Gibbs Energy JChE

8/12/2019 Gibbs Energy JChE

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Published: October 25, 2011

Copyrightr 2011 American Chemical Society andDivision of Chemical Education, Inc. 87 dx.doi.org/10.1021/ed100477x |J. Chem. Educ. 2012, 89, 8793

ARTICLE

pubs.acs.org/jchemeduc

First-Year University Chemistry Textbooks Misrepresentationof Gibbs Energy

Juan Qulez*

Departamento de Fsica y Qumica, IES Benicalap, Nicasio Benlloch, 46015 Valencia, Spain

Research on learning difficulties associated with thermody-namics is well documented. These studies have characterizedstudent conceptions of energy,1 phase changes,2,3 equilibrium,47

and the second law of thermodynamics.810 Comprehensive re-views covering studentsconceptual difficulties about several ther-modynamic ideas such as chemical equilibrium,7 chemical ener-getics, chemical thermodynamics,1 and entropy11 establish thatstudents have signicant learning difficulties with thermodynamics.

Research studies12,13 suggest that one of the sources of thestudents learning difficulties in physical chemistry lies in howtextbooks and teachers deal with key chemistry concepts. Forexample, several authors4,1420 have made an inventory ofuniversity studentsmisconceptions due to a poor understandingof the spontaneity concept. Some of those misunderstandingsmay have their origin in the way this concept is taught.

Project 2061s Benchmarks for Science Literacy21 and theNational Standards for Science Education22 called for the inclusionin textbooks of terms meaningfully dened and of appropriaterepresentation of key ideas.23 These documents recognized theimportance of textbooks and their evaluation. Thus, evaluation ofscience textbooks has become an important area of research and

the inconsistencies in presentation of the subjects among text-books are a major concern for both teachers and learners.In a recent study,24 it was found that chemistry textbooksoften

do not explicitly distinguish between thermodynamic (K) andpractical equilibrium constants (Kc and Kp). For example, inmany cases,Kc(orKp), instead ofK, were used to calculate rGand rG. Thus, it was asserted that students could not beintroduced appropriately to Gibbs energy. Hence, this work isaimed at analyzing if Gibbs energy is misrepresented by collegechemistry textbooks.

This article deals with the concepts of spontaneity andequilibrium. First, a thermodynamic discussion will allow us todifferentiate some important thermodynamic quantities: G,

G, rG, and rG. The different meanings of these quantitieswill be discussed with the help of one gure. We will focus mainlyon discussing the meaning of spontaneity; that is, this conceptrefers both to determining whether a reaction is product orreactant favored and to predicting the direction in which areacting system shifts in response to a disturbance. This founda-tion addresses some current misrepresentations. Finally, keepingthis analysis in mind, we will study how general chemistrytextbooks deal with all these related concepts and report someof the possible sources of misleading thermodynamic treatments.

Although we are going to deal with some advanced thermo-dynamic concepts, the main purpose of this study is not toprovide a full background in these concepts. Nonetheless, ourreview of prior work in the aforementioned areas may be usefulfor those who need an extended and more detailed mathematicalor conceptual approach.

METHODOLOGY

The analysis of textbooks has involved a qualitative approachfor achieving the aim described above. For this purpose, 30rst-

year university chemistry textbooks2554

have been analyzed.These texts are well-known rst-year chemistry textbooks thathave gone through several editions, thereby showing theiracceptance by chemistry teachers. Although the textbooks wereoriginally written in English and their authors are mainly fromUnited States and Great Britain, most of them are found on theshelves of the libraries of many chemistry colleges in countrieswhere English is not the rstlanguage. They are (or were) usuallyrecommended to rst-year university chemistry students, andmost of them have been translated into several languages. Also,

