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This paper is aimed at providing an accurate and non-ambiguous description of reaction systems occurring in closed or open systems and involving possible density changes during the reaction. Owing to its systematic character, the proposed method is well suited to implementation on the computer for quantitative calculations, as those which are required for chemical engineering applications. The treatment proposed below is based on standard methods used in Chemical Reaction Engineering (CRE). Unfortunately, the notations universally accepted in the CRE community, which created the corresponding concepts, are different from those recommended in the "Green Book" [ I ] from IUPAC. This especially applies to the rate of reaction which is universally denoted r in the CRE literature instead of v , used by chemists. Related quantities such as the rate of production of species are denoted Rj (CFE) instead of rj (IUPAC). In order to avoid confusion among the chemist's community, the treatment below follows the Green Book's recommendations. However, as this report may also be used by chemical reaction engineers, a summary of the main relationships is given with CRE notations in the Appendix. FOREWORD The proposal below is the final version of a report prepared for the Commission on Chemical Kinetics of IUPAC. Comments on the first draft from Professors J.A. Kerr, K.J. Laidler, Yu.N. Molin and P.J. Van Tiggelen are gratefully acknowledged. The second draft was discussed at the 34th General Assembly, Boston, August 22nd-25th 1987 and the third draft at the 35th General Assembly, Lund, August 9th-15th 1989 by the commission. The fourth draft was further modified according to suggestions from Professor R.A. Alberty, which were particularly helpful. The present version takes into account remarks and criticisms from 15 experts (mainly chemists) among whom it was circulated. Their contribution is greatly acknowledged. CONTENTS 1. 2. 3. 4. 5. 6. Normalized extents of reaction 7. 8. 9. Matrix notation References Appendix : Main relationships. Notations used in chemical reaction engineering Summary of notations and definitions Stoichiometry of a composite reaction network Closed systems. Rates of transformation of species. Rates of reaction Closed systems. Extent of reaction Open or flow systems (purely convective flow only). Expression of rates of production Extent of reaction in a flow system at steady state Density variation during the reaction Expression of various quantities involved in kinetic laws 2642 2643 2643 2644 2644 2645 2645 2646 2648 2649 265 1 2652 2653 Kinetics of composite reactions in closed and open flow systems 2643 1. STOICHIOMETRY OF A COMPOSITE REACTION NETWORK It is assumed that N species Aj , j = 1, 2, 3, ..., N are involved in a system of R independent reactions i = 1, 2, 3, ..., R. In many situations, the reactions are assumed independant, which means that none of them can be obtained by a linear combination of the others. But they may involve common species. The independence assumption is not necessary and many relationships derived below also apply to any reaction network. The stoichiomehic equations are written N C vij Aj = 0 j= 1 i = 1, 2, ... R The vg are the stoichiometric numbers. They may be considered as elements of a matrix yT of rank R (see section 9 below). Example : steam reforming of methane. In traditional form, the chemical transformation inay be described by two equations CH4 + H20 = 3 H2 + CO i = l CO + H20 = CO2 + H2 i = 2 In canonical form j = 1 2 3 4 5 CH4 H20 + 3H2 + CO = O H20 + H2 CO + CO2 = O the stoichioinetric matrix is -1 -1 3 1 0 0 -1 1 -1 1 In the case of one single reaction R = 1 and one has simply N 2. REACTION CLOSED SYSTEMS. RATES OF TRANSFORMATION OF SPECIES. RATES OF Let nj be the instantaneous amount of Aj in a closed system of volume V. For a single reaction, the rate of transformation of species A, is defined as This also constitutes a definition of the rate of reaction v which is thus independent of the considered species Aj (3) v = It must be strongly emphasized that this relationship is only valid for a Single reaction in a closed system. 1 % V j v ' dt The SI unit for v is mol m-3 s-1 2644 COMMISSION ON CHEMICAL KINETICS For composite reactions, each reaction may contribute to the transformation (ix. the formation or the consumption) of Aj whose rate of transformation is R V i is the rate of the z~ reaction. In the example of the steam reforming of methane above rj was defined here as the rate of transformation per unit volume. This convention is well adapted to homogeneous reactions. The rate of transformation may be referred to other quantities, e.g. the mass of catalyst in the case of heterogeneous reactions. This point is thoroughly discussed in textbooks on Chemical Reaction Engineering. The case of homogeneous reactions is not restrictive and was chosen here only for illustration purpose. 