Chapter 37
Complex Reaction
Mechanism
Engel & Reid
Figure 37.1
Figure 37.2
Figure 37.3
Catalysis
37.4 Catalysis
k1
S  C  SC
k 1
k2
SC  P  C
d P 
 k 2 SC
dt
steady - state approximat ion
d SC
 k1 SC  k 1 SC  k 2 SC  0
dt
k  k2
SC  k1 SC  SC
( K m  1
)
k 1  k 2
Km
k1
d P 
k SC
 k 2 SC  2
dt
Km
S0  S  SC  P  S  S0  SC  P
C0  C  SC  C  C0  SC
37.4
Catalysis
SC
Since SC 
Km
K m SC  SC  S0  SC  P C0  SC
C0 S0  P  SCS0  C0  P  K m   SC2  0
Two assumptions :
1.
[SC] is small, [SC]2 can be neglected
2.
At early stage of the reaction [P] can be neglected
SC 
R0 
S0 C0
S0  C0  K m
d P 
k 2 S0 C0

S0  C0  K m
dt
Case 1: [C]0<<[S]0
37.4 Catalysis
R0 
k 2 S0 C0
S0  K m
When S0  K m
 Km
1

 k C
R0
0
 2
 1
1


 S
k 2 C0
0

When S0  K m
R0  k 2 C0  Rmax
R0 
Case 2: [C]0>>[S]0
k 2 S0 C0
C0  K m
Figure 37.4a
Figure 37.4b
Michaelis-Menten Enzyme Kinetics
Figure
37.6
E  S  ES  E  P
k1
k2
k1
 S 0   E 0
Michaelis-Menten rate law
R0 
k2  S 0  E 0
 S 0  K m
When S0  K m
K m : Michaelis constant
R0  k2  E 0  Rmax
Lineweaver-Burk equation
K
1
1
1

 m
R0 Rmax Rmax  S 0
37.4 Catalysis
Example Problem 37.1
DeVoe and Kistiakowsky [J. American Chemical Society 83 (1961), 274]
studied the kinetics of CO2 hydration catalyzed by the enzyme carbonic
anhydrase:
-1
CO2 + H2O HCO3
In this traction, CO2 is converted to bicarbonate ion. Bicarbonate is
transported in the bloodstream and converted back to CO2, in the lungs, a
reaction that is also catalyzed by carbonic anhydrase. The following initial
reaction rates for the hydration reaction were obtained for an initial enzyme
concentration 0f 2.3 nM and temperature of 0.5 oC:
Rate (M s-1)
[CO2] (mM)
2.7810-5
1.25
5.0010-5
2.5
8.3310-5
5.0
1.6710-4
20.0
Determine Km and k2 for the enzyme at this temperature.
Intercept=
1
=4000 M -1  Rmax  2.5 10 4 M s -1
Rmax
Rmax 2.5 104 M s -1
k2 

 1.1105 s 1
9
 E 0 2.3 10 M
Slope=


Km
=40 s  K m  slope  Rmax   40s  2.5 10 4 M s -1  10mM
Rmax
Figure 37.7
Figure 37.8a
Figure 37.8b
Figure 37.9
Figure 37.10
Figure 37.11
Figure 37.12
Figure 37.13
37.8 Photochemistry
37.8.1 Photophysical Processes Figure 37.14
Figure 37.14
A Joblonski diagram depicting
various photo-physical processes,
where S0 is the ground electronic
singlet state, S1 is he first excited
singlet state, and T1is the first
excited triplet state. Radiative
processes are indicated by the
straight lines. The nonradiative
processes of intersystem crossing
(ISC), internal conversion (IC),
and vibrational relaxation (VR)
are indicated by the wavy lines.
37.8 Photochemistry Figure 37.15
Figure 37.15
Kinetics description of photo-physical processes. Rate constants are
indicated for absorption (ka), fluorescence (kf), internal conversion
(kic), intersystem crossing from S1 to T1 (ksisc), and phosphorescence
(kp)
Table 37.1
37.8.2 Fluorescence and Fluorescence quenching
S1  Q  S0  Q
kq
Rq  kq  S1 Q 
Steady-State approximation
d S1 
S
S1   kq S1 Q
 0  k a S 0   k f S1   kic S1   kisc
dt
Absorption
Internal
Conversion
Fluorescence
Intersystem
crossing
Quenching
Fluorescence life-time, f
1
f
S
 k f  kic  kisc
 k q Q 

d S1 
S1 
 0  k a S 0  
dt
f
S1   ka S0  f
Fluorescence Intensity, If
I f  k f S1   k a S 0 k f  f
k f f 
kf
k f  kic  k  k q Q 
S
isc
f
S 
k q Q 
1
1  kic  kisc


1
I f k a S 0  
k f  k a S 0 k f
s 

k q Q 
1  kic  kisc 
1

0
k f  k a S 0 k f
I f k a S 0  
kq

 1  Q 
s 
If
kf

1  kic  kisc 
1
k a S 0  
k f 
37.8 Photochemistry
Fluorescence and Fluorescence Quenching
Stern-Volmer plots
I
0
f
If
 1
kq
kf
Q 
Figure 37.16
A Stern-Volmer plot. Intensity of
fluorescence as a function of
quencher concentration is plotted
relative to the intensity in the
absence of quencher. The slope of
the line provides a measure of the
quenching rate constant relative to
the rate constant for fluorescence.
37.8.3 Measurement of f
Fluorescence life-time  f
S
 f  k f  kic  kisc
 kq  Q 
When kf >> kic and kf >> ksisc
1
f
 k f  kq Q 
Example Problem 37.4
Thomaz and Stevens (in Molecular Lumiescence, Lim, 1969)studied
Example Problem 37.4
the fluorescence quenching of pyrene in solution. Using the following
information, determine kf and kq for pyrene in the presence of the
quencher Br6C6.
[Br6C6] (M)
f (s)
0.0005
2.66×10-7
0.001
1.87×10-7
0.002
1.17×10-7
0.003
8.50×10-8
0.005
5.51×10-8
slope = 3.00×109 s-1 = kq
intercept = 1.98×106 s-1 = kf
P37.31) For phenanthrene, the measured lifetime of the triplet state
P is 3.3 s, the fluorescence quantum yield is 0.12, and the
phosphorescence quantum yield is 0.13 in an alcohol-ether class at
77 K. Assume that no quenching and no internal conversion from
the singlet state occurs. Determine kp, kTisc, and kSisc/kr.
kP
P 
T
kP  kISC
f 
S
k ISC
1

1
kf
f
1

1
0.12
 7.33
kP 
P
P
kf
S
k f  k ISC
0.13

3.35 s
kP  3.88 10 –2 s –1
and kP P   P

1
S
k ISC
1
kf
k
T
ICS

kp
P
 kP
3.88 10 –2 s –1

 3.88 10 –2 s –1
0.13
T
kics
 0.260 s –1
Figure 37.17
Figure 37.18
Example Problem 37.1
Example Problem 37.21
Example Problem
37.2-2