Describing Chemical Transformations From the Extent of Reaction 5 to the Reaction Advancement Ratio x A. ~ u m o n ; A. Lichanot, and E. Poquet Groupe de Recherche en Didactique de la Chirnie, Universite de Pau et des Pays de I'Adour, 64000 PAU - France The multiplicity of concepts, symbols, and terminology used to express the advancement of a reaction in a chemical system can hamper our grasp of phenomena. I t oRen impedes mutual comprehension among practicing chemists and excludes beginners. Thus, standardizing this terminology is imperative. The conventional description of the evolution of chemical systems is riddled with a multiplicity of symbols and subtleties interminology, oRen causing confusion in usage. (See the table.) Conventionally, 6is the extensive property that represents the extent of reaction. It is defined by the following equation ni - nio
The Multiplicity of Symbols and Terminologies (Examples Issued Principally in French Literature) symbol
5
Its use is rewmmended by IUPAC (5). This equation of definition shows that the same state of advancement of a reaction can be described by very different values oft, d e pending on the following
-state of advancement -degree of advancement
reference Jouquet 1917 (in Dod6) mole De Donder 1920 Prigogine Defay 1944 mole Balesdent 1969 iUPAC 1979 mole Levet 1988 dimensionless Gromb 1969
x, X A, 1
X a r
5(-v0
dimension
degree of advancement advancement generalized advancement normalized advancement degree of dissociation conversion yield yield
mole mole dimensionless dimensionless dimensionless dimensionless dimensionless
advancement ratioa
dimensionless Rouquerol 1985
-chemical variable -degree of advancement
-
=-
Vi
name
advancement
Aris 1965 Vidal 1988 Villermaux 1982 Villermaux 1989
(1) (2) (3)
(4
cn
id (7)
(8) (s)
(10)
(11)
(12)
X 1
advancement ratiob dimensionless Gaboriaud 1988 (13) the value of n, cr' 5_ degree of advancement the reaction scheme chosen, stemmingfrom advancement ratio dimensionless Boltin 1989 (14) the indetermination of the staichiometric 5' equation, for example, L indicates that if is relative to fhelimaing reactant;b represents the initial amount of substance of the limiting reactant. H,+ bz O, H20 The index means that the limiting reactant has totally disappeared. 2
-
or 2%
+ 0, s Z%O
Thus, there is difficulty surrounding the use of 5, leading to confusion-even inaccuracies-when this property is presented in textbooks. And what is one supposed to make of the expression 5 = 1lorsque la reaction a avancd une fois [k = 1when the reaction has advanced one go (2).1? The Extent of Reaction Parameter The Minimal Qualities Required
A quantity t h a t is attached to the reaction itself is needed. It should have the following properties independent of the choice of stoichiometrie coefficients 'independent of the absolute value of the amounts of substance equally valid for use in microscale and industrial-scalework independent of the component used to follow the reaction a numerical value that is easily understood-that can be related to the m e n t notions of reaction yield without dXidty
' Author to whom correspondence should be addressed.
"Premier cycle" is the equivalent of the first two years at university.
Also, this quantity should be accessible to all users of chemical reactions: beginning chemists, school children, students, teachers, engineers, and technicians. I t should be easily applicable within the various fields that study chemical reactions: thermodynamics, kinetics, and chemical engineering. Our Proposition: The Reaction Advancement Ratio x Its Origins The followingthree terms and their usage influenced our development. The extent of reaction 5 (51, a dimensioned property (amount of substance in moles), of the same kind as the degree of advancement initially presented by De Donder (2). The dimensionless degre d'auancement 5 introduced by Gromb (7), which is at the basis of our proposition. The t a u d'avancement of reaction, presented in 1985 by Rouquerol and Lafitte (12).
Its Symbol: We use x because it is a symbol with little historical and current use and-above all-because it is different from the symbol that represents the dimensioned advancement of a reaction. Like the term "chemistry" itself, "x" can be Volume 70 Number 1 January 1993
29
used without the usual risk of confusion in chemical situations.
