Transition state theory and reaction kinetics

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Transition state theoryand reaction kinetics

• Lecture 6
• September 20th

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Outline

• Review thermodynamics from previous lectures
• What does the kinetics say in addition to
  thermodynamics?
• Design of the Gibbs free energy profile (e.g.,
  single-step
• reaction, and two-step reaction)
• First-order and second-order reactions
• Arrhenius equation and transition state theory
• Temperature-dependence of the reaction rate
  constant

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Equilibrium constant

• Keq products reactants
• For a chlorination reaction
• Keq 1.1 x 1019
• Large value indicates reaction goes to
  completion.

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Free Energy Change

• ?G free energy of (products - reactants),
  amount of energy available to do work.

• Negative values indicate spontaneity.

?Go -RT(lnKeq) where R 1.987 cal/K-mol and T
temperature in Kelvins
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Factors Determining ?G?

• Free energy change depends on
• enthalpy
• entropy

• ?H? (enthalpy of products) - (enthalpy of
  reactants)

• ?S? (entropy of products) - (entropy of
  reactants)

?G? ?H? - T?S?
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Enthalpy

• ?Ho heat released or absorbed during a
  chemical reaction at standard conditions.

• Exothermic, (-?H), heat is released.

• Endothermic, (?H), heat is absorbed.
  gt

• Reactions favor products with lowest enthalpy
• (strongest bonds).

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Entropy

• ?So change in randomness, disorder, freedom of
  movement.
• Increasing heat, volume, or number of particles
  increases entropy.
• Spontaneous reactions maximize disorder and
  minimize enthalpy.
• In the equation ?Go ?Ho - T ?So the entropy
  value is often small.

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Thermodynamics vs. Kinetics

• Sometimes (e.g., when rates are fast!) we ignore
  kinetics and deal only with products and
  equilibrium.
• In other situations, we need to focus on
  kinetics, not equilibrium (although eqbm
  considerations may be useful in predicting
  kinetics!)

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Kinetics

• Answers question, How fast?
• It tells us about intermediate sub-states, if
  any.
• Rate is proportional to the concentration of
  reactants raised to a power.
• Rate law is experimentally determined.

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Reaction Order

• For A B ? C D, rate kAaBb
• a is the order with respect to A
• a b is the overall order
• Order is the number of molecules of that reactant
  which is present in the rate-determining step of
  the mechanism.
• The value of k depends on temperature as given by
  Arrhenius ln k -Ea/RT lnA (see later
  slides for discussion)

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Activation Energy

• Minimum energy required to reach the transition
  state.
• At higher temperatures, more molecules have the
  required energy.

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Reaction-Energy Diagrams

• For a one-step reactionreactants ? transition
  state ? products
• A catalyst lowers the energy of the transition
  state.

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Energy Diagram for a Two-Step Reaction

• Reactants ? transition state ? intermediate
• Intermediate ? transition state ? product

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Rate-Determining Step

• Reaction intermediates are stable as long as they
• dont collide with another molecule or atom,
• but they are very reactive.

Trapping agents are used to determine intermediate
Transition states are at energy maxima.
The reaction step with highest Ea will be the
slowest,
therefore rate-determining for the entire
reaction.
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Reaction Coordinate Diagram
The course of a reaction can be illustrated by
means of a reaction coordinate diagram. The
Transition State is the point of highest energy
along the minimum energy trajectory (i.e., the
reaction coordinate) of a reaction. The Energy of
Activation is defined as the energy required to
attain the Transition State.
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Transition State and Reaction Velocity
?Gfinal - ?Ginitial constant
?Gactivation has changed
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Prerequisites for chemical reactions

• The reactants must engage in an encounter
  (collision) event. The probability of encounter
  is dependent on reactant concentration (k2 108
  - 1011 M-1 s-1) and diffusion constants (or
  solvent viscosity). Note that k2 denotes the
  second-order rate constant.
• The encounter must proceed with the reactive
  functional groups aligned with proper orientation
  for reaction.
• The encounter must provide sufficient energy to
  surmount the "energy barrier" (Activation
  energy).
• Reaction spontaneity is determined by the Gibbs
  Free Energy a negative free energy is required
  for a reaction to occur spontaneously (ie. there
  is a decrease in free energy).

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Reaction Rate is Dependent on Activation Energy
Absolute Reaction Rate Theory predicts that the
rate of a chemical reaction is dependent on the
free energy of activation.
where kB 1.38
x 10-23J.K-1 is the Boltzmann constant, h 6.63 x
10-34J.s is Planck's constant. The exponent
includes the term for the Free Energy of
activation. Either an increase in temperature or
a decrease in the activation energy will result
in an increase in reaction rate. For example a
decrease in the activation energy of 8 kcal/mol
yields a 106 enhancement in rate.
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Catalysis Reduces ?G
A catalyst lowers the Energy of Activation but
does not alter reactant or product free energies.
The equilibrium constant is unchanged, although
both forward and reverse rates are enhanced.
A B C D
The equilibrium constant under standard
conditions, Keq, is defined as Keq
CD/AB ?G -RT ln Keq -2.303 RT log
Keq,
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KINETICS
Rate law a mathematical function describing the
turnover rate of the compound of interest as a
function of the concentrations of the various
species participating in the reaction May or may
NOT have a theoretical basis For example
a, b, c indicate the order of the reaction with
respect to each species overall reaction order
abc
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First order reactions
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Pseudo first order reactions

• pseudo-first order concentration of one
  reactant remains essentially constant over time
  (often because it is in large excess compared to
  the other reagent)

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First order reaction with back reaction
Example conversion of aldehyde (A) to diol (D)
At equilibrium
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For formaldehyde,
thus at pH7 at equilibrium, formaldehyde is 99.8
in the diol form the time to steady state is the
sum of the forward and back rate constants
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Arrhenius Equation and Transition State Theory
reactions occur as a sequence of elementary
steps. usually one of these steps is much slower
than the others ? Rate Determining
Step empirically, the effect of T on the rate of
this reaction step (and therefore on the overall
reaction rate) is described by the Arrhenius
equation
pre-exponential factor or frequency
factor describes collision frequency and the
orientation probability
Activation energy describes the fraction of
species with energy greater than Ea
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Temperature dependence of reaction rate constant
is
Ea is therefore analogous to the DH of a phase
transfer process Ea is usually 40 to 130 kJ/mol,
i.e. usually bigger than DH for phase transfer
processes. Reaction rates are more sensitive to
temperature than partitioning A 1012 1016 for
unimolecular reactions A 107 1012 for
bimolecular processes
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Activated complex or transition state theory
B C ? BC ? D E BC is the activated
complex or transition state maximum energy
barrier
k Boltzmann constant h Planks constant
Ea potential energy of activation, ?H is the
total
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For the next week!
Please decide on the topic of your semester
report. A great attention has to be given on the
quality of writing, a solid outline, good
questions and big daunting challenges in the
field, updated references.
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References
1. Biological Thermodynamics, Chapter 8
Donald T. Haynie (Cambridge University Press,
Cambridge, 2001). 2. Principles of Physical
Biochemistry, chapter 1.6 Kensal E. van
Holde, W. Curtis Johnson, P. Shing Ho (Prentice
Hall, Upper Saddle River, New Jersey,
1998). 3. Molecular Biophysics. Structures in
Motion. Michel Daune (Oxford University
Press, Oxford, 1992)