwell relation is obtained at isobaric conditions: ij ∂ε yz i ∂S y jj zz = −jjj zzz k ∂T { P , Z k ∂Z { P , T
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where Q is the reaction quotient, T the temperature, and R the gas constant. At this point, we recall that the maximum electrical work is given by the Gibbs free energy via the expression:7 ΔG = −nFε
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and the Nernst equation is obtained by dividing eq 3 by the number of mols (n) and the Faraday’ constant (F): ε = εo −
RT ln Q nF
Figure 1. Electric potential difference versus the potentiometer resistance in the Daniell cell.
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shows that in the range of 400 kΩ and 500 kΩ the measured EPD was essentially constant as only negligible current flowed at those resistances. Thus, in that range of resistances, the EPD was numerically equivalent to the electromotive force within experimental resolution. Further decrease in resistance, however, allowed current to circulate, which led to a steep decrease in EPD and divergence from the electromotive force ε value.
Here the standard electromotive force, ε°, is also introduced. Unlike the electric potential difference, the electromotive force can only be assessed at zero-current conditions, which implies open-circuit or imposition of a sufficiently large external resistance (a high potential energy barrier that ensures partial equilibrium) to impede electron flow. If the chemical reaction is allowed to advance by removing external B
DOI: 10.1021/acs.jchemed.8b00249 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Demonstration
following points were acquired by slowly turning the slider of the potentiometer toward lower resistances to permit electric current I to circulate. In this case, information about electromotive force ε was lost because the system was no longer reversible or at partial equilibrium and the values registered by multimeter 1B were now only the EPD, which consistently decreased with current I augmentation. At the other extreme of the slider position, the potentiometer resistance was virtually zero, which was equivalent to short circuit the Daniell cell. It is important to observe that when electricity circulates in a cell (or battery) its internal resistance, r*, resists to the flow of current causing further potential drop:
Figure 2 shows the relationship between EPD and current upon variation of the potentiometer resistance. At the
ε = I(r + r *) ε = Ir + Ir *,
Figure 2. Relationship between the observed electric potential difference of the Daniell cell as the current is changed by varying the potentiometer resistance. As the potentiometer resistance approaches zero, the cell becomes short-circuited and EPD → 0.
ε = EPD + Ir * EPD = ε − Ir *
beginning of the demonstration, the slider of the potentiometer was set to the maximum resistance (500 kΩ) allowing only a negligibly small current to flow. Under this essentially open-circuit condition, a partial equilibrium was attained and the first value recorded in multimeter 1B for EPD was 1.10 V, which was the known standard electromotive force ε° of the Daniell cell. This value can be calculated by selecting the appropriate reactions from the standard potential electrode table,8 as presented in Table 1.
Reaction
ε° (V)
Cu (aq) + 2e → Cu(s) Zn2+(aq) + 2e− → Zn(s) Cu2+(aq) + Zn(s) → Cu(s) + Zn2+(aq)
0.3419 −0.7618 1.1037
−
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where Ir* the potential drop caused by the internal resistance. Fitting the data of Figure 2 to eq 7 gave y-intercept of 1.10 V, the electromotive force ε of the cell. This translates into a measured Gibbs free energy of −212 kJ/mol by eq 4. The linear regression also gave a slope of 705 Ω, which is the internal resistance r* of the cell, comprising those of the salt bridge, electrolyte, and ion concentration gradients produced at the electrode surfaces due to cell operation. Once the internal resistance r is obtained, one can now calculate, at any given electric potential measured, both the ̇ , and the available electric power generated by the cell, Wcell energy dissipated power as heat, qcell ̇ , from eqs 8 and 9 below, respectively. The results are presented in Figure 3, showing that the generated electric cell power had a maximum at an optimum EPD ∼0.60 V: such a behavior is similar to the ones obtained for irreversible (thermal) engines optimal configuration studies. On the other hand, the dissipated power increases exponentially, as expected, with the increment of the process irreversibility:
Table 1. Relevant Reactions for Standard Electromotive Force 2+
and since Ir is the EPD
Since the concentrations of Zn2+(aq) and Cu2+(aq) and the mean ionic activity coefficients of the salts are practically equal,9 the logarithm term of the Nernst eq 5 is zero because the reaction quotient Q is 1. Hence, the EPD measured was also the standard electromotive force ε° for the reaction. The
̇ = Wcell
dWcell = I × EPD dt
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Figure 3. Relationship between electric power generated and available power dissipated as heat, upon electric potential difference variation by controlled resistance variation in the Daniell cell. C
DOI: 10.1021/acs.jchemed.8b00249 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Demonstration
Figure 4. Relationship between electric work generated and available work dissipated as heat upon electric potential difference variation by controlled resistance variation in the Daniell cell for 1 mol of reactants.
qcell ̇ =
dqcell dt
= rI 2
concepts that would otherwise be propagated in the wrong direction.
