Le Chatelier`s Principle and the laws of van`t Hoff.

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 textbook sa 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 areas l l 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
publications 12 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. Some 16
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 chapter 13
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 1884 8 was
shortened in 1888 13 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
authors 21 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 co nfuSing,
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-a uthor
who have to xplain th prin ipl in
h t Ii r
detail, J2 a ta k whi h L
hims If did not att mpt.
Th virtually unavoid bl I os n
of languag and thought in many
hat Ii
textb ok xp siti n of L
tap or xampl to
Principl
stud nts who ar usually ju st 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 th e word s ar
value or m mori s d
int IIigibl at fa
v rbatim , how an th impli it
r asoning be und rstood , in
th e
con lu sion s 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 th e
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
a In Kp
\
( aT /p
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.
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 N0 2 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
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 ~ H 2 + 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 2 0 4 in the
equilibrium mixture, (since the left
hand side of the equation contains
fewer molecules and thu s, at the same
temperature and pressure, corre spond s
84
+ 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
= AHO
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 (tran s. by H . C. Cooper). New
York: Wiley , 1916; A. Reychler, Outlines
of physical chemistry (trans. by J.
McCrae). London: Whittaker and Co. ,
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Francisco: W. N. Freeman and Co.,
1963.
(b) Chemistry - students' textbook, pp
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8. H . Le Chatelier, Compt. Rendus, 1884,
99, 786.
'Tout systeme en equilibre chimique
stable soumis ('influence d 'une cause
exterieure qui tend 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 celui resultant de la cau e
exterieure. '
a
a
a
EDU(ATIO
I
(HEMI TRY , MAY 1985
'Any system in stable chemica l
equilibrium , when subjected to the
influence of an external ca u 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,
157-3 82.
(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
fa c teur 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,
17.
18 .
19 .
20.
767; A. Aries, Compt. Rendus, 1914 ,
158,492 .
J. Gold and V. Gold, Chem . Br., 1984 ,
20,802 .
K. Po thumus, Rec. Trav. Chim ., 1933 ,
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H . Le Chatelier, Compt. Rendu , 1 33,
196,155 7.
S. H. Maron and J. B. Lando (0,
26.
on
27 .
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th
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American College or Univ rsity t xL)
For example: J. R. Palmer and B. A . J.
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1964.
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W.
twald , rundlini n d r
Anorgani ch n Chemie, p 10 337.
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D . arvie, J. Hughes, J. R id and
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28.
29.
30.
31.
2.
33.
nt nary
I
Nor k
34.
5.
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