CHEE 323J.S. Parent1 Reaction Kinetics and Thermodynamics We define a catalyst as a substance that increases the rate of approach to equilibrium of a reaction without being substantially consumed in the reaction  note that the equilibrium condition is governed by thermodynamics, and a catalyst does not alter the equilibrium state, but the rate at which this state is reached. What bearing does thermodynamics have on reaction kinetics?  Ultimate yield  Restriction of reaction orders  Influence of activity on the reaction rate

CHEE 323J.S. Parent2 Ultimate Reaction Yield The equilibrium composition of a system is dictated by thermodynamics.  Reactions serve to minimize the Gibbs Free energy of the system.  The state to which reaction kinetics lead is always the equilibrium state. Consider the gas phase isomerization of 2-butene: The thermodynamic properties of the components are: 2-Butene (673K) cistrans  H f : kJ/mole  S f : kJ/Kmole  G f : kJ/mole What is the final composition of the system?

CHEE 323J.S. Parent3 Reaction Rates: Concentration Dependence In simple reactions of perfect gases, it is found from experiment that volume concentration is the key variable.  reaction velocity is not a function of alternate variables such as chemical potential, or mole fraction. For the forward reaction of a simple system of near perfect gases: it is often found experimentally that the rate is proportional to small powers of concentration: where, k is independent of concentration  and  are not necessarily equal to a, b, respectively A simple interpretation of this result is generated by collision theory, assuming that reactions occur by molecular collisions whose frequency increases with the spatial density of reactants.

CHEE 323J.S. Parent4 Thermodynamic Restrictions on Reaction Order For many reactions, the equilibrium distribution of products is not displaced predominately in one direction or the other. One example is the decomposition of hydrogen iodide vapour: Experimental work shows the rate of HI decomposition may be expressed in the form: where k and k’ are constants. For given concentrations, only the net rate of decomposition can be measured. The forward and reverse rates have meaning only by interpretation.

CHEE 323J.S. Parent5 Thermodynamic Restrictions on Reaction Order Thermodynamics requires:  the reaction rate be positive in the direction that decreases the free energy of the system  at equilibrium, the rate must reduce to zero As the decomposition of hydrogen iodide reaches an equilibrium condition, -d[HI]/dt must approach zero, or which is the correct form of the equilibrium constant for this system.  The ratio k’/k of the experimental velocity constants (Kistiakowsky, 1928) equals the measured equilibrium constant (Bodenstein, 1899)  thermodynamic conditions are satisfied by this rate expression

CHEE 323J.S. Parent6 Thermodynamic Restrictions on Reaction Order If we consider a generic, elementary gas-phase reaction: we have at equilibrium: If we measure the formation of C from A,B at low concentrations of the product, we are effectively measuring the forward reaction rate. Suppose we can express the formation of C as: (commonly,  =1,  =0) If we wish to represent the reaction velocity over all concentrations of A,B and C, we must consider the reverse reaction, which yields: k k’

CHEE 323J.S. Parent7 Having determined the reaction orders  by experiment, thermodynamics restricts the values of  ’  ’  ’. At equilibrium the reaction rate must reduce to zero, therefore: or, The equilibrium relationship derived from the kinetic expression is: Eq. A while that known from the stoichiometry of the reaction is: Eq. B Thermodynamic Restrictions on Reaction Order

CHEE 323J.S. Parent8 Thermodynamic Restrictions on Reaction Order For the kinetic rate expression to be consistent with thermodynamics (Eq. A equivalent to Eq. B) the parameters  ’  ’  ’ must comply with: Eq. C where n is any positive value. Suppose, for example, the reaction is: If by experiment we determine the forward rate of reaction to be, then permissible expressions for the reverse reaction include,

CHEE 323J.S. Parent9 Reactions in Non-Ideal Solutions The use of volume concentrations in describing reaction kinetics has is origins in experimental research near perfect gas mixtures. In liquid phase reactions, we know that the equilibrium relationship for a reaction such as: in solution must be expressed as: Given that this is the ultimate limit of a kinetic rate expression, the reaction rate should (strictly speaking) depend on activities rather than concentrations. which, provided the reaction orders satisfy Eq. C, will generate the appropriate equilibrium expression.

CHEE 323J.S. Parent10 Reactions in Non-Ideal Solutions Treatment of reaction kinetics with simplified expressions derived from gas behaviour, such as, is done routinely. However, the kinetic rate “constants” prove to be functions of concentration when extended over a wide range. This is particularly true in reactions involving ions and/or ionic intermediates. Roughly speaking, the reaction velocity may be regarded as being largely determined by the collision frequency (volume concentration), but non-ideality resulting from complex molecular interactions requires the application of activity coefficients or an analogous treatment.

CHEE 323J.S. Parent11 The influence of solution non-ideality on reaction rates is frequently observed in the dependence of reaction velocity on solvent. Alkylation of triethylamine: Alcoholysis of Acetic Anhydride: Reactions in Non-Ideal Solutions

CHEE 323J.S. Parent12 Summary - Kinetics and Thermodynamics The common use of volume concentrations in reaction kinetics is derived from experimental research on perfect gas mixtures. Thermodynamics requires any kinetic rate expression to:  be positive in the direction of decreasing Gibbs Energy  reduce to zero at an equilibrium condition  represent the equilibrium condition accurately Reactions in solutions are, in a strict sense, poorly represented by rate equations that make no reference to component activities:  In some cases (pH dependent reactions, ionic equilibria) it may be necessary to adopt an activity coefficient approach  Beware that reactions in solution are usually solvent dependant, and rate constants derived from data in one solvent may not accurately represent the system in another.