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It is important to stress that these results cannot yet properly express the energy loss for irreversible processes in comparison to reversible ones. To do so, the processes need not be normalized in terms of time (as in power calculations), but rather in terms of amount of energy needed to accomplish the same task. This can be performed by using the electric current generated to calculate how long would take for the reaction to convert the same amount (for instance, 1 mol) of reactants into products at each given current:
Δt =
ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.8b00249. Assembly of experimental system and hazards associated (PDF, DOC)
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AUTHOR INFORMATION
Corresponding Author
nF I
*E-mail:
[email protected].
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ORCID
It is important to notice how slow this reaction is even at the optimum condition of ∼0.60 V it would still take 1.5 days for the cell to consume 1 mmol of reactants. As such, one can easily consider that the concentrations and hence the reaction quotient, Q, would be fairly constant throughout a typical class. The time calculated in eq 10 multiplied by eqs 8 and 9 provides the amount of available energy, both in electrical and heat forms, used in each state of the potentiometer to react 1 mol of reactants (or to transfer 2 mol of electrons). This leads to the constant (as expected) measured Gibbs free energy change observed in Figure 4. As such, two alternative and out-of-equilibria measurements of the Gibbs free energy of the built Daniell Cell are available, both reproducing the traditional equilibrium method result (−212 J/mol attained here, 0.36% deviation). First, the ̇ Δt is −212 J/mol. Second, averaged total of qcell ̇ Δt and Wcell the amount of available work dissipated as heat for the shortcircuited cell (potentiometer resistance = 0) can be extrapolated: the linear regression applied at the lowest values of EPD results in lim qcell ̇ Δt = − 211 J/mol (0.60%
Luiz H. S. Gasparotto: 0000-0002-4711-393X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors would like to acknowledge the grants (process 442087/2014-4) provided by CNPq. The authors thank Dr. Tiago Falcade for the fruitful discussions and important suggestions to the manuscript.
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REFERENCES
(1) McSwiney, H. D. Thermodynamics of a galvanic cell: A physical chemistry experiment. J. Chem. Educ. 1982, 59 (2), 165. (2) Zuza, K.; De Cock, M.; van Kampen, P.; Bollen, L.; Guisasola, J. University students’ understanding of the electromotive force concept in the context of electromagnetic induction. Eur. J. Phys. 2016, 37 (6), 1−13. (3) Varney, R. N. Electromotive force: Volta’s forgotten concept. Am. J. Phys. 1980, 48, 405. (4) Rose-Innes, A. C. Electromotive Force. Phys. Educ. 1985, 20, 272−274. (5) Gomez, E. J. M.; Duran, E. F. R. Didactic problems in the concept of electric potential difference and an analysis of its philogenesis. Science & Education 1998, 7 (2), 129−141. (6) Darken, L. S.; Gurry, R. W. Physical Chemistry of Metals, 1st ed.; McGraw-Hill: New York, 1953; pp 423−424. (7) Beaulieu, L. P. A general chemistry thermodynamics experiment. J. Chem. Educ. 1978, 55 (1), 53−54.
EPD → 0V
deviation).
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CONCLUSION In this manuscript, we demonstrated how to differentiate properly electromotive force from electric potential difference. It is interesting how well-established and straightforward systems, such as the Daniell cell, may help clarify underlying D
DOI: 10.1021/acs.jchemed.8b00249 J. Chem. Educ. XXXX, XXX, XXX−XXX
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(8) Bindel, T. H. Understanding electrochemical thermodynamics through entropy. J. Chem. Educ. 2000, 77 (8), 1031. (9) Robinson, R. A.; Jones, R. S. The activity coefficients of some bivalent metal sulfates in aqueous solution from vapor pressure measurements. J. Am. Chem. Soc. 1936, 58 (6), 959−961.
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DOI: 10.1021/acs.jchemed.8b00249 J. Chem. Educ. XXXX, XXX, XXX−XXX