Its Equation of Definition: from t to x Its stoichiometric equation would be the following
Chemical Kinetics
From the IUFW recommendations we report the following The rate of conversion
The rate of reaction based an the concentration
with vi
(stoichiometricnumber) > 0 for products < 0 for reactants
At the initial time t = 0, the system is made up of ni, moles of A,. If the mixture is realized in any proportions, then there is a limiting reactant, called AL. It corresponds to the lowest value of
Under their apparent simplicity, these formalisms hide the difficulty attached to the extensive character of 5. Like 5.5 is extensive. Thus, if the amounts of the chemical species are multiplied by x, the value of 6is multiplied by I. Replacing 6by &- X , we obtain
c
=S r n k
Thus. r is an "intrinsic" rate of conversion that is linked to the chLmical process itself. It is dissociated from the extensive effect, which is clearly localized in the following term
which is
where aL> 0, that is, aL is a whole or fractional quantity expressed in moles. When n i is the amount ofAj present at time t in the system, the advancement of the reaction between t = 0 and t for each component Ai is such that dni = vi dc and
t )introduced by takThe reaction advancement ratio ~ ( is ing the limiting reactant as a reference. When this react&t has compiktely disappeared, that is, when the reaction is complete, nL(t)= 0. We can then write
The rate of reaction, which is based on concentration and expressed as a fundion of X ,is given below
It can be kept and exploited in the traditional way, in all developments of chemical kinetics. Note that the hypothesis, implicit or explicit, of a mixture of reactants "in stoichiometricproportions and quantities" used for the classical mathematical treatment of kinetic equations allows one to get around the difficulties linked to the use oft. In fan, it is nothing other than relating to jl.
5
Conclusion
t )the reaction advancement ratio at time t. It is where ~ ( is a dimensionless number whose extreme values are given below 0 Before the chemical reaction starts. 1 When the limiting reactant has completely disappeared The amount of any chemical species in the reaction mixture at any time t is given by the following relation Examples of the Use of x Thermodynamics
The reaction heat at a constant pressure Q p is shown below using the reaction advancement ratio x Q P = ~ = I ~ P~ T, +~ S ~ ~ ~ H P , T .-;6) ( X To
30
=
f$
Literature Cited 1. Jouquet'Meehaniea of mlosi-, Doin. 1917'InFunhntolBosrs of Ckmiml % d y " o m l c . ; D d e , Ed.; Sedea: Paria,19%. 2. van Der Dungen; van Lerbughe, G. In Lam" on T k m d y w m i u r a d Physiml Chemistry;De Dander, Ed.; Gauthier-Villara: Patis. 1920. 3. Pngagins, I.; M a y , R. Chemlcoi T k d y m m i c s ; GauthierVdlars: Pa*, 1944 4. Balesdenf,D. In Ckmlcd T k d y n a m i c D ; Monographs WSAm. 6,Rouaquet. J., Ed.;Masson: Paris.1969. 5. Manuul of Symbols and Terminolagy for Physlcmhomial Quantities and Uni&; P u n a d A p p i . Ckm.; Milla, I., Ed 6. Levet, J. C.B.U.P. 1888,1704,561576. 7. Cmmb, S.;J0ussat-Dubien, J. 1ntmdvction to chemim1 m m d y m m i q Dunod Uniueraite: Patis, 1969. 8. Ms. R. lnhodudion to the Anolvsi. of Ckmiml Reocfws: Rentiee-Hall: En&wdod Cliff%NJ,1965. 9. Vidal, C.; Lwarehand. H.TheCmtiwF2mtion; Hermam: Paris. 1988. et Dmumentstisti: Paria, 10. Villermsua,J.GoniusoftkCkmim1Re~tiOio;T~hni4i4e
.
19R2 - ~
where AH is the variation of the enthalpy of the system; A,Hp,~o is the reaction enthalpy; and
% ,
The variable X , the reaction advancement ratio, can easily replace the extent of reaction t, which is recommended by IUPAC. It also frees us from the use of various associated variables, such as "yield" and "dissociation coefficient". Thus, it simplifies and unifies the description of the chemical reaction. Since 1969 we have integrated the use of x into our "Premier Cycle" teaching Our experience has led us -program.2 . to conciude that students can use it without the slightest problem.
of the limiting reactant
Journal of Chemical Education
~
.
-
11. V i u e m u r , J. Kinetics ofcwnpmitp Reaction in C l o d oM! opn n u Sya&m: Repmt presented tothe Chemical Kinetics Committeeofthe IUPAC. 1988. 12. Rouqueml, F.:LeAite.M.EAefuolifp Chimigm; 1986 November 5155. 13. Gsborisud,R.;Lelievre, J.: Lemordant, D.; Letellier, F.;Millot F Chemiml Thermody-lcsApplied to the Chemistry ofSdutim; Ellipse: Paris,1988. 14. Battin, J.; Mallet, J. C. Chemism h m m ; Dunod:Pa% 1989.
