Teaching chemical equilibrium

Jean Gold and Victor Gold Le Chatelier's Principle

and the laws of van't Hoff. The teaching of chemical equilibrium is considered to be difficult and its place in the school curriculum is under discussion. This article shows that the difficulties stem largely from over-emphasis of Le Chatelier's Principle and that a clearer understanding can be gained by the alternative use of van't Hoff's laws.

The concept of chemical equilibrium and the: factors wh ich affect it are fundamental and central to the teaching of chemistry at all levels. Knowledge of the effects of temperature, pressure and concentration on the proportion of reactants and products of a reaction is of practical as well as of theoretical importance.

Unfortunately this basic topic has been so beset by conceptual problems that it has acquired the reputation of being difficult to teach. 1 This has been re-emphasised in a recent article,2 published since the completion of our review of the field, in which Allsop and George cite a number of the conceptual problems that arise from the use of Le Chatelier's Principle at A-level. It is interesting to discover that similar anxieties were being expressed as early as 1922,3 for by then the teaching of chemical equilibrium using Le Chatelier's Principle had become established via books such as Chwolson's and popular teaching textbooks in Engl ish. 4

The statement was made 100 years ago, in 1884, and it is pertinent to examine Le Chatelier's Principle in relation to its place in modern teaching. Allsop and George entitled their paper 'Le Chatelier - a redundant principle?' We emphatically agree with their point of view, and would go even further; the question mark at the end of their title is also redundant!

A glance at most present-day general textbooks of chemistry will show that the 'Principle' still occupies a surprisingly prominent and authoritative position. For example, the textbooksa Chemistry (Teacher's Guide) for the influential CHEM-study course states that 'Le Chatelier's Principle is worth stressing as a tool for predicting the effect of various changes on the equilibrium of the system,' and many references are made to Le Chatelier's Principle in the students' text. Sb In the Teacher's guide I to Nuffield Physical Science (A-level), it is assumed that the Principle is known from O-Ievel. 6 In the course-book Chemical systems of the Chemical 82

Bond Approach Project, there are several references to Le Chatelier and his Principle. In contrast this same Principle is omitted from or hardly mentioned in most modern undergraduate textbooks of thermodynamics and physical chemistry. It follows that knowledge of Le Chatelier's Principle cannot be a pre-requisite to a deeper understanding of chemical equilibrium. Its inclusion in more elementary teaching can therefore be justified only if it provides an easier and conceptually simpler introduction.

In the past, material in the school syllabus was also frequently included if it was thought to mark an important milestone in the historical development of ideas but, by itself, this is no longer considered suitable during a pupil's first exposure to a subject (cf the omission of the phlogiston theory).

In the current phase of syllabus construction, should one therefore not look rather carefully into the case for and against mentioning Le Chatelier in school chemistry courses? It is our view

that Le Chatelier's role in the development of the subject hardly justifies the inclusion of his contribution simply for historical reasons,

2 that it is not easy to state the principle in an unambiguous form,

3 that the u~ual formulations of the principle to be found in elementary textbooks are scientifically incorrect, and

4 that a simple and correct introduction to the principles of chemical equilibrium, suitable for school teaching, is to be found in the work of van't Hoff.

We shall now seek to justify these assertions in turn.

History The first published statementB by Le Chatelier of his principle was made in 1884. He emphasised that it was an experimental law, derived partly from

a consideration of Lippmann's general theory of reciprocal phenomena,9 itself based on Lenz's law of induction. In his brief paper, Le Chatelier also acknowledged, as his other source of inspiration, van't Hoff'slO principle of mobile equilibrium (the effect of temperature on equilibrium). Since the modern treatment of chemical equilibrium is based on the further development of van't Hoff's prior ideas, Le Chatelier's intervention may be viewed as a digression which did not significantly contribute to the advance of this topic. (In fairness, it must be emphasised that le Chatel ier worked in many other areasll of applied chemistry and that he achieved much recognition for these researches.) In the literature, especially outside France or Britain, the principle is often referred to as the le Chatelier-Braun Principle. However, Braun's publications12 were certainly subsequent to Le Chatelier's first paper. Braun's version of that principle, though in some ways more impressive, suffers from many of the same weaknesses as Le Chatelier's statement. These are discussed below.

