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Complex Reaction Mechanisms
Chapter 36
Reaction Mechanisms:
Reaction mechanism is a collection of elementary (one step) reactions that would add up to result in the overall reaction. Generally elementary (simple) reactions are bimolecular and unimolecular, rarely are termolecular.
Experimentally determined rate law does not conform with the stoichiometric coefficients of reactions, in general; unless the mechanism itself is simple. Therein lies the need to propose a mechanism for the reaction.
A valid reaction mechanism must be consistent with the experimental rate law.
For example;
Rate Law is of the ‘form’; R k N O [ 2 5 ]
The form of the rate law signals that the reaction involves multiple steps (a ‘complex’ mechanism).
Mechanisms involve many single step reactions (sum of them is the overall reaction), creation of intermediates (allowing use of steady state approximation) and equilibria.
Proposed mechanism:
Reaction rate law can be written as;
Invoking SSA for NO and NO 3.
[NO] =
Viola!!
Pre-equilibrium Approximation: A useful concept for reactions that can proceed via an equilibrium involving an intermediate I. (1)
(2)
and rate=
Upon rearrangement
Substituting for [I] in rate expression
Reaction rate =
Applying SSA to A*.
Reaction rate =
For k (^) -1 [A]>>k (^2) For k (^) -1 [A]<<k (^2)
True for [A] large.
uni (^) bi
[A] large
For the general case - Lindeman Theory :
with
[M] ~ constant k (^) app = k (^) uni is not simplistic.
uni
Reactions in solutions or gases at high pressure - k (^) -1 [A] >>.
Upon rearrangement;
[M]
k (^) uni
E’ (^) a
< E’ (^) a
Ea
Low T
Reaction progress: Energy diagram Part of E (^) a – energy required to overcome repulsive forces among electron clouds of reacting molecules.
E’ (^) a
Increasing reaction rates amounts to increasing reaction rate constants.
One strategy would be to lower E’a. Thereby increase the fraction of molecules with energy > E’a.
Catalysis
Catalyst remain unchanged after the reaction, it changes the reaction mechanism by combining with reactant(s)/ intermediates and therefore changes the reaction coordinate.
S-C complex
Reaction rate;
Applying SSA to SC;
Catalysis – a mechanism
Reactant = S
invert
alternatively
Reciprocal plot
(b) if [S] 0 >> Km
(1) For [C] 0 << [S] (^0)
[R] 0 reaches a limiting value and zero order w.r.t. [S].
Again,
using;
(2) For [C] 0 >> [S] (^0)
(a) if [C] 0 < Km
2
0 [ C^^ ] [ ] 0 S 0
m
k
R
K
[R] 0 linear to [C] 0 & [S] 0.
(b) if [C] 0 > Km
R 0 k 2 [ ] S 0
[R] 0 linear to [S] 0.
Michaelis-Menten Enzyme Kinetics
enzyme
substrate
Michaelis-Menten Enzyme Kinetics Enzymes are reaction specific catalysts.
Mechanism
C
For [E] 0 << [S] 0 ;^ Rate =
Km = Michaelis-Menten constant
Michaelis-Menten rate law
and also if [S] 0 >> Km above equation simplifies to,
The reaction rate plateau is at k 2 [E] (^0)
invert
Lineweaver-Burk Equation
Km?
Determination of Km
With Rmax known, evaluate Rmax / substitute in
Setting [A] low,
l A
I abs I
( ^ [^ ])
Keeping I 0 a constant and l = 1, substitute for I (^) abs ;
[ A ]
abs
d
I
dt
0
A
[ ]
(. ) [ ]
d
I A
dt
First order loss
In terms of number of molecules; A = # molecules of A,
0
A
[ ]
(. ) [ ]
d
I A
dt
A = absorption cross section.
k (^) a
Jablonski Diagram
1 2’ (2’) 3 F
4, 8 ISC T S
2, 5, 9 VR
1 2 4 5 6 P
7 IC S 1 S 0
(paths)
Jablonski Diagram shows the electronic states of a molecule and the photo-physical transformations between them in an energy diagram.
The energy states are grouped horizontally by their spin multiplicity.
Non-radiative transitions are shown by wavy arrows and radiative transitions by straight arrows.
The vibrational ground state of each electronic state is indicated by heavy lines.
Kasha’s rule: Photon emission (fluorescence or phosphorescence) occurs only from the lowest-energy excited electronic state of a molecule.
Kinetics of photo-physical processes
Quenching: Excited molecules can lose its energy by way of collisions with other molecules (quenchers) and thereby relax non-radiatively. This must be considered another kinetic process.
# photons emitted as fluorescence
# photons absorbed
Fluorescence yield: f
0 0
1 1 1 1 Q
[S] [S]
f ic isc q^ [^ ]
f a f f a f
k k k k
I k k k k
- invert
- substitute
0
0 0 0 0
If
with no quenching, we get pure flourescence
[S]
[S]
f ic isc
f
f a f a
k k and k
I
I k
I k
:Q present and k (^) f dominating
Stern-Volmer Plot
q
f
k
slope
k
Measurement of f
Excite molecules with a short pulse of photons, monitor decay afterwards.
Creates S 1 species, with excitation turned off monitor the fluorescence decay of S 1.
time
time
[S 1 ]
For S 1 ;
1 1 0 0
ln ln ln ln f
f f f
S S t I I t
[ ] [ ] [ ] [ ]
If conditions are such that k f k and kic isc
f k f kic kisc kq [ Q ] k f kq [ Q ]
q
f
slope k intercept k
SVE q
f
k
slope
k
Plot
