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
• a and 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, -dHI/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,b1, g0)
• 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

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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,

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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.

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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

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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.