Ambiguities in Le Chatelier's Principle Le Chatelier's verbally convoluted, qualitative and non-mathematical principle was described 13 by him as 'tres simple' implying that he grossly underestimated the difficulty of giving an all-embracing general statement. According to Prigogine and Defay,14 'the principle of Le Chatelier and Braun suffers from a number of important exceptions. Many workers have attempted to restate this principle in a completely general form; but this form, if it exists at all, is necessarily very complex'.

These distinguished thermo­dynamicists have not been alone in their criticisms. Others 1 5 have objected to its lack of clarity and precision and its predictive unreliability. Some16

have attempted to re-state the principle more accurately by a process of analysis and re-synthesis, but the resultant complex formulations are still unsuitable for teaching purposes. Thus, the scientific inadequacy of Le Chatelier's Principle has long been appreciated by experts in the field. The reader is referred to a recent review! 7

for further discussion of this aspect.

EDUCATION IN CHEMISTRY, MAY 1985

le Chatelier: over-emphasising the use of his Principle makes for difficulties in teaching chemical equilibrium.

Restatements of Le Chatelier's Principle in textbooks In view of these objections it is not surprising to find many simplified or 'personalised' reformulations in text books. In fact, virtually every teaching book that mentions Le Chatelier has its own version.

Le Chatel ier undoubtedly meant his principle to be a ' law of opposition' (which is the heading of the chapter13

in which it is discussed); this must arise from its origin in Lenz's Law. It is interesting to note that Le Chatelier himself did not keep to one statement. The detailed one of 18848 was shortened in 188813 to (in translation) 'Any system in chemical equilibrium will undergo, as a result of a variation of a single one of the factors governing the equilibrium, a change in such a direction that, had that change taken place by itself, it would have brought about a variation in the opposite direction of the factor under consideration,' but in 1933 , after criticism from Posthumus, 18 Le Chatelier decribed this 1888 version as 'inexact' replacing it by yet another, 19 closer in spirit to the original in the 1884 paper.

This original interpretation is typically paraphrased in teaching text books as: 'Whenever stress is placed on any system in a state of equilibrium, the system will always react in a direction which will tend to counteract the applied stress.' 20 Some authors21 have adopted a similar version. Over the years this concept of a law of opposition has been changed by others into a 'principle of moderation '. To take one example: 22

'When a stress is brought to bear on a system at equilibrium, the system tends to change so as to relieve the stress'.

EDUCATIO IN CHEMISTRY, MAY 1985

(See also reference 23) Words su h as ' relieve' and 'minimise' imply that th system yields to the acting stress, whereas 'counteract' and 'oppo ' suggest a concept of confl ict or antagonism.

Another, more subtle, point whi h seems to have been ov rlooked in textbooks is the confusion of ' tr s ' with the 'effect of stres '. Wher as a translation of Ostwald' 24 textbook gives: 'If one exerts a con traint on a system in equilibrium which caus s a displacement of that equilibrium th n a process takes place which oppo s that constraint, ie it partially annuls th effect of that constraint' (s e al 0

reference 25), this is changed by Partington 26 into: 'If a system in equilibrium is subjected to a constraint, whereby the equilibrium is modified, a change takes plac , if possible, which partially annuls th constraint' .

Sometimes attempts are made to distinguish between intensive and extensive variables as in 'A change in any of the variables such as temperature, pressure or concentration, that determin th conditions of equilibrium in a physicochemical system will shift the equilibrium to reduce the magnitud of this change' 27 (see also referenc 28). However, even this stat ment ca nnot escape the criticism that it fails to alert the student to the need for distinguishing clearly between temperature and heat. The s eming confusion of these concepts is one of the reasons why attempts to apply Le Chatelier's Principle oft n s em to follow a tortuous line of argument.

