Chemical kinetics Chapter 19

1
Chemical kineticsChapter 19

• Sune Nørhøj Jespersen

2
Learning objectives

• After working with this material, you should be
  able to
• Define reaction rate constants.
• Write down basic differential equations for
  chemical kinetics, including law of mass action,
  and solve simple cases.
• Explain the principle of detailed balance.
• State the Arrhenius law

3
Reaction rates

• Equilibrium
• Kinetics

kf
A
B
kr
Rate constants kf Probalility of one A molecule
to convert to B per unit time. kr Same but in
the opposite direction.
4
Kinetic rate equations

• In a short time interval dt
• and like wise
• Coupled first order differential equations

5
General solution
Eigenvalues of k (in this example, one will be
0) V eigenvectors
6
General solution

• For example

Can be solved analytically only in simple cases
for more involved reaction. Otherwise numerical
solutions are valuable.
7
Example
?
if is conserved
8
Detailed balance

• From reversibility of microscopic laws
• Principle of detailed balance
• This implies steady state
• Comparing to the equilibrium constant of chapter
  13

9
Example
I
I
kAI
kAI
kBI
kIB
kBI
kIA
kAB
B
A
kBA
A
B
kBA
Figure 19.1 The principle of detailed balance is
satisfied by mechanism (a) between three states
A,I, and B, but violated by mechanism (b).
Forward rates must equal reverse rates for each
pair of states.
10
Mass action
Here we stipulate
is proportional to the propability that a A
molecules are close
Number of pairs
Note
11
Arrhenius
depends strongly on temperature. In equilibrium
Kinetics
activation energies.
12
Arrhenius
Population
Transition state
Reactants
Products
Energy