IV. Kinetics
Introduction
(Pseudo) First Order Approx.
Steady State Approximation
Role of Kinetics
• Atmosphere is an open system- equilibrium
does not apply
• Determine chemical fate of a species
• Determine concentration of a species
• Compare time scales for processes
– Chemical
– Physical
– Meteorological
Simple Kinetics vs. Complex Models
Simple Kinetics (here)
• Approximations to give insight
Complex Models
• Quantitative but
– Numerical solutions
– Transport
– Lack of insight
First Order Kinetics
• Photochemistry (J is 1st order rate constant)
O3 + hn → O2 + O
d [O3 ]
  J [O3 ]
dt
[O3 ]t  [O3 ]0 e  Jt
Lifetime, t
t = 1/J
What is the photolysis lifetime of O3 at 10 km?
Elementary versus Complex Reactions
•
Elementary – balanced reaction reflects molecular-level events
(mechanism): CH4 + OH → CH3 + HOH
H
H
. OH
H
H
+
H . H
H
+
HOH
So the Rate Law reflects the mechanism
d [OH ]
 kCH 4OH [CH 4 ][OH ]
dt
•
Complex – multiple elementary reactions
CH4 + 2 O2 → CO2 + 2 H2O
Pseudo-First Order Approximation
Reduces 2nd order to 1st order
[O3] >> [Cl]
Major trace species vs. highly reactive radical
[O3] effectively constant
d [Cl ]
k’ = pseudo-1st
order rate
constant
dt
 kCl O 3[Cl ][O3 ]
k'  k
Cl O 3
[O3 ]
d [Cl ]
 k ' [Cl ]
dt
[Cl ]t  [Cl ]0 e k 't
Lifetimes and Halflife
photochemistry t = 1/J
Pseudo-1st order rxn. t = 1/k’
Halflife (t1/2) = 0.693 t
k'  k
ClO3
[O3 ]
kCl+O3 = 8.8 x 10-12 cm3 molecule-1 s-1 (218 K)
[O3] = 5 x 1013 molecule cm-3 (25 km)
What is the lifetime of Cl with respect to reaction with O3 ?
Rate Constants
Sources – JPL Data Evaluation, IUPAC, NIST
Arrhenius (empirical)
k(T) = Ae-Ea/RT
A = Arrhenius pre-exponential factor
Ea = activation energy
For Cl + O3:
k(T) = 2.9 x 10-11 e-2.2 kJ/mole/RT cm3 molecule-1 s-1
e-Ea/RT = e-(Ea/R)/T
k(T) = 2.9 x 10-11 e-260/T cm3 molecule-1 s-1
What is k at 218 Kelvin ?
Steady State Approximation
Applied to ClO, means [ClO] changing very slowly:
d [ClO ]
0
dt
1)
2)
3)
4)
Cl + O3  ClO + O2
ClO + NO  Cl + NO2
ClO + NO2  ClONO2
ClONO2 + hn  ClO + NO2
d [ClO]
 k1[Cl ][O3 ]  k2 [ClO][ NO]
dt
 k3[ClO][ NO2 ]  J 4 [ClONO2 ]  0
Steady State Approximation, con’t
k1[Cl ][O3 ]  J 4 [ClONO2 ]  k2 [ClO][ NO]  k3[ClO][ NO2 ]
k1[Cl ][O3 ]  J 4 [ClONO2 ]
[ClO ]ss 
k 2 [ NO]  k3[ NO2 ]
Local noon, [radicals] at daily maximum, changing slowly
 Steady State Approximation okay
Key Points
• Pseudo-first order approximation
• Steady state approximation
• Data sources abound