WHAT CAN KINETICS LEARN FROM NONSTATIONARY THERMODYNAMICS Miloslav Pekař Faculty of Chemistry Institute of Physical and Applied Chemistry Brno University of Technology Brno, Czech Republic

INTRODUCTION Evolution of experimental methods in chemical kinetics. Fine details of chemical processes and their mechanism can be obtained. Evolution of thermodynamics up to several general theories not limited by space or time homogeneity. Kinetics and thermodynamics – two different and independent, though complementary approaches to description of chemically reacting systems.

INTRODUCTION Most often thermodynamic-equilibrium restrictions on chemical processes and rate equations are discussed. Rational thermodynamics + Samohýl  new approach to chemical kinetics. Direct derivation of rate equations with new insights on the relationships between mechanism and kinetics. Overview of this method and its potential relevance in kinetic research and data treatment.

ESSENCE – function Rational thermodynamics proof: for fluids with linear transport properties reaction rate is function of only temperature and densities or, alternatively, concentrations: J = J(T,c)

ESSENCE – approximation Proved general function is approximated by a polynomial of degree M: J = (J 1, J 2 …, J p ) p…number of independent reactions n…number of components rate constants vector: Z…number of polynomial terms

ESSENCE – consistency Fundamental thermodynamic requirement: equilibrium concentrations found from kinetic equilibrium condition, J = 0, must accord with the values of equilibrium constants restrictions on approximating polynomial follow

ESSENCE – procedure 1.Independent reactions are selected. 2.Approximating polynomial of selected degree is constructed. 3.Equilibrium constants are used to express some concentrations as functions of remaining ones. 4.Modified polynomial should be zero for arbitrary equilibrium values of remaining concentrations. 5.Simplified polynomial results.

EXAMPLES – adsorption “Atoms”: A, S “Components”: A, S, AS One independent reaction; selected: A + S = AS second-degree polynomial  standard mass-action law third-degree polynomial gives following rate equation: J A = – J

EXAMPLES – adsorption interpretation of individual terms as reactions A + AS = 2 A + S 2 AS = A + S + AS A + 2 S = S + AS

EXAMPLES – dissociation adsorption for components A 2, S, AS, A 2 S two independent reactions are possible selected A S = 2 AS A 2 + S = A 2 S second degree polynomial – two terms A 2 + S = A 2 S A 2 S + S = 2 AS

EXAMPLES – dissociation adsorption third degree polynomial – nine terms both independent adsorptions included desorption by impact: A 2 + A 2 S = 2 A 2 + S desorption by surface mobility: AS + A 2 S = A 2 + S + AS surface rearrangement: S + 2 A 2 S = 2 AS + A 2 S

EXAMPLES – isomerisation “Atoms”: A, S “Components”: A, S, AS, RS, R lead to three independent reactions, e.g.: A + S = AS AS = RS RS = R + S

EXAMPLES – isomerisation second degree polynomial may contain up to 9 terms, e.g. A + S = AS A = R A + AS = A + RS A + R = 2 R AS + S = RS + S R + S = RS AS + RS = 2 RS RS + R = AS + R 2 A = 2 R

EXAMPLES – isomerisation the term corresponding to AS + S = RS + S reads and can be interpreted as surface reaction with concentration dependent rate “constant”

EXAMPLES - CO oxidation CO + ½ O 2 = CO 2 Atoms: C, O, S Components: CO, O 2, CO 2, S, OS, COS 3 independent reactions are possible, e.g.: O S = 2 OS CO + S = COS OS + COS = 2 S + CO 2

EXAMPLES - CO oxidation second degree polynomial approximation: three reactions “appear” CO + S = COS CO + OS = CO 2 + S O 2 + COS = CO 2 + OS O S = 2 OS CO + S = COS OS + COS = 2 S + CO 2

EXAMPLES - CO oxidation appearing in rate equation CO + S = COS CO + OS = CO 2 + S O 2 + COS = CO 2 + OS selected O S = 2 OS CO + S = COS OS + COS = 2 S + CO 2 reactions “appearing” are combinations of reactions “selected”, but the terms in rate equation could not be combined in this way

EXAMPLES - CO oxidation rates of formation:

EXAMPLES - CO oxidation dissociative oxygen adsorption requires third degree polynomial: resulting rate equations are rather complicated and may contain up to twenty terms, many steps describe various displacements by attack of gaseous species onto adsorbed ones or various trimolecular reactions of low probability, rate constants of all these steps set to zero:

EXAMPLES - CO oxidation five reactions can be identified: CO + S = COS CO + OS = CO 2 + S O 2 + COS = CO 2 + OS OS + COS = 2 S + CO 2 O S = 2 OS CO + S = COS OS + COS = 2 S + CO 2

EXAMPLES - CO oxidation adding also non-dissociatively adsorbed oxygen (O 2 S) to the component list four independent reactions are possible, e.g.: O S = 2 OS CO + S = COS OS + COS = 2 S + CO 2 O 2 + S = O 2 S

EXAMPLES - CO oxidation in second degree polynomial approximation following reactions are found: CO + S = COS O 2 + COS = CO 2 + OS O 2 + S = O 2 S S + O 2 S = 2 OS O S = 2 OS CO + S = COS OS + COS = 2 S + CO 2 O 2 + S = O 2 S

EXAMPLES - CO oxidation For the oxidation itself only the first two steps are necessary. The last two can be viewed, in their reversed direction, as liberation of active sites occupied by oxygen For oxidation of one CO molecule only “a half” of oxygen molecule is needed. In the forward directions, the last two steps block the active sites. CO + S = COS O 2 + COS = CO 2 + OS O 2 + S = O 2 S S + O 2 S = 2 OS

PRINCIPAL FEATURES operates with independent reactions only, but resulting rate equations “contain” also other reactions, relevant for the kinetic description, kinetic equilibrium criteria are fulfilled with more general equation than usual Guldberg-Waage with no need for “kinetic” equilibrium constant, reaction mechanism for given set of species directly appears,

PRINCIPAL FEATURES effects of other reactions or inert species on the rate of particular reaction are possible and naturally included, rates of all dependent reactions can be unambiguously expressed from the rates of selected independent reactions, independent reactions with “single simple” intermediate, i.e. intermediate which is sole product in one reaction (step) and sole reactant in another step, are not supported,

PRINCIPAL FEATURES reaction orders are only whole numbers, importance of “additional” terms in the rate equation should be well assessed when the equilibrium constants of selected independent reactions are known, no need to determine the backward rate constant from kinetic experiments, not all rate constants must be positive (second law of thermodynamics).

APPLICATION SUGGESTIONS (…see the following flowchart)

Detection of “all” components in reacting mixture  atoms, components  number of independent reactions Proposal of independent reactions  stoichiometric matrix — chemical intuition — algebraic method (e.g. Hooyman’s) Selection of degree of approximating polynomial (usual 2 or 3) + rational thermodynamics method  rate equations for independent reactions Rates of components’ reactions  “hidden” mechanism with kinetically significant reactions Experimental tests and verification some

LIMITATIONS function form is valid strictly only for the fluids with linear transport properties, polynomial approximation is purely formal, although it can be given (classical) kinetic interpretation, more complex rate equations with higher number of constants to be determined than usual, “all components” should be known, (non-unique rate equation).

Acknowledgements Ivan Samohýl (Institute of Chemical Technology, Prague) Milan Roupec (Brno University of Technology, Brno)