Consecutive Reactions PreEquilibrium

1
Consecutive Reactions(Pre-Equilibrium)
k2 k-1
k1
(1)

• A B (AB)
  C

steady state
(2)
Pre-equilibrium is possible when k-1 gtgt k1, but
not for k1 gtgt k-1 Assume k2 and k-1 gtgt k1, then
(3)
and
(4)
2
Consecutive Reactions(Pre-Equilibrium)
(5)

• Since equilibrium constant

• Then

(6)

• And

• i.e. 2nd order and k1K combined, is the 2nd order
  rate constant

• Another example of pre-equilibrium is the
  Michaelis-Menten Mechanism for enzyme action

3
Consecutive Reactions(Pre-Equilibrium)Michaelis-
Menten Mechanism for Enzyme Action
k2 k-1
k1

• E S (ES)
  P E

(7)

• E enzyme, S substrate, (ES) enzyme
  substrate complex, P product molecule

Assume steady-state for (ES)
(8)

• Difficult to measure E, but Eo, the initial
  ( total) enzyme concn is known (i.e. Eo E
  (ES)) and E Eo (ES).
  Substitute into eqn (8) to give

4
Consecutive Reactions(Pre-Equilibrium)Michaelis-
Menten Mechanism for Enzyme Action
(9)
(10)
(11)
(12)
(13)

• Now

5
Consecutive Reactions(Pre-Equilibrium)Michaelis-
Menten Mechanism for Enzyme Action

• Eqn (13) divided through by k2 to give

(14)

• Where KM is the Michaelis constant.

• Linear dependence on Eo, complicated dependence
  on S.

• Usually S gtgt KM and equation 14 becomes.

(15)

• since all the enzyme is in the form ES, i.e. ES
  Eo

6
Consecutive Reactions(Pre-Equilibrium)Michaelis-
Menten Mechanism for Enzyme Action

• make

• maximum velocity when all enzyme is complexed in
  the form ES, i.e. when Eo ES

• Therefore

• More useful linear forms are

or
y m x c y
c m x
Where experimental data for v at varying S is
required.
7
Consecutive Reactions(Pre-Equilibrium)Michaelis-
Menten Mechanism for Enzyme Action

• Recall

• At low S, KM gtgt S and

1st order in S

• At high S, KM ltlt S and

zero order in S
v
S
8
CHAIN REACTIONS

• Reactive intermediates are usually atoms or
  radicals

• Three processes
• (i) Initiation
• (ii) Propagation
• (iii) Termination

• e.g. thermal decomposition of acetaldehyde

?
CH3CHO CH4 C2H6 CO
9
CHAIN REACTIONSThermal Decomposition of
Acetaldehyde
ka

• CH3CHO ?CH3 ?CHO
• ?CH3 CH3CHO CH4 ?CH3CHO
• ?CH3CHO CO ?CH3
• 2 ?CH3 C2H6

kb
kc
kd