Electrochemical Reaction Gibbs Energy: Spontaneity in

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Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX

Electrochemical Reaction Gibbs Energy: Spontaneity in Electrochemical Cells Tomasz Pacześniak,* Katarzyna Rydel-Ciszek, Paweł Chmielarz, Maria Charczuk, and Andrzej Sobkowiak Department of Physical Chemistry, Rzeszow University of Technology, al. Powstancow Warszawy 6, 35-959 Rzeszow, Poland

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S Supporting Information *

ABSTRACT: Spontaneity criteria for processes with useful (especially electrical) work have been discussed based on total differentials of thermodynamic functions. Reaction Gibbs energy (ΔrG) and electrochemical reaction Gibbs energy (ΔrG̃ ) have been juxtaposed. Three-dimensional graphs showing the dependencies of ΔrG̃ on the extent of reaction (ξ) and the cell voltage (φR − φL), in connection with their sections, enable both coherent and intuitive discussion of equilibrium in electrochemical systems. It was clearly indicated that important, commonly known dependencies can be justified and illustrated using these graphs.

KEYWORDS: Upper-Division Undergraduate, Physical Chemistry, Misconceptions/Discrepant Events, Analogies/Transfer, Electrochemistry, Equilibrium, Electrolytic/Galvanic Cells/Potentials

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INTRODUCTION It is a frequently used procedure to use a reaction Gibbs energy (ΔrG) for considerations on spontaneity in closed systems, not only in chemical but also in electrochemical processes at constant temperature and pressure.1 Nevertheless, one should be careful when applying this function, as a naive usage (which disregards the presence of a useful work) can lead to confusion. For example: • How can one explain the course of the process, for which ΔrG > 0, occurring in electrolytic cells? Does one really experience unspontaneous phenomena? • Or why, despite the fact that ΔrG < 0 in open electrochemical cells, does the reaction not proceed? • Or why can electrolysis actually proceed in electrochemical cells in chemical equilibrium, for which ΔrG = 0? While some authors aptly point out the sources of students’ misconceptions related with electrochemistry,2 the difference between chemical and electrochemical equilibrium has scarcely been discussed.3 Even then the authors usually do not invoke electrochemical reaction Gibbs energy when discussing electrochemical spontaneity. In contrast to considerations based on ΔrG, electrochemical reaction Gibbs energy (ΔrG̃ ) analysis provides an elegant and coherent approach to electrochemical equilibria. Many popular physical chemistry or electrochemistry textbooks do not mention ΔrG̃ . However, some authors have recently given attention to this function.4 In this article we demonstrate how the concept of electrochemical reaction Gibbs energy can be © XXXX American Chemical Society and Division of Chemical Education, Inc.

helpful in understanding electrochemical equilibrium and reaction spontaneity. Parallel discussion of G-family thermodynamic parameters (G and ΔrG) and their electrochemical counterparts (G̃ and ΔrG̃ ) enables us to draw both general and more specific conclusions concerning chemical and electrochemical equilibria. We believe that our model, based on elementary thermodynamic principles, and illustrated by relevant graphics of electrochemical reaction Gibbs energy surfaces, can be a method of choice for teaching undergraduate students about electrochemical equilibrium.

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MODEL DESCRIPTION

Gibbs Energies in Electrochemical Systems and Spontaneity

It is a tempting but erroneous procedure to use the chemical spontaneity condition1a−c dG < 0

(1)

where G is Gibbs energy, as an analogous criterion for the processes with useful work at constant temperature and pressure. Notwithstanding, adding useful work term −dw̅ gives (see Supporting Information, section SI1) (2) dG − dw̅ < 0 which is a correct spontaneity indicator of the process with useful work;1b therefore it is also valid for electrochemical Received: November 14, 2017 Revised: July 1, 2018

A

DOI: 10.1021/acs.jchemed.7b00871 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Article

Table 1. ΔrG̃ Compared to ΔrG in Derivation of Reaction (van ’t Hoff) Isotherm Electrochemical Reaction Gibbs Energy, ΔrG̃

Chemical Reaction Gibbs Energy, ΔrG As follows from denotation recommended by IUPAC6, Δr ≡

i ∂G y Δr G = jjjj zzzz k ∂ξ {T , P

( ) ∂ ∂ξ

(10a)

T ,P

; therefore the definitions are

i ∂G̃ y Δr G̃ = jjjj zzzz k ∂ξ {T , P

(10b)

