C23J KINETICS

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C23J KINETICS - 3
Intermediate (meta-stable)
Energy
reactant
product
Reaction coordinate

• Consecutive Elementary Reactions
• (Reactions going through an intermediate)

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Consecutive Reactions

• Which reaction controls the overall rate of the
  reaction?

...(1) ...(2) (3)
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Consecutive Reactions

• Equation (1) is normal 1st order, hence rate law
  is

(4)
At
time

• Solve for the intermediate concn of I condition
  Io 0, and substitute eqn (4) into eqn (2)

(5)

• Equation 5 can be rearranged to give

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Consecutive Reactions
(6)

• Integrate, setting Io 0

(7)

• and since, at all times

(8)

• then

(9)
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Consecutive Reactions

• Substituting for It and Pt into equation (9)

(10)

• Which step controls rate? When k1 gt k2 (e.g.
  k1 10 k2)

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Consecutive Reactions

• If k1 gtgt k2, there is rapid build up of the
  intermediates concn.

k2 step is RDS
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Consecutive Reactions

• When k1 k2

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Consecutive Reactions

• When k1 lt k2 (e.g 10 k1 k2)

• As soon as the intermediate is formed almost all
  of it is used up. Its concn is not allowed to
  build up appreciably.

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Consecutive Reactions

• When k2 gtgt k1 , there is no build up of
  intermediates concn

k1 step is RDS

• When k2 gtgt k1 , there is no build up of
  intermediates concn

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Consecutive Reactions

• In all cases, Pt eventually reaches a final
  value of Ao, where all A has been converted to
  P
• The overall rate of the reaction is controlled by
  the slower step.

• Equations can become more complex and the math
  more difficult.
• Hence, make assumption that

• and that I remains small and hardly changes
  during the course of the reaction.
• This is known as THE STEADY STATE ASSUMPTION

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Consecutive Reactions THE STEADY STATE ASSUMPTION
A
P
concn
I
time
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Consecutive Reactions THE STEADY STATE ASSUMPTION

• since

• i.e. the rate of formation of P is first order in
  A
• i.e. P is formed by the first order decay of A
  with rate constant of k1 and the solution is