Chapter 37Chapter 37

Complex Reaction Complex Reaction MechanismMechanism

Engel & Reid

Figure 37.1

Figure 37.2

Figure 37.3

37.4 Catalysis

SCP

CPSC

SCCS

2

2

1

1

kdt

d

k

k

k

m

22

1

21

21

1

211

CSSC

P

) (CSCS

SC

0SCSCCSSC

ionapproximat state-steady

K

kk

dt

d

k

kkK

Kkk

k

kkkdt

d

mm

Catalysis

37.4 Catalysis

0SCPCSSCPSC

SCCPSCSCSSC

CSSC Since

SCCCSCCC

PSCSSPSCSS

20000

00

00

00

m

m

m

K

K

K

Two assumptions :

1. [SC] is small, [SC]2 can be neglected

2. At early stage of the reaction [P] can be neglected

m

m

K

k

dt

dR

K

00

0020

00

00

CS

CSP

CS

CSSC

37.4 Catalysis

max020

0

020020

0

0

0020

C

SWhen

C

1

S

1

C

1

SWhen

S

CS

RkR

K

kk

K

R

K

K

kR

m

m

m

m

Case 1: [C]0<<[S]0

Case 2: [C]0>>[S]0

mK

kR

0

0020 C

CS

Figure 37.4a

Figure 37.4b

Figure 37.6

1 2

10 0

2 0 00

0

0 2 max0 0

0 max max 0

Michaelis-Menten rate law

: Michaelis constant

When S

Lineweaver-Burk equation

1 1 1

k k

k

mm

m

m

E S ES E P S E

k S ER K

S K

K R k E R

K

R R R S

Michaelis-Menten Enzyme Kinetics

Example Problem 37.1DeVoe and Kistiakowsky [J. American Chemical Society 83 (1961), 274] studied the kinetics of CO2 hydration catalyzed by the enzyme carbonic anhydrase:

CO2 + H2O HCO3-1

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:

Determine Km and k2 for the enzyme at this temperature.

37.4 Catalysis

Rate (M s-1) [CO2] (mM)

2.7810-5 1.25

5.0010-5 2.5

8.3310-5 5.0

1.6710-4 20.0

-1 4 -1max

max

4 -15 1max

2 9

0

4 -1m max

max

1Intercept= =4000 M 2.5 10 M s

2.5 10 M s1.1 10

2.3 10 M

Slope= =40 s slope 40s 2.5 10 M s 10mMm

RR

Rk s

E

KK R

R

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 Photochemistry37.8.1 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 (ks

isc), and phosphorescence (k

p)

Table 37.1

37.8.2 Fluorescence and Fluorescence quenching

QSkSkSkSkSkdt

Sdq

Siscicfa 11110

1 0

1 0

1

qk

q q

S Q S Q

R k S Q

Steady-State approximation

AbsorptionAbsorption

FluorescenceFluorescence

Internal Internal

ConversionConversion

IntersystemIntersystem

crossingcrossing

QuenchingQuenching

fa

fa

qSiscicf

f

SkS

SSk

dt

Sd

Qkkkk

01

10

1 0

1

Fluorescence life-time, f

Fluorescence Intensity, If

fa

q

f

Siscic

af

fq

Siscicf

fff

ffaff

kSk

Qk

k

kk

SkI

Qkkkk

kk

kSkSkI

00

01

111

Qk

k

kkk

Sk

kSk

Qk

kkk

Sk

I

I

f

q

f

siscic

a

fa

q

f

siscic

a

f

f

1

11

11

0

000

37.8 Photochemistry

Fluorescence and Fluorescence Quenching

0

1f q

f f

I kQ

I k

Stern-Volmer plots

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

Q

f

Sf f ic isc qk k k k

f qk k Q

f

1

When kf >> kic and kf >> ksisc

Example Problem 37.4

Example Problem 37.4

Thomaz and Stevens (in Molecular Lumiescence, Lim, 1969)studied 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, kT

isc, and kSisc/kr.

PP P P PT

P ISC

S

and

1

1

ff S

ISCf ISC

f

kk

k k

k

kk kk

S 11

1 1

0.12 7.33

ISC

f f

k

k

PP

P

–2 –1P

0.13

3.35 s

3.88 10 s

k

k

pTP

P

–2 –1–2 –1

T –1

3.88 10 s 3.88 10 s

0.13

0.260 s

ICS

ics

kk k

k

Figure 37.17

Figure 37.18

Example Problem 37.1

Example Problem 37.2-1

Example Problem 37.2-2