C23J KINETICS

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C23J - KINETICS 6

• Activated Complex Theory

Attempt to identify the principal features
governing the size of a rate constant in terms of
a model of the events that take place during the
reaction.
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Activated Complex Theory
Activated complex
Transition state
Reactants
Potential Energy
Products
Reaction Coordinate
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Activated Complex Theory
Activated complex
Association (of molecules or atoms) more
resembles the reactant
Association (of molecules or atoms) more
resembles the product
Potential Energy
Reaction Coordinate
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Energy
Reaction Coordinate
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Activated Complex Theory

• The Eyring Equation
• Reaction between A and B proceeds through the
  formation of the activated complex (AB) in a
  rapid pre-equilibrium.

K
k
A B (AB) ? product

• Rate, v k(AB)

• Now, rate, v k2AB

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Activated Complex Theory

• Rate of decay of activated complex

• Factors affecting the Activated Complex going
  through the Transition State
• ? vibration frequency
• Centrifugal effect of rotation

• It is supposed that k ? ? and k ??

? is the transmission coefficient (the
probability that the activated complex will pass
through the transition state to form product).

• Usually assume, ? ? 1

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Activated Complex Theory
Concentration of activated complex
A B (AB)

• If reaction is gas phase, then

• Recall the Ideal Gas Law

• Substituting for gas pressure in K

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Activated Complex Theory
Concentration of activated complex (contd)

• Recall rate, v k(AB)

Therefore rate, v k KRTAB
For a bimolecular reaction rate, v
k2AB Therefore k2 k KRT
Need to determine k and K
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Activated Complex Theory

• K, the equilibrium constant between the
  reactants and the activated complex can be
  written in terms of the standard molar partition
  functions (q ) of the species involved.

F
F
F
F

• Where

• And Eo is the molar energy of the species
  involved

F
Obtain q from spectroscopic data for A and B
but not for (AB)
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Activated Complex Theory

• Assume that a vibration of the activated complex
  (AB) tips it through the transition state (TS).
  (i.e. a vibrational mode converts to translation
  and TS breaks a bond). The partition function for
  this vibration is

• ? is the same frequency that determines k.
• ? is much less than a normal molecular vibration
  frequency, since the complex is falling apart
  (hence much weaker bond) and force constant is
  very low.

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Activated Complex Theory

• For small values of ?, assume

• The partition function reduces to

• We can therefore write

where denotes the partition function for all
the other modes (trans, rot ) of the complex.
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Activated Complex Theory

• K can now be written as

• where is a modified equilibrium constant
  with one mode of vibration of (AB) removed.

The rate constant
Recall that k2 k KRT where k ??
Substitution gives
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Activated Complex Theory

• In terms of molar concentration (and application
  of the Ideal Gas Law), it can be shown that

• Substitution gives

Eyring Equation
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Eyring Equation(Thermodynamic Aspects)

• Assume ? 1, and rearranging gives

• recall

• and

• ?

• Substitution and rearrangement gives

Plot LHS vs 1/T Slope -?H?/ R Intercept ?S?/ R
Another form of Eyring Equation