ABSTRACT:This study analyzes the misrepresentation of Gibbs energy by college chemistrytextbooks. The article reports the way rst-year university chemistry textbooks handle theconcepts of spontaneity and equilibrium. Problems with terminology are found; confusionarises in the meaning given to G, rG, G, and rG, which results in many textbooks notdifferentiating between Gand rG. Also, there is confusion over when standard conditionsapply and when they do not. A problem with the proper use of units is also found. Finally, it issuggested that most of these difficult concepts could be removed from the rst-year universitychemistry syllabus because (i) an accurate presentation of Gibbs energy would be far beyondan introductory chemistry level and (ii) current attempts to introduce those difficult concepts

in rst-year university chemistry courses are usually full of misleading formulations.KEYWORDS:First-Year Undergraduate/General, Curriculum, Physical Chemistry, Miscon-ceptions/Discrepant Events, Textbooks/Reference Books, Equilibrium, Thermodynamics
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88 dx.doi.org/10.1021/ed100477x |J. Chem. Educ. 2012, 89, 8793

Journal of Chemical Education ARTICLE

various studies published in science education journals haveincluded these textbooks. The total number includes recenttextbooks (16) as well as textbooks published before 1997 (14textbooks that were published between 1971 and 1996). Thisselection will reveal if there is any difference over time in the way

chemistry textbooks deal with Gibbs energy.

SPONTANEITY, EQUILIBRIUM, AND THE MEANINGOF G, RG, G, AND RG

To ground our textbook study, rst the different meanings ofG, rG, G, andrGneed to be explained. Doing so involvesthe presentation of two thermodynamic energies: Gibbs (G) andHelmholtz (A). The fundamentals of this introduction are usuallydevelopedwith moredetail in physical chemistrytextbooks,5559 aswell as in advanced thermodynamics textbooks.6063 Ultimately,those current approaches are rooted on the modern thermo-dynamic denition ofaffinitydue to de Donder.64 That is, thefundamentals of Gibbs energy6567 will serve as a basis for

discussion. Eventually, this previous analysis will help whenwe later review howrst-year university chemistry textbooksdeal with both equilibrium and spontaneous reactions.

The change in the Gibbs energy (G) at constant pressure andtemperature for an ideal gas chemical reaction (i.e., sponta-neous process) is presented. This procedure may also beapplied to the thermodynamic energyA (i.e., chemical reac-tion at constantTandV). The development and integration ofthese mathematical treatments lead to the determination ofthe general condition for spontaneity. Keeping in mind thisgeneral condition, we will be able to account for the differentmeanings of G, rG, G, and rG.

68 All this previousdiscussion will serve as a proper reference when we analyzehow rst-year textbooks dene and use the aforementioned

Gibbs quantities.The change in the Gibbs energy (dG) is given by

dG SdT VdP rGd 1

Similarly, the change in the Helmholtz energy (dA) is as follows

dA SdTPdV rGd 2

where rG= iiiis the so-called free energy of reaction, andrepresents the rate of change ofG with respect to the advance-ment of reaction (), at constant Tand p, and also the rate ofchange ofA with respect to the advancement of reaction, at

constantTandV,

rG G

T,p

A

T, V

3

The meaning of this equation must be emphasized: rG is aderivative and not an ordinary difference despite the use of,as signaled by the subscript r feature.

If there is a proper control of the variables involved, theconditions that the second law establishes for both spontaneousprocesses and chemical equilibrium (Table 1) can be obtained.Furthermore, as

dGp, T dAT, V rGd 4

a general equation that embodies the two conditions for sponta-neity outlined in Table 1 can be obtained:

rGd 0, then rG< 0. For the reaction to reverse spontaneously[aA(g) +bB(g)r rR(g) +sS(g)], dGp,T< 0 [or dAT,V< 0], andbecause d< 0, then rG> 0. Thus, the sign ofrGpredicts thedirection of the spontaneous chemical reaction.

Similarly, the general equilibrium condition can nally bewritten as follows

rGd 0 6

That is, ifrG= 0, equilibrium has been attained. The generalconditions of forward and backward reaction, as well as that ofequilibrium, are summarized in Table 2. It must be stressed that

Table 1. Summary of Both Spontaneous and EquilibriumConditions in Usual Chemical Reaction Systems