Single component parameter 0

μi = μi + RT ln ai

μĩ = μi 0 + RT ln ai + ziFφi

(11a)

(11b)

For the system at T = const, P = const k

G=

k

∑ niμi i=1

G̃ =

(12a)

∑ niμĩ i=1

(12b)

After differentiation (νi = dni/dξ) k

Δr G =

∑ νi μi i=1

k

Δr G̃ =

(13a)

Δr G = Δr G° + RT ln Q

i=1

(13b)

Reaction parameter (νizi = νe; Supporting Information section SI4) (14a) Δr G̃ = Δr G° + RT ln Q + νeF(φR − φL)

processes. The left side of the expression is then called the “electrochemical Gibbs energy” and denoted dG̃ :

dG̃ < 0

(4)

The spontaneity criteria for chemical (eq 1) and electrochemical (eq 4) processes are respectively equivalent to the conditions (section SI2) Δr G < 0

(5)

where ΔrG is the reaction Gibbs energy, and Δr G̃ < 0

(6)

ΔrG̃ is the electrochemical reaction Gibbs energy. Electrochemical Gibbs energy and electrochemical reaction Gibbs energy are related to electric properties of the system. The differential of electric work can be expressed by (section SI3) dw̅ = −νeF(φR − φL) dξ

Electrochemical Reaction Gibbs Energy (ΔrG̃ ) Surface and Its Section with ΔrG̃ = 0 Plane: Nernst Equation and Reason for Reaction

The spontaneity of electrochemical processes and the classification of electrochemical systems can be discussed in a way that appeals to visual perception by analysis of threedimensional graphs showing the dependence of electrochemical reaction Gibbs energy (ΔrG̃ ) on cell voltage (φR − φL) and the extent of reaction (ξ) (Figure 1a). The presented graphs were obtained after conversion Q to ξ in eq 14b for simple model reaction A + B = C + D (section SI5) and can be constructed by addition of two-dimenssional (ΔrG̃ vs ξ) precursors at different (φR − φL) (section SI6). To the best of our knowledge, a graph of this kind, i.e., displaying an electrochemical reaction Gibbs energy surface, has neither been presented in the literature nor proposed for educational purposes. As follows from eq 6 the electrochemical spontaneity criterion is ΔrG̃ < 0. Consequently, the condition ΔrG̃ = 0 defines equilibrium. Out of the infinitely many cell voltages

(7)

where νe is stoichiometric number for electrons, F is the Faraday constant, ξ is the extent of reaction, and (φR − φL) is the cell voltage1b (also known as a cell potential;1a,5 however, the former name is frequently used in a non-equilibrium sense4b and will be used here to stress this possible meaning). We should remember that cell voltage is always related to two individual processes occurring at different electrodes. Combining eq 3 and eq 7 gives dG̃ = dG + νeF(φR − φL) dξ

(14b)

As follows from eq 9, electrochemical reaction Gibbs energy differs from reaction Gibbs energy by cell-voltage-related factor. ΔrG̃ can also be related to system composition. The intensive thermodynamic parameters of the system’s components, the chemical potentials (μi), need to be replaced by electrochemical ones (μ̅ i) when discussing equilibrium in electrochemical systems. In Table 1, starting from the definitions, ΔrG and ΔrG̃ functions have been juxtaposed, and their relations with system compositions, represented by the reaction quotients Q have been derived. For electrochemical systems the resulting equation (eq 14b) corresponds to eq 9 and relates electrochemical reaction Gibbs energy (ΔrG̃ ) to Q and to cell voltage (φR − φL). Composition-related reaction quotient (Q) can be converted to a function of an extent of reaction (ξ). The form of this simple relation follows from a given process stoichiometry (section SI5).

(3) dG̃ = dG − dw̅ Therefore, the electrochemical spontaneity criterion can also be expressed as

(8)

Differentiating eq 8 with respect to ξ results in Δr G̃ = Δr G + νeF(φR − φL)

∑ νi μĩ

(9) B



Article

E = E0 −

RT ln Q νeF

(21)

The equilibrium state is characterized by the absence of effective changes. It should be emphasized that every electrochemical cell, regardless of its composition or open cell voltage can be in electrochemical equilibrium provided that the cell is open. The most rudimentary application of the graphics presented is to help to answer the question: what makes the reaction proceed in an electrochemical cell? We choose any extent of reaction (e.g., ξx in Figure 2) corresponding to an initial system

Figure 1. Dependence of electrochemical reaction Gibbs energy (ΔrG̃ ) on cell voltage (φR − φL) and extent of reaction (ξ) (a) and two-dimensional representation of section of ΔrG̃ surface with ΔrG̃ = 0 plane (b). ξe, equilibrium extent of reaction; ξe,ch, equilibrium chemical extent of reaction; emf, electromotive force. Figure 2. Electrochemical reaction Gibbs energy surface and the reason for reaction.