It is not uncommon to aim at complete generality by omitting the variables altogether, as in: ' If

conditions of a system, initially at equilibrium, are changed, the equilibrium will shift in such a direction as to tend to restore the original conditions' 29 (see also reference 30). How ver, this is not very helpful to either tudent or teacher. What is meant by 'conditions' ?

The various combination of word and phras s, some of which are discussed above, give ri to a wid choice of definitions of the princ iple.

Different version of th same id a may be illuminating (or a chall nge) to those familiar with its fundam ntal content. However, young students, s eking clarifi ation nd guidan ,ar bound to find such vari ty confuSing, particularly in a statem nt th l i pres nt d a on of th important laws of chemistry. T a h r ,31 similarly, consid r ch mi al quilibrium to be a difficult topic, and on c n only sympathi with tho tach r-author who have to xplain th prin ipl in detail, J2 a ta k whi h L h t Ii r hims If did not att mpt.

Th virtually unavoid bl I os n of languag and thought in many textb ok xp siti n of L hat Ii Principl tap or xampl to stud nts who ar usually just at th stage bing xhort d t b I ar in th ir d finitions and fastidious in th ir us of physi 0 h mi al unit and syst mati h mi al n m n latur .

Th original formulati n of th principle wa ou h d in languag with a v ry high ' fog ind x', so perhap it i not urpri ing that v n the simpler v rsion r quir a languag ski II b yond that appropriat to th ag (or I v I of attainm nt) at whi h th oncept of quilibrium i inlrodu d.

Moreo v r, v n if the words ar int IIigibl at fa value or m mori s d v rbatim, how an th impli it r asoning be und rstood , in the con lusions from th applic tion of L Chat lier's Principl are fr qu ntly wrong?1 7

Van't Hoff's laws If L Chat Ii r' Prin ipl is th refore inappropriate for t a hing in chool , what ould be taught in it pia e? Th equilibrium law (' law of ma a tion ') or 'law of Guldb rg and Waage'3l is indep nd nl of considerations of pr s ur or temp rature chang sand pre-dat s Le Chateli r's Principle by several y ars.

Chemical quilibrium and the equilibrium constant can be und rstood as xperimenlal fact without recours to later and more advanced ideas, and without r f ren to Le Chatelier .

Apart from chang s in on ntration

83

van't Hoff: his laws of chemical equilibrium were stated before Le Chatelier's, and are more suitable for teach i ng.

(adequately covered by the law of mass action) the effects of temperature and pressure (or volume) changes are the most important influences on equilibrium systems to be considered, and the only ones relevant to the treatment of the subject at a simple level. They were lucidly stated and explained by van't Hoff and in part, as acknowledged by Le Chatelier, preceded Le Chatelier's Principle. Moreover, van't Hoff's treatment can be made quantitative. It is compatible with a logically evolving progress in learning by leading on to more advanced work in chemical thermodynamics. Van' t Hoff's principal laws concerning chemical equilibrium can be stated in the form of two brief statements taken from his Lectures on theoretical and physical chemistry. 34 Their language is simple and they seem to offer a suitable approach for use in schools.

I. Increase in press ure favours the system pos essing the sma ller volume (a t constant temperature). The converse case, ie decrease in pressure favouring the system of larger volume, i included by implication. It also follows that, if the two systems in equilibrium occupy equal volumes, eg

2HI ~ H2 + 12 A

a change in pressure can have no effect on the equilibrium position.

In the ca e of gaseous equilibria between systems of unequal volumes eg

B

an increase in pressure will produce a higher proportion of N 20 4 in the equilibrium mixture, (s ince the left hand side of the equation contains fewer molecules and thu s, at the same temperature and pressure, corresponds

84

to a smaller volume). Van't Hoff also gives the alternative

form ' Increase of volume favours the system possessing the greater volume', that is, a volume increase of the reaction vessel would lead to the production of more N02 in the reaction. These laws can be applied also to phase changes eg the effect of pressure on the melting point of ice, or to solubilities.