Constant variables T,V T,p

Spontaneity condition dA< 0 dG< 0

Equilibrium condition dA= 0 dG= 0

Table 2. Values ofrG and Their Meaning [aA(g) + bB(g)arR(g) + sS(g)]

rG d Spontaneous Reaction

< 0 > 0 forward

> 0 < 0 backward

= 0 = 0 equilibrium

Figure 1. Variation ofG as a function of in a chemical process, atconstantp and T. The determination of the sign of (G/)T,p= rG

provides the condition of the direction of the spontaneous reaction (ifrG < 0: reactants f products; ifrG > 0: products freactants).Furthermore, the equilibrium condition corresponds to (G/)T,p =rG= 0 (minimum value ofG). This way, the minimum value of Gibbsenergy (Geq) and vanishing rGare approached from either direction.Gis a nite difference; two cases are illustrated: G1 =Geq Greactantsand G2=Geq Gproducts. But, rGis not a nite difference: it is therate of change of Gibbs energy with respect to the advancement ofreaction.
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those conditions are not restricted to reactions at constantpandT, for they apply also to systems at constantVandT.

Keepingin mindthe mainpurpose, thediscussion will exclusivelybe concentrated on Gibbs energy (G). The variation ofG as afunction of in an ideal gas chemical process isshown inFigure 1. Inthis particular case, it is assumed that Gproducts Greactants> 0.When starting with unmixed reactants in their standard states at the

same temperature T and there is no mixing of reactants withproducts, the Gibbs energy changes linearly as the reaction pro-gresses, and eventually the reactants are completely converted tounmixed products in their standard states at the same temperatureT. But when reactants are mixed, their pressures drop below theirstandard state values and thus there is a drop in their Gibbs energyvalues (Greactants 0, the forwardreaction is spontaneous (rG< 0).

A proper calculation of rG makes use of the followingequations55,63 (in which the intensive function nature of bothrGand rGshould not go unnoticed)

rG rG RTlnQ 13

rG RTln K 14

where,Q is the reaction quotient, which has the form of theequilibrium constant, K, but is not equal to the equilibriumconstant [notice that when rG= 0 (equilibrium), thenQ=K],

Q

pR

p

!rpS

p

!s

pA

p

!apB

p

!b 15

We must remark that only whenQ= 1 does rG= rG. Ofcourse, this is not the case for most chemical reactions. Thus, wemust stress that in most cases the sign ofrG does not serve as acriterion for the spontaneity of a chemical process. The relation-ship ofrGwithKmay be used to state how far the reaction hasgone before equilibrium hasbeen attained, forKmaybe obtainedfrom rG

K erG=RT 16

IfrG< 0, then K> 1 (i.e., the process is product favored).Conversely, ifrG> 0, thenK< 1 (i.e., the process is reactantfavored). This determination does not depend on the isothermal


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conditions (p = constant or V= constant) under which K iscalculated,73,74 as suggested by Antonik.75

rGdiffers from rG, for at a given temperature the value ofrGis xed, but the value ofrGis determined by two terms:rGand a concentration-dependent term. These two terms canbe joined into only one term, which depends on the quantityQ/K. That is, making use of eqs 13 and 14, the following equationcan be obtained

rG RTlnQ

K

17

This expression allows us to calculate the value of rG and,therefore, to discuss the direction of the spontaneous reaction(Table 2). That is, the value of the quotient Q/Kmay be the basisof an easier condition for spontaneity (Table 3).

The limitations of Le Chateliers principle, as well as themisconceptions students and teachers hold when trying to applyit, have received great attentionin the literature.7,12,67,7684 QKinequalities (Table 3) are also easy-to-apply conditions in theprediction of the evolution of disturbed equilibria. They have theadvantage of having no limitations, which is a powerful alter-native to Le Chateliers qualitative rules.12,67,8184

SPONTANEITY AND EQUILIBRIUM: TEXTBOOKSMISREPRESENTATIONS

Authors of rst-year university chemistry textbooks scarcelypay attention to the basis of the above discussion. In most ofthose textbooks, there is confusion in terminology, for the termsused in the treatment of Gibbs energy are usually misrepresented(Table 4), which may lead to imprecise or even incorrectconclusions. Some of these misleading statements are reported.The equilibrium condition is often dened as G= 0, instead ofrG = 0.