(φ − φ ) possible for any system composition (defined by ξ), each composition has only one specific cell voltage (emf, electromotive force) that corresponds to equilibrium conditions (ΔrG̃ = 0). The values of emf are determined by the line of intersection of the ΔrG̃ = 0 plane with the ΔrG̃ surface (Figure 1a). The relation emf = f(ξe) (Figure 1b) is invertible. It is important that emf corresponds to only one particular cell voltage for every extent of the reactionthe one related to electrochemical equilibrium7 and ΔrG̃ = 0 conditions. Consequently substituting 0 for ΔrG̃ and emf for (φR − φL) into eq 14b gives R

L

0 = Δr G° + RT ln Q + νeF emf

composition. In the open cell, for the given extent of reaction, the cell voltage is (φR − φL) = emf and ΔrG̃ = 0. Due to the shape of the electrochemical reaction Gibbs energy surface, after diminishing the cell voltage (i.e., connecting the electrodes by an external circuit in a galvanic cell or using an external power source in an electrolyzer) also ΔrG̃ decreases (line a). This spurs the process in the forward direction (line b), because, as shown previously (eq 6), negative ΔrG̃ corresponds to a spontaneous process. It is characteristic, that the ΔrG̃ < 0 condition is equivalent to (φR − φL) < emf. It is also obvious from the picture that any process at (φR − φL) > emf is thermodynamically forbidden, because then ΔrG̃ > 0.

(15)

therefore, 0 = Δr G + νeF emf

Section of Electrochemical Reaction Gibbs Energy (ΔrG̃ ) Surface with (φR − φL) = const Planes. Chemical vs Electrochemical Conditions and Electrochemical Equilibrium

(16) 1a−c

which leads to a popular

equation,

Δr G = −νeFemf

(17)

The condition (φR − φL) = 0 is inherent in any chemical reaction. For zero value cell voltage eq 14b converts into eq 14a and ΔrG̃ = ΔrG. The section of ΔrG̃ surface with the plane corresponding to (φR − φL) = 0 condition (Figure 3a) results in the two-dimensional dependence ΔrG̃ = f(ξ) (Figure 3b, curve 0) identical to the graph presented customarily for chemical reactions.1a Consequently, in this case the zero value of ΔrG̃ corresponds to chemical equilibrium with chemical equilibrium extent of reaction, ξe,ch. In view of the above, chemical equilibrium can thus be perceived as a specific case of an electrochemical equilibrium. In closed systems, various cell voltages (φR − φL) create different equilibrium outcomes during electrolysis, in the same way as an extent of reaction defines the equilibrium cell voltage in a galvanic cell. Thus, (Figure 3b, curve 1) positive (φR − φL) corresponds to diminished (with regard to ξe,ch) equilibrium extent of reaction (ξe,1). Negative cell voltage

or for standard conditions, Δr G° = −νeFemf 0

(18)

In turn rearranging eq 15 gives emf = −

Δ r G° RT − ln Q νeF νeF

Next, using emf0 for −

Δ r G° νeF

(19)

(according to eq 18) leads to the

Nernst equation: emf = emf 0 −

RT ln Q νeF

(20)

The cell voltage (φ − φ ) is the most frequently denoted E;1,4,5,8 therefore, in (and only in) equilibrium conditions, for which (φR − φL) = emf, one can also write R

L

C



Article

equilibrium constant (K̃ ) is also cell-voltage-dependent. Inserting 0 for ΔrG̃ and emf for (φR − φL) into eq 14b gives for equilibrium 0 = Δr G° + RT ln K̃ + νeF emf

(22)

therefore, K̃ = e−ΔrG° / RT e−νeF emf/ RT = K e−νeF emf/ RT

(23)

where K is the value of K̃ for emf = 0, i.e., chemical equilibrium constant.8d Therefore, a chemical equilibrium constant is a specific example of an electrochemical equilibrium constant. By analogy to K̃ , an electrochemical reaction quotient Q̃ can be expressed by eq 24: Q̃ = Q e−νeF(φ