II. Rise in temperature favours the system formed with absorption of heat Taking as example the gas-phase equilibrium,

2H 20 ~ 2H2 + O 2 (AH positive)

a temperature rise will favour the formation of the gases hydrogen and oxygen , and cooling will favour the production of water. Another example is evaporation, for which the law predicts an increase in vapour pressure with rise in temperature.

It follows that reactions that do not involve the absorption or liberation of heat cannot be affected by a temperature rise . Van 't Hoff includes in this context an interesting consideration of the interconversion of enantiomers in a racemic mixture. Since this process cannot involve the liberation or absorption of heat, it is impossible to effect a partial resolution of the mixture simply by changing its temperature! Unlike Le Chatelier, van't Hoff, in this case clearly distinguishes between temperature and quantity of heat.

It is not necessary to expound here the quantitative side of van ' t Hoff's ideas and their place in the development of the science of chemical thermodynamics . It is sufficient to remind ourselves that van't Hoff's well known equation

(a In Kp\ = AHO

aT /p RT2

is the quantitative expression of the second of the laws cited above, implying that not only the algebraic sign of the effect of a temperature change is predictable, but also its magnitude. A similar equation applies to the pressure effect.

In conclusion we hope that this discussion will lead to a re-appraisal of the historically prior work of van't Hoff and its suitability for teaching even at a relatively elementary level. Perhaps this will also help to dispel some of the fog surrounding chemical equilibrium, arising from the over-use of Le Chatelier's Principle. Let it not be written, as it was in 1889 in the translator's preface to W. Ostwald 's35 Outlines of general chemistry, 'the singular disregard of the discoveries of van't Hoff .. . amongst the Engl ish speaking scientific public must be in great measure attributed to the want of a connected account of them' .

Victor Cold is professor and head of the Department of Chemistry, King/s College London, Strand, London. Jean Gold is tutor in history and philosophy of science at the Open University.

References 1. A. H. Johnstone, J. J. MacDonald and G.

Webb, Educ. Chem., 1977, 14, 169. 2. R. T. Allsop and N . H. George, Educ.

Chem., 1984, 21, 54. 3. C. Benedicks, Z. Phys. Chem., 1922,

100, 42 . 4. O. Chwolson, Lehrbuch der Physik, 3.

Bd., Braunschweig, 1905, p 474, and, for example, A. F. Holleman and H. C. Cooper's A textbook of inorganic chemistry (trans. by H. C. Cooper). New York: Wiley , 1916; A. Reychler, Outlines of physical chemistry (trans. by J. McCrae). London: Whittaker and Co. , 1899; H. J. H . Fenton, Physical chemistry for schools, Cambridge Unviersity Press, 1916.

5. (a) Chemistry - teacher'S guide, Chem. Ed. Material Study, NSF, p 273. San Francisco: W. N. Freeman and Co., 1963. (b) Chemistry - students' textbook, pp 149, 150, 181 , 188,2 14, 337,360.

6. Physical science (Teacher's guide I) , Nuffield Advanced Science, Harmondsworth : Penguin Books, 1972.

7. Chemical systems (Chemical Bond Approach Project) . ew York: McGraw-Hili, 1964.

8. H . Le Chatelier, Compt. Rendus, 1884, 99, 786. 'Tout systeme en equilibre chimique stable soumis a ('influence d 'une cause exterieure qui tend a faire varier soit a temperature, soit sa condensation (pression, concentration, nombre de molecules dans I'unite de volume) dan sa tatalite ou seulement dans quelques-unes de ses parties, ne peut eprouver que des modificatiOns interieures, qui, si elles e produisaient seules, ameneraient un changement de temperature ou de con den alion de signe contraire a celui resultant de la cau e exterieure. '

EDU(ATIO I (HEMI TRY, MAY 1985

'Any system in stable chemica l equilibrium, when subjected to the influence of an external cau e which tends to change either it temperature or condensation (pressure, concentration, number of molecules in unit volume) throughout or in only some of it parts, can undergo only such internal modifications which, if they occurred on their own , would bring about a change of temperature or of conden ation of a ign contrary to that resulting from th external cause' .