3. CLOSED SYSTEMS. EXTENT OF REACTION For one single reaction, De Donder [2] introduced the extent of reaction 5 such that tlj = t1jo + Vj 5 (5 ) t i p is the amount of Aj in a reference state (e.g. at the beginning of the reaction). For several simultaneous reactions (composite xeactions), (5) may be easily generalized. There are R independent chemical variables such that R We must note that with this notation, ti has the dimension of t i j This is a disadvantage if one wishes to measure the extent of reaction with a dimensionless quantity. This problem will be solved by introducing normalized extents of reaction in Section 6 below. 4. EXPRESSION OF rj OPEN OR FLOW SYSTEMS (PURELY CONVECTIVE FLOW ONLY). Let F, be the molar flow rate of species A, in a given cross-section (SI unit mol s-1). I I Assuming that the vessel is well-mixed and of uniform composition, the material balance of Aj in the reactor is written dni dt Fjo + V r j = Fj + (input) (Chemical (output) (accumulation) transformation) (7) 1 dti. It is clear here that rj ?C TJ $. The equality is true only if Fj = Fjo = 0 (closed system). Kinetics of composite reactions in closed and open flow systems 2645 Thus, the rate of reaction must not be defined from 2 in an open system, At steady state For a single reaction This relationship is the basis of the measurement of reaction rates by use of a continuous stirred (well mixed) reactor. 5 . EXTENT OF REACTION IN A FLOW SYSTEM AT STEADY STATE Froin the stoichiometry, one may write (3 = 0) Fj = Fjo + vj 5 and for simultaneous reactions Fj = Fjo + C V i j t i 1 However, ti has the dimension of F, (for which the SI unit is mol s-1). 6. NORMALIZED EXTENTS OF REACTION In order to define a dimensionless (or normalized) extent of reaction, applicable in closed as well as in open systems at steady state, it suffices to normalize ti or ti by an appropriate quantity. . Closed system : Let ti0 = c tijo. For a single reaction, the normalized extent X is defined by i In the case of a non-equilibrated reaction, X increases from 0 (if the reference state is chosen at the beginning) up to a value XL determined by the total consumption of the limiting reactant AL (tiL4) for simultaneous reactions Comparing (6) and (13), one obtains 2646 COMMISSION ON CHEMICAL KINETICS It is advantageous to consider that the sum ti0 =c tIj0 is concerned only with reacting species (e.g. those which are actually involved in the chemical reactions). Non-reactinr or inert species (denoted by index I below) are not included in the sum, in order to give a broader range of variation to Xi , but this is only a matter of convention. Open system at steady state : Let Fo = c Fjo , then i i F j = Fjo + Fo VjX (15) or for composite reactions R i= 1 Fj = Fjo + FO C Vij X i Obviously, X i is the same for a closed or an open system. The dimensionless extent of reaction is thus a vector (see section 9 below). whose components are the R values of X i The advantages of this definition are : X i is unique, both for closed or steady state open systems, X i is dimensionless, X i is exactly equal to the fractional conversion of the reactant in the case of a single reaction consuming this reactant, e.g. A +products )1A = )lAO (1 X A ) In all other cases, the fractional conversion of a reactant Aj may be expressed as a function of the X i but is a quantity of different nature. Concludinc remark Other normalization factors for ti are possible, depending on the problem. For instance, ti may be normalized by the total mass m of the reacting phase X'i = &/m (closed system) or by the mass flowrate X'i = {i/Q,l, (open system). But X ; is no longer dimensionless. X A = X , extent of reaction 7. DENSITY VARIATION DURING THE REACTION Closed system : The variations of volume can be easily accounted for by using the concept of normalized extent of reaction. For a single reaction in the gas phase, in the presence of inerts (I) : ) l j = )tjo + Vj ti0 X The total amount of substance is N j= 1 t i = C )lj + 111 = )lo + + C vj x Kinetics of composite reactions in closed and open flow systems 2647 Let A V = C vj i I = I no Av a = 1 +I The total amount of substance is 11 = (r10 + 111) (1 + ax) In an ideal gas, pV = riRgT, where Rg is the gas constant Let the physical dilation factor (or volume strain) be then v = p vo (1 + 03) The rate of reaction is such that where co = rio/Vo More generally, defining the chemical dilation factor (or amount strain) as a = co Avo with Aco = C vjzljo, where zljo is the molar volume of species A,, (23) holds for any phase (especially for liquids). It is assumed here that partial molar volumes in mixture are the same as pure molar volumes. i These relationships can be easily extended to the case of composite reactions. (23) is generalized to \ where C vij &=2-1__ Av. . 1+1 1+I for gases VijVjo for any phase But, now the relationship between v; and X ; may involve the normalized extents of all reactions 2648 COMMISSION ON CHEMICAL KINETICS Ooen flow system at steadv state Analogous relationships are obtained for

Kinetics of composite reactions in closed and open flow systems (IUPAC Recommendations 1993)