Reaction Kinetics and Thermodynamics

1. 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

2. 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) • cis trans • DHf : kJ/mole -13.8 -17.2 • DSf : kJ/Kmole 0.331 0.325 • DGf : kJ/mole 91.7 89.1 • What is the final composition of the system?

3. 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 • aand b 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.

4. 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.

5. 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

6. 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, a,b=1, g=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’

7. Thermodynamic Restrictions on Reaction Order • Having determined the reaction orders a,b,g by experiment, thermodynamics restricts the values of a’,b’,g’. • 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

8. Thermodynamic Restrictions on Reaction Order • For the kinetic rate expression to be consistent with thermodynamics (Eq. A equivalent to Eq. B) the parameters a’,b’,g’ 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,

9. Thermodynamic Restrictions on Reaction Order • Consider the following base-catalyzed addition of water to acetophenone to generate the corresponding hydrate. • Can you describe the equilibrium state of this reaction? • The mechanism is straightforward: • Can you derive a rate expression from this mechanism that is consistent with the thermodynamic expression?

10. 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.

11. 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.

12. Reactions in Non-Ideal Solutions • 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:

13. 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.

14. Food for Thought… • Working as an Engineering Chemist in an isoprene polymerization facility, you meet a salesperson that wishes to sell your company a new catalyst technology. According to the sales literature, the new organometallic complex polymerizes isoprene to produce cis-poly(isoprene) in 99% yield versus the thermodynamically more stable trans-poly(isoprene). • Argue whether this is possible using a free energy diagram to illustrate your point of view.