25,28,30,33,38,41,4446,48,51,52,54 Freemantle36 states thatthis condition is G= 0. Also, the condition for spontaneity isalways dened as G< 0 (instead ofrG< 0), which is usuallyexemplied by calculating G. Thus, the discussion of sponta-neous reactions is normally restricted to standard conditions,

although this situation is not always stated explicitly. That is,these presentations do not stress that restriction, which oftenleads to the assumption that G< 0 corresponds to a generalcondition for spontaneity: two textbooks31,50 include a sectionentitled G as a criterion for spontaneity; conversely, it isassumed that ifG> 0, the forward reaction is forbidden.

Moreover, the values ofGare usually reported in kJ unitsfor calculations involving the equation G = RT lnK.2528,30,32,33,38,41,49,85,86 Moore et al.43 and Whitten et al.40

report G in kJ in one exercise, but in the next one, it isexpressed in kJ/mol. Gilbert et al.54 calculateG in kJ, but theseunits change to kJ/mol when introducing the calculated value inthe above equation. Reporting rGin units of kJ is mainly due

to not using correct units ofR(that is, usually the incorrect unitsare kJ/K). All the possible sources of this error have beendiscussed previously at greater detail.72 Four textbooks36,39,46,47

report Gin kJ/mol.In addition, QK inequalities are normally employed to

decide the direction of a system disturbed from equilibrium.This discussion is usually based on the following equation

G RTlnQ

K 27

(instead ofrG= RTln(Q/K)). In those cases, Gis usuallyreported in kJ units,25,29,32,35,41,42,51,87 for authors have not paidattention to the correct units of R. But, in other cases,authors36,37,45,48 make use of G having kJ/mol units. Still,Umland and Bellama45 explain

We have been writing J or kJ for the units ofGandG. ...However, G andG areextensive properties andreally doinclude units of mol1 because, in thermodynamics, equa-tions are always interpreted in terms of moles.In calculationsthat involve both GorG and R, the unit J/mol (or kJ/mol)must be used forGandG0. (authorsemphasis)

On the other hand, authors do not enlarge this topic to cases inwhich Le Chateliers principle is limited. On the contrary, it isused to demonstrate its supposed validity. For example, a QK

discussion can help when considering the limited character ofthat principle when predicting the evolution of a disturbedchemical equilibrium system when adding a reactant at constantpandT.12,61,67,71,72,76,81,84

CONCLUDING REMARKS AND SUGGESTIONS FORTEACHING

The misleading assumptions reported in this study arise fromthe quantitative and mathematical emphasis given to thethermodynamic concepts involved, but without explainingthem in a proper way. A sound qualitative discussion wouldhelp in the clarication and differentiation ofG, rG, G,and rG. This way, many authors have proposed a revision of

Table 3. A Simple Condition for Both Spontaneity andEquilibrium

rG Q/K Spontaneous Reaction

< 0 < 1 (Q 0 > 1 (Q>K) backward

= 0 = 1 (Q=K) equilibrium

Table 4. Summary of General Chemistry TextbooksMisre-presentation of Gibbs Energy

The equilibrium condition is often dened as G= 0 (also, G= 0),

instead of rG= 0.

Thecondition forspontaneityis alwaysdenedas G 0 the forward reaction is forbidden.

In many cases, the value ofrGis reported in kJ in calculations involving

the equation Go = RTlnK, for authors usually do not pay attention to

the correct units ofR(in this case, kJ K1 mol1).

QK inequalities are normally employed to decide the direction of a

disturbed equilibrium system. This discussion is usually based on the

following equation G = RT ln(Q/K), instead ofrG = RT ln(Q/K).

Consequently, Gis reported in kJ units. Once again, some authors do not

pay attention to the correct units ofR.


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the symbolism,5,8891 but their suggestions have not beenheeded. Still, modern physical chemistry textbooks usuallycomply with the IUPAC recommendations.68

Themain conclusion of this study is that inrst-year chemistrytextbooksG, rG, G, and rG are notproperly dened andare only used in algorithmic calculations. Hence, this teachingapproachwould promote robotic learning rather thanconceptual

understanding and even might be the origin of studentsmis-understandings. Still, this article cannot go further stating in

which specic way this widespread misleadingtextbookapproachcan lead to student misconceptions, for our attempt has been tocontribute to both the distinction and proper use of each of thequantities involved in the discussion of spontaneous reactions.