9. G. Lippmann , Ann. Chim . Phy ., 1881, 24,173 .

10. J. H. Van' t Hoff: (a) Etudes de dynamique chimique, 1884 ; (b) Studies in chemica l dynami s, (tran by T. Ewan and revised by E. Cohen), London : Williams and Norgate, 1896.

11. Bibliography of H. Le Chatelier' published papers : Bull . oc. Chim., 193 7, T4, 1596-161l.

12. F. Braun, Wied. Ann. d . Phys u . Chem., 1888, 33, 337 . See al 0 Ann. Phy . 141, 1910, 32, 1102.

13 . H . Le Chatelier, Ann. Mine, 1888, 13, 157-382. (Tout y teme en equi/ibre chimique eprouve, du fait de la varia tion d 'un eul des facteur de I'equilibre, une transformation dan un sen lei que, i elle e produi ait seule, elle amenerait une variation de igne contraire du facteur considere.)

14. I. Prigogine and R. Defay, Chemical thermodynamic (trans by D. H . Everett). London: Longmans Gre n, 1954.

15 . For example, P. Ehrenfest, Z. Phy . Chem ., 1911 , 77, 227; M . Plan k, Ann . Phys., 1934, 19,759; P. Epstein, Textbook of thermodynamic, hap. 21. New York: Wiley, 1937.

16. C. Raveau , Compl. Rendu , 1909, 148,

767; A. Aries, Compt. Rendus, 1914, 158,492 .

17. J. Gold and V. Gold, Chem . Br., 1984, 20,802 .

18. K. Po thumus, Rec. Trav. Chim ., 1933 , 52, 25; 1934, 53,308.

19. H . Le Chatelier, Compt. Rendu , 1 33, 196,155 7.

20. S. H. Maron and J. B. Lando (0, Fundamental of phy ica l hemi try , p 365. New York: Macmillan, 1974. (In this and the following r fer n th letter 0, A, C in parenthese following the authors' name indi ate th I v I of the book : GCE O-Ievel, A-lev I, American College or Univ rsity t xL)

21. For example: J. R. Palmer and B. A. J. Shaw (0), Chemistry explain d, p 240 . Slough: Univer ity Tutorial Pr , 1980; G. F. Liptrot, J. J. Thomp on, G. R. Walker (A), Modern phy i al h mi try, p 268. London : Bell and Hyman, 1982; G. W . Castellan (0, Ph y ica l hemi try, p 221. Reading, Mass: Addi on-W I y, 1964.

22 . C. W . K nan and J. H. Wood ( ), General college chemi try , 4th edn, p 199. New York : Harp r and Row, 1971 .

23. D . N. Underwood and D. E. W b t r (0 )' Ch mi try, 4th dn, p 171. London : E. Arnold , 1979; P. W . Atkin nd M . J. Clugston (A), Prin iple of phy i al chemi try, p 155. London : Pitman, 1982; M . J. Sienko and R. A. Plane ( ), Chemi try, 5th dn, p 186. N w York : McGraw-Hili , 1976.

24. W . twald , rundlini n d r Anorgani ch n Chemie, p 10 337. Leipzig; Eng Imann, 1900.

25 . D . arvie, J. Hughes, J. R id and A. Rob rt on (0), on i e h mi try, p 246. ford University Pr , 1 7 ; I. W . Buttle, D. J. Daniels and P. J. B k tt (A),

26.

27 .

28.

29.

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31.

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34.

5.

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