R

− φL)/ RT

(24)

The electrochemical reaction quotient Q̃ is therefore a general system-composition-defining parameter for equilibrium and non-equilibrium and electrochemical and non-electrochemical conditions: ̃ Q̃ = eΔrG / RT e−ΔrG° / RT e−νeF(φ

R

− φL)/ RT

(25)

For ΔrG̃ = 0 (equilibrium), an electrochemical reaction quotient Q̃ reduces to K̃ , whereas, for (φR − φL) = 0 (chemical system), it becomes Q. When both conditions are fulfilled, Q̃ turns out to be a chemical equilibrium constant K. We believe that electrochemical reaction quotient has never been defined, but it deserves definition to make the equilibrium description complete.

Figure 3. Electrochemical reaction Gibbs energy surface: sections of ΔrG̃ surface with (φR − φL) = const planes (a) and two-dimensional representation of sections as ΔrG̃ = f(ξ) dependencies (b).

(Figure 3b, curve 2) corresponds to increased equilibrium extent of reaction (ξe,2). Consequently the electrochemical

Figure 4. Electrochemical reaction Gibbs energy surface: sections of ΔrG̃ surface with ξ = const planes (a) and two-dimensional representation of sections as ΔrG̃ = f [(φR − φL)] dependencies (b−d). D



Article

Sections of Electrochemical Reaction Gibbs Energy (ΔrG̃ ) Surface with ξ = const Planes. Relations between emf, ΔrG̃ , and ΔrG for Various Electrochemical Systems

It is also possible to analyze the electrochemical spontaneity using the single, informative graphic. Based on the presented consideration one can distinguish several types of electrochemical systems, depending on their location on the electrochemical reaction Gibbs energy surface. The surface can be divided by three characteristic planes into six areas (Figure 5).

The planes corresponding to selected values of ξ cross the ΔrG̃ surface giving two-dimensional, linear ΔrG̃ = f(ξ) dependencies (Figure 4). The graphics enable us to discuss the relations between emf, ΔrG̃ , and ΔrG in different electrochemical systems. The nonhatched, “spontaneity areas” in Figure 4b−d correspond to ΔrG̃ < 0 condition; i.e., they relate to a negative electrochemical reaction Gibbs energy for a forward reaction. Zero of a ΔrG̃ function match emf. The function ΔrG̃ has constant value, independent of the cell voltage and characteristic of the specific ξ. Section 1 of Figure 4a,b is typical of a reactant-rich system (ξ < ξe,ch) for which emf > 0 and ΔrG < 0. A negative ΔrG̃ condition can be implemented by connecting electrodes with an external circuit of finite resistance (galvanic cell, effectuating 0 < (φR − φL) < emf relation), short-circuiting the electrodes (chemical-like system, then (φR − φL) = 0) or using an external power source, which diminishes the cell voltage (φR − φL) < 0 and additionally boosts the reaction. Section 0 of Figure 4a,c) corresponds to a discharged galvanic cell (ξ = ξe,ch), for which emf = 0 and ΔrG = 0. To make the reaction spontaneous, it is necessary to apply an external power source and decrease ΔrG̃ . This results in (φR − φL) < 0 relation, which turns the system into an electrolyzer. Section 2 (Figure 4a,d) corresponds to a product-rich system (ξ > ξe,ch), for which emf < 0 and ΔrG > 0. It is only possible to make ΔrG̃ be negative by using an external power source and enforcing a (φR − φL) < emf relation. The system is a typical example of an electrolyzer. It is characteristic that the ΔrG̃ < 0 spontaneity condition always correlates with the relation (φR − φL) < emf. The red part of the ΔrG surface in Figure 4a and the hatched areas in Figure 4b−d are the realms of a reverse reaction; however, the discussion of the reverse reaction thermodynamics has been deliberately omitted here.

Figure 5. Dependence of electrochemical reaction Gibbs energy (ΔrG̃ ) on cell voltage (φR − φL) and extent of reaction (ξ). Characteristic areas, important for the discussion of equilibrium and spontaneity.

