10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 4: Reaction Mechanisms and Rate Laws
Fundamentals of Chemical Reactions
­PSSA (SS, QSSA, PSSH)
­long chain approximation
­rate­limiting step
A+B
Stable molecules: neutral, closed shells
(­)
(e­)
nucleus
(+)
nucleus
bond
Figure 1. Stable molecules.
Pauli Exclusion Principle
­You can’t put 2 identical e­ in the same exact spot
Figure 2. Two electrons in an orbital have opposite spin.
Bond Forming
0 e­
2 e­
H
+
H
+
empty
orbital
H
H
Figure 3. Bond formation. On the left, an empty orbital receives two electrons from
another orbital. On the right, half­filled orbitals on the H atom mix to form a filled
bonding orbital with two electrons.
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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Boltzmann Distribution
p ( E ) ∼ e − E k BT
kB =
R
NA
E ≫ k BT → very unlikely
E A + EB > E Activation
Barrier
B
A
Small fraction will
collide correctly
and react
k (T ) ∼ Ae − Ea
k BT
A is the prefactor, proportional to the number of ways the molecules get together
with sufficient energy to react.
Reactive Intermediates
­charged
acid/base chemistry
­empty orbital
metal catalyst
­single e­ orbital
free radical
Example:
O
O
RC
OR + H2O ⇌ RC
O
OH + ROH
(endo­
thermic)
O­
k2
k1
⇀
RC OR → R
OH + RC OR ↽
k−1
O
­
OH
(base catalyzed)
minor
species (SS)
(acid)
k3

→
O
R
O­
+ ROH
minor
species (SS)
O
O
R
OH
+ RO­
­
O
+ H2O ⇌
R
OH
+ OH­
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 4
Page 2 of 4
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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­
 O

d RC OR
 OH 
≈0
dt
­
O


O
 k1 OH­  
RC OR
RC OR  ≈


k−1 + k2

 OH
­
 O



RC
OR
k2



RO­  ≈  OH
k3 [acid]
d [RO­ ]
≈0
dt
­
rROH
O

O

kk
­
= k3 RO  [ acid] = k2 RC OR = 1 2 OH­  

RC OR

 k−1 + k2

 OH 
keff
Rate Limiting Step
­Only 1 rate constant of keff is really relevant
­What do you have most of in a reaction mix? This is the material preceding the rate
limiting step.
O
O
RC
OR + H2O
⇌ RC OH + ROH
OH
O
k2
⇀
→
RC OR 
H + RC OR ↽
k−1
R
+
k1
+
(SS)
+
OH
(acid)
(acid catalyzed)
R
O
+ R+
minor
species (SS)
k3
+ H2O 
→ ROH+H+
 OH 
d RC OR
 +  ≈0
dt
d [R + ]
≈0
dt
O
+ 



k
H
1
 OH 
  RC OR


RC OR ≈
k−1 + k2
 +

 OH 
k2 RC OR
 +


R +  ≈ 
k3 [H2O
]
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 4
Page 3 of 4
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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 OH 
 O

kk
rROH = k3 R+  [H2O] = k2 RC OR = 1 2 H+  

 +
 k −1 + k 2
RC OR


keff
Ethylene
(in plastics)
C2H6 → H2 +C2H4
Ethyl radical
C2H6 + H → H2 + C2H5
i
i
C2H5 → C2H4 + H
i
i
−rC2H6 = k1 Hi  [C2H6 ]
C2H6
i
CH3
slow

→ 2CH3i
inefficient, but important (radical creation)
+ C2H6 → CH4 + C2H5i
i
2C2H5
→ C2H6 + C2H4
(radical destruction)
(disproportionation)
C2H6 + C2H4 → 2C2H5 reverse disproportionation also happens
i
10.37 Chemical and Biological Reaction Engineering, Spring 2007
Prof. William H. Green
Lecture 4
Page 4 of 4
Cite as: William Green, Jr., course materials for 10.37 Chemical and Biological Reaction Engineering,
Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].