Physical Chemistry Photochemical and sensitized steps Unimolecular [PDF]

Photochemical and sensitized steps Light is sometimes used to activate processes

Physical Chemistry Lecture 7 Special steps; chain reactions; surface and enzyme kinetics



dProducts dt

“Simple” reactions are more complex than they seem Frederick Lindemann proposed intervention of a mediator to produce a highly reactive intermediate in unimolecular reactions A  A

A*

M 

M



A

k



Explicit energy dependence of the rate constant

Rice and Ramsperger, and independently Kassel developed a theory (RRK theory)

Explicit account of molecular vibrational state

Products

Refined RRK theory in a number of ways

Modern version is called RRKM theory 

Predicts functional dependence of unimolecular reaction rates well

Chain reactions Many reactions have multiple steps in the mechanism Chain reactions, once started, continue  

Polymerization Some photochemical reactions

Initiation steps Photochemical steps

Cl2





Initiation - produce reactive species Propagation - remove and produce reactive species Termination - remove reactive species

h

 2 Cl 

Thermal steps

Classes of steps 

 Cl 

Hinshelwood





3 

A*

 Cl2  NaCl

Variations and refinements of Lindemann’s mechanism



M

k

k2



k1k 3[ M ] k3  k2 [ M ]

Na

Marcus

1 

M



*

k eff

 keff [ A]

v   Ia

  quantum yield

Some added materials produce reactive species by reaction

Unimolecular reactions: Lindemann’s mechanism

h

 2 Cl 

Cl2

H2

 2H

Sensitized steps

Na

 Cl2



NaCl

 Cl 

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Propagation steps

Termination steps

Steps that use and create reactive species Examples:

Br  

H2



HBr



H

Steps that remove reactive species Stable-product formation

2 C2 H5   C4 H10 Wall deactivation

R 

wall  stable wall complex

Stable-radical formation; scavenging

H   Cl2



HCl  Cl 

R 

Vinyl polymers “Simple” chain reaction

M



polymer Mn

Chain reaction Generally initiated with some radical 

X 

Sidechain, X H CH3 Cl

Polymer Poly(ethylene) Poly(propylene) Poly(vinyl chloride)

 RM n   RM x  

Mathematics of vinyl polymerization 

Rate of initiation is equal to rate of termination

Radical-combination termination vp

 kp

ki f [ M ][ In]1/ 2 kt

Other possible termination steps  

Deliberately added Photochemically induced In  R  R   M  RM 

Poly(styrene)

Approximation at steady state

RNO

Vinyl polymerization

n (monomer )  n

NO 

M  RM n 1  RM y   RM x  y R

Reactions at surfaces Very often reaction happens at “special” sites  

Enzyme action Heterogeneous catalysis

Simple surface reaction scheme A ( gas)

ads  

k

A (adsorbed )

A (adsorbed )



A (adsorbed )

react  

P (adsorbed )

P ,des  

k des

k k

A ( gas) P (adsorbed ) P ( gas)

Disproportionation Chain transfer

2

Langmuir-Hinshelwood kinetics

Langmuir isotherms Assume equilibrium between gas-phase A and adsorbed A 

[ Aadsorbed ]  [ Asat ] 

Second-order surfaceRate  determining Step mediated reaction Rate depends on the Aads  Bads  Product partial pressures of A and B

Langmuir isotherm gives relation between gas and surface concentrations

bPA 1  bPa



Generalize for multiple materials adsorbed, as in a chemical reaction

[ Aads ]  S0



bA PA 1   b j Pj

At low pressure, rate is second-order in the gas pressure At high pressures of both reactants, the rate becomes zero-order in pressure

vk react [ Aads ][ Bads ] k react S 02

bAbB PA PB (1   b j Pj ) 2 j

j

Langmuir-Hinshelwood versus Eley-Rideal kinetics

Eley-Rideal kinetics Second-order surfacemediated transformation One of the reactants comes in from the gas phase (without adsorption) 



Langmuir-Hinshelwood kinetics Rate  determining Step Agas  Bads  Product

v  k react PA [ Bads ]

Always first order with respect to A Usually requires a highly reactive gas-phase species such as H atom

 k react S 0



j

 

Form complex Complex may  Fall apart  React

E

 S

1  k

E~S

E~S



E

E~S



P 

k 1 k2

Velocity is found assuming fast equilibrium of first two steps k2 v  [ E ]0 [ S ] KM  [S ]

One partner of a second-order reaction held at the surface Second comes directly from the gas phase One or both must be highly reactive

Example of Michaelis-Menten kinetics

Mechanism is similar to surface catalysis 



Both partners of a second-order reaction at the surface Partners diffuse on surface until meeting to react

Eley-Rideal kinetics

bB PA PB 1   b j Pj

Michaelis-Menten enzyme catalysis 



 S E

Hydrolysis of N-glutamyl-Lphenylalanine with chymotrypsin J. Chem. Ed., 50, 149 (1973). Lineweaver-Burk plot  Plot 1/v versus 1/[S] Obtain Michaelis-Menten parameters from slope and intercept of plot

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Summary Complex reactions usually described in terms of elementary steps Lindemann’s mechanism  Modern version is RRKM theory (Rice, Ramsperger, Kassel, and Marcus) Polymerization occurs by a chain reaction   

Initiation Propagation Termination

Surface chemistry  Adsorption and desorption steps included  Langmuir-Hinshelwood versus Eley-Rideal mechanisms Enzyme kinetics  Formation of complex  Michaelis-Menten kinetics

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