The dividing planes are as follows: • P1the plane corresponding to ΔrG̃ = 0 condition (equilibrium, open cells), separating spontaneous and unspontaneous (i.e., spontaneous in the forward direction) processes; • P2the plane corresponding to the (φR − φL) = 0 condition (chemical processes), differentiating electrochemical cells into those exploiting and those not exploiting an external power source; • P3the plane corresponding to the ξ = ξe,ch condition (chemical equilibrium), sectioning off the “external power source areas” into those “absolutely requiring an external power” (to enforce the reaction) and those “nonabsolutely requiring an external power” (to realize the reaction). The latter ones could actually settle for a wire connection. More details concerning the specific parts of the graphic presented in Figure 5 are given in (section SI7). The regions outlined by the above-mentioned planes are as follows: • F1the area corresponding to a spontaneous reaction (because ΔrG̃ < 0) after connecting the electrodes with a wire of a finite resistance [the reaction would also be spontaneous in chemical conditions (because ΔrG < 0 in this region)]; • F2the area corresponding to a spontaneous reaction (because ΔrG̃ < 0) after connecting to an external power source [the reaction would also be spontaneous in

Reaction Spontaneity in Different Types of Electrochemical Systems

It is possible to formulate the cell-voltage-based spontaneity criterion for an electrochemical process. Based on eq 17 one can write dG = −νeF emf dξ

(26)

Inserting eq 26 and eq 7 into eq 3 and rearranging gives dG̃ = −νeF[emf − (φR − φL)] dξ

(27)

and after differentiation Δr G̃ = −νeF[emf − (φR − φL)]

(28)

Finally, as an alternative to a quite general (and a little abstract for a chemistry student) spontaneity criteria for electrochemical process (eq 4 or eq 6), it is possible to formulate a more concrete and conceptually easier one (by combining eq 28 with eq 6): (φR − φL) < emf

(29)

Any electrochemical process is spontaneous if the cell voltage is less (i.e., less positive or more negative) than the electromotive force of the cell. E



Article

Table 2. ΔrG̃ and Spontaneity/Unspontaneity Criteria for Electrochemical Process parameter ΔrG̃ (φR − φL) ξ

spontaneous ΔrG̃ < 0 (φR − φL) < emf ξ < ξe

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chemical conditions (because ΔrG < 0) and so, in fact, could also proceed after the electrodes were connected by a wire]; • F3−the area corresponding to a spontaneous reaction (because ΔrG̃ < 0) after connecting to an external power source [the reaction is nonspontaneous in chemical conditions (because ΔrG > 0 in this region) and the usage of an external power source is a necessary condition for running the forward process]; • R1, R2, and R3the nonspontaneity regions (unavailable for a forward reaction). Analysis of the characteristic features of the particular regions of the ΔrG̃ surface, detailed in Table SI1 , leads to general spontaneity criteria for electrochemical systems. For every spontaneous process, ΔrG̃ < 0. The other conditions follow from this one. The distinction of the systems with regard to spontaneity is summarized in Table 2. Therefore, for example, we can claim that the process is a spontaneous one if the cell voltage is less than the electromotive force or if the extent of reaction is less than the equilibrium (electrochemical) one. Additionally, because any chemical system can be regarded as a special case of an electrochemical one (when (φR − φL) = 0), a chemical equilibrium is a special case of an electrochemical equilibrium. Consequently, inserting zero for the cell voltage in the third column of Table 2 transforms the electrochemical equilibrium indicators to chemical ones: ΔrG = 0, emf = 0, and ξ = ξe,ch.

equilibrium ΔrG̃ = 0 (φR − φL) = emf ξ = ξe

nonspontaneous ΔrG̃ > 0 (φR − φL) > emf ξ > ξe

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.7b00871.

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Derivation of the equations and details of the graphic illustrating the electrochemical reaction Gibbs energy surface (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Tomasz Pacześniak: 0000-0002-9877-4826 Paweł Chmielarz: 0000-0002-9101-6264 Notes

The authors declare no competing financial interest.

