Meteo 465 -- The Middle Atmosphere

Problem set #2 – Stratospheric Chemistry

assigned: 21 February,2003

due: 3 March 2003

1. Suppose we have the following sequence of reactions:

CCl₃F + hv ® CCl₂F + Cl

Cl + CH₄ ® HCl + CH₃

a. These two reactions dictate the stratospheric production and loss of chlorine atoms.

b. Write down the rate equation for Cl.

c. Assume steady state (d[Cl]/dt = 0). Find the mathematical expression for the steady-state concentration of Cl.

d. Determine the diurnally averaged Cl concentration at 30 km. You will need to estimate the average photolysis rate of CFC-11. Use the technique that I showed you in class to make this estimate.

e. What is the lifetime of Cl at 30 km?

f. What is the chemical lifetime of CH₄ at 30 km?

2. Consider the following reactions involving chlorine compounds:

(R1) Cl + O₃ --> ClO + O₂
(R2) ClO + NO --> Cl + NO₂
(R3) ClO + O --> Cl + O₂
(R4) NO₂ + hn --> NO + O
(R5) O + O₂ + M --> O₃ + M

Assume that the reactions are occurring at 30 km in the midlatitude stratosphere.

a.  What is the net result of all the reactions? (you can multiply some of them by a factor of two in order to eliminate some terms.)
b.  Which reactions form a catalytic cycle that destroys ozone?
c.  Which reactions cycle chlorine but do not destroy ozone.
d.  Derive a steady-state expression for the ratio of [Cl]/[ClO].
e.  Which is the faster of steps (R2) and (R3)? Demonstrate this for 30 km.

 3. Ozone loss at 25 km. Using figures 10-14 in the chapter on Stratospheric Chemistry,

a. Write down the chemical reactions that determine the rate of ozone loss for each chemical family

b. Write down the ozone loss equation

c. Determine the ozone loss due to each chemical family

d. Determine the total ozone loss.

e. How does your answer compare to Figure 18 in the chapter?