With respect torG andG, the confusion in textbooks arisesdue to the overuse of the symbol in teaching thermody-namics in introductory university chemistry courses. That is, it isassumed that Gplays the role ofrG. Also, there is a great dealof confusion when reporting their units. Moreover, some authorsstate that G < 0 is a general condition for spontaneity.Signicant differences were not found over time in the waycollege chemistry textbooks deal with G, rG, G, and rG.

The thermodynamic foundation outlined in this article goesbeyond the scope required for an introductory course.5564

However, current college chemistry textbooks include a greatamount of information on difficult thermodynamic concepts.The stress on the Gibbs energy has not been the case historically.A glimpse at chemistry textbooks published 50 years ago9295

reveals that authors did not include Gibbs energy. The chemicalprinciples shift that occurred in the mid-1960s96,97 and theincreasing number of pages of each new textbook edition98,99

may explain the current emphasis given to thermodynamics inrst-year university textbooks.

At this point, it is interesting to note that some authors havewritten general chemistry textbooks32,42 as well as physicalchemistry textbooks.55,57 It is rather surprising that the mislead-

ing assumptions reported in this study (e.g., confusing GwithrG) are only present in introductory textbooks. Perhaps, thoseauthors have tried to simplify the thermodynamic topics theyintroduce to students at the rst-year level, but their attemptsmight have gone too far. Therefore, maybe, it would be better toremove most of those difficult topics from the rst-year uni-versity syllabus, leaving them for an advanced treatment, insteadof continuing to teach them using oversimplied and misleadingthermodynamic statements. The accurate thermodynamic ap-proach given by some rst-year chemistry authors53 to theconcepts analyzed in this study would seem to be far beyondthe level required in an introductory college chemistry course. Abalanced general chemistry course should not be focused mainlyon thermodynamics because there would not be enough time to

develop properly all the other essential topics to be covered.Thus, general chemistry students would not be capable ofunderstanding those difficult thermodynamics topics, in spiteof being accurately treated in their textbook, because teacherscould not devote the proper time to develop such a large quantityof information.

In a recent study,24 it was suggested that rst-year universitystudents should be introduced to practical equilibrium constantsonly, leaving the discussion of the thermodynamic equilibriumconstant (and its relationship to rGand rG) to an advancedlevel. This recommendation is also suggested in this studybecause a sound introduction to the Gibbs energy may be toodifficult for rst-year students to understand.

QK inequalities (i.e., QcKc or QpKp) could be intro-duced at this level as a rst basic criteria for spontaneity inisothermal conditions.100 That is, one does not need thermo-dynamics to distinguish betweenQandKfor a reaction. Indeed,it is probably a mistake to wait until the discussion of thermo-dynamics to make this point. One merely needs to distinguishbetween the ratio of partial pressures or concentrations at a

degree of reaction progress (Q) and the value when the system isat equilibrium (K). Eventually, this mathematical discussioncould be justied in an advanced course dealing with the secondlaw of thermodynamics.81

Still, defenders of the current rst-year thermodymics empha-sis would argue, among other things, that engineers needthermodynamics earlier than suggested in this article or thatbiologists could never get to Gibbsian thermodynamics; also,many teachers would support the view that directionality andspontaneity rationalized by the meaning ofQKinequalities areenriched if Gibbs energyis introduced. Therefore,they maythinkthat Figure 1 could be used to provide beginning students withconceptual understanding that could be expanded on in latercourses. Moreover, they would also add that Gibbs energy is

useful in teaching electrochemical phenomena. Unfortunately,the scarcity of time at the introductory level would not allow theGibbs energy to be taught well and thus might not favor mean-ingful learning. If Gibbs thermodynamics do have to remain inthe general chemistry syllabus, it must be stressed to authors thatany attempt to introduce them to rst-year students mustsimplify the conceptual approach given in this study, but withoutcontinuing current textbook errors. The teaching of thermody-namics should pay careful attention to the precise meaning of theterminology involved as well as to the demanding difficulty of theconcepts to be learned. Thus, the debate about what, how, andwhen thermodynamics should be taught is still open, challengingfuture research on this topic.1

AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

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