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REFERENCES

(1) (a) Atkins, P. W.; de Paula, J. Atkins’ Physical Chemistry, 9th ed.; Oxford University Press: Oxford; New York, 2010. (b) Mortimer, R. G. Physical chemistry, 3rd ed.; Academic Press/Elsevier: Amsterdam; Boston, 2008. (c) Chang, R.; Thoman, J. W., Jr. Physical chemistry for the chemical sciences; University Science Books: Mill Valley, CA, USA, 2014. (d) Monk, P. M. S. Physical chemistry: Understanding our chemical world; Wiley: Chichester, England; Hoboken, NJ, USA, 2004. (2) (a) Bonicamp, J. M.; Clark, R. W. Textbook error: Short circuiting an electrochemical cell. J. Chem. Educ. 2007, 84 (4), 731− 734. (b) Sanger, M. J.; Greenbowe, T. J. Students’ misconceptions in electrochemistry: Current flow in electrolyte solutions and the salt bridge. J. Chem. Educ. 1997, 74 (7), 819−823. (c) Sanger, M. J.; Greenbowe, T. J. An analysis of college chemistry textbooks as sources of misconceptions and errors in electrochemistry. J. Chem. Educ. 1999, 76 (6), 853−860. (d) Ozkaya, A. R. Conceptual difficulties experienced by prospective teachers in electrochemistry: Half-cell potential, cell potential, and chemical and electrochemical equilibrium in galvanic cells. J. Chem. Educ. 2002, 79 (6), 735−738. (3) (a) Birss, V. I.; Truax, D. R. An Effective Approach to Teaching Electrochemistry. J. Chem. Educ. 1990, 67 (5), 403−409. (b) Thompson, R. Q.; Craig, N. C. Unified electroanalytical chemistry: Application of the concept of electrochemical equilibrium. J. Chem. Educ. 2001, 78 (7), 928−934. (4) (a) Girault, H. H. Analytical and physical electrochemistry; EPFL, Marcel Dekker: Lausanne, Switzerland,;New York, NY, USA, 2004. (b) Bard, A. J.; Inzelt, G. R.; Scholz, F. Electrochemical dictionary, 2nd rev. & extended ed.; Springer: Heidelberg, Germany, 2012. (5) (a) Brett, C. M. A.; Brett, A. M. O. Electrochemistry: Principles, methods, and applications. Oxford University Press: Oxford, U.K.; New York, 1993. (b) Linder, B. Elementary physical chemistry; World Scientific: Hackensack, NJ, USA, 2011; DOI: 10.1142/7690. (6) Cohen, E. R.; Cvitas, T.; Frey, J. G.; Holmström, B.; Kuchitsu, K.; Marquardt, R.; Mills, I.; Pavase, F.; Quack, M.; Stohner, J.; Strauss, H. L.; Takami, M.; Thor, A. J. Quantities, units, and symbols in physical chemistry, IUPAC Green Book, 3rd ed.; IUPAC & RSC: Cambridge, U.K., 2007. (7) Bagoŝkiĭ, V. S. Fundamentals of electrochemistry, 2nd ed.; WileyInterscience: Hoboken, NJ, USA, 2006.

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CONCLUSIONS The collective answer to each of the questions raised at the beginning of the article is: it is the ΔrG̃ , and not the ΔrG function, that determines the spontaneity in closed electrochemical systems. That is why even chemically nonspontaneous reactions (ΔrG > 0) can proceed in electrolyzers provided ΔrG̃ < 0. Similarly an open galvanic cell (ΔrG < 0) will not work, since ΔrG̃ = 0. Discharged galvanic cells (ΔrG = 0) will readily realize a forward reaction, provided ΔrG̃ < 0 condition is assured by harnessing an external power source. It was demonstrated, that basic thermodynamics parameters related to electrochemical equilibrium follow from dG̃ = dG − dw̅ condition (eq 3) and the ΔrG̃ = ΔrG° + RT ln Q + νeF(φR − φL) (eq 14b) relation. Three-dimensional graphics of ΔrG̃ surfaces enable convenient discussion of rudimentary electrochemical principles ruling electrochemical equilibrium and visualization of spontaneity in electrochemical cells. Both chemical system or equilibrium conditions correspond to just one of many possible 2-D sections of the three-dimensional ΔrG̃ surface. The presented model provides not only a visual stimulus for the students, frequently bored with equation-based instruction, but also helps to discern the meeting points of apparently disparate equations, enforces general thinking, and prevents the flawed temptation of applying the chemical equilibrium rules to electrochemical systems. F



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(8) (a) Rogers, D. W. Concise physical chemistry, Wiley: Hoboken, NJ, USA, 2011. (b) Zoski, C. G., Ed. Handbook of Electrochemistry, 1st ed.; Elsevier: Amsterdam; Oxford, 2007. (c) Scholz, F.; Bond, A. M. Electroanalytical methods: guide to experiments and applications, 2nd, rev. and extended ed.; Springer: Heidelberg; New York, 2010. (d) Oldham, K. B.; Myland, J. C. Fundamentals of electrochemical science; Academic Press: San Diego, 1994.

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Electrochemical Reaction Gibbs Energy: Spontaneity in

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