Meteo 532  --   Atmospheric Chemistry  --   Fall 2002

 

Final Take-home Examination

 

 

assigned:      02 December 2002

due:              16 December 2002

 

 

Please keep your answers brief.  As Strunk and White say: “Omit needless words.”  If you think that you need additional values for parameters to solve the problems,  assume reasonable values and state your assumptions.  Please use JPL for any rate coefficients that you might need.  You can use any books or notes, but please work alone.

 

1. (10 points)  Catalytic stratospheric ozone production.  Consider the catalytic cycle:

ClO + O  ®  Cl   +  O2

Cl  +  O3 ®  ClO +  O2

net:         O + O3 ®  2O2                         .

 

     In the expression or ozone loss, we can write: d[O3] / dt = -2 kClO+O [ClO][O].

     Why can’t we write this expression as:  d[O3] / dt = - 2 kCl+O3 [Cl] [O3]?

 

2. (25 points)  Tropospheric ozone production.

a) Write down the expression for the net tropospheric ozone production:

d[O3]/dt = P-L=?

b) We know that ozone is actually produced from NO2+hv -->NO+O, followed by O+O2+M -->O 3+M.  Why does the expression for d[O3]/dt contain no terms for these two reactions?

c)  What is the net ozone production rate, in ppb hr-1, at 10 km altitude if NO=200 pptv, HO2 =5 pptv, OH=0.5 pptv, O3=60 ppbv,  H2O=200 ppmv, and JO3=2x10-5 s-1?   Assume also the p=250 mb and T=235 K and that [RO2] is negligible.

d)  Consider the set of reactions:

OH+CO -->H+CO 2

H+O2+M--> HO2+M

OH+O3 -->HO2+O2

HO2+NO -->OH+NO2

HO2+O3 -->OH+2O2 

     Write down the rate equation for OH, assuming that the second reaction is much faster than the others. 

e) Assuming that OH and HO2 are in steady-state, write down the [HO2]/[OH] ratio in terms of [NO], [CO], [O3], and the rate coefficients.

 

3. (10 points)  The aircraft industry recently considered creating a fleet of 500-1000 High-Speed Supersonic Civilian Transports (HSCTs) that would carry passengers across the oceans in about ˝ of the time of existing subsonic aircraft.  It was estimated that these aircraft would double the NOx in the lower stratosphere.  An environment study indicated that, if these aircraft flew below 18 km, ozone destruction would be minimal.  Use the attached schematic to explain why so much pollutant might have so little effect on ozone. 

 

 

 

4. (15 points)  Aerosol size distributions.  Explain why, in a collection of aerosols, the larger ones generally have more mass than the smaller ones, even though the smaller ones are more numerous.  How should a aerosol number distribution vary as a function of size in order for the mass to be independent of size? 

 

5. (25 points)  An urban pollution plume comes into equilibrium with clouds that have a liquid water content of 1 g m-3.  The initial equilibrium values for SO2 is 20 ppbv and for HNO3 is 0.01 pptv.  The atmospheric pressure is 1013 hPa and the temperature is 298 K.  Assume no CO2.  We assume that all the HNO3 in the aqueous phase is in the form of nitrate (NO3-), and that HHNO3 = 2.1x105 M/atm and that the equilibrium constant between HNO3·H2O Ű NO3- + H+ is 15.4 M.

a)  What is the equation for the ion balance?

b)  What is the initial pH of the clouds?

c)  What fraction of the acidity is due to S(IV) and what fraction is due to NO3-?

    Assume that all the S(IV) in both the aqueous and gas phase is reacted to S(VI) and all the NOx is reacted to HNO3.  Assume that all the S(VI) is in the aqueous phase.  Note that the amount of NO3- depends on [H+].

d)  What is the new pH of the clouds?

e)  What fraction of the acidity is due to S(VI) and which fraction is due to NO3-?

Is [NO3-] now different from its initial value? 

  

6. (15 points)  Ozone isopleth diagram.

(a) Ozone isopleths are usually plotted with VOCs on the x-axis and NOx on the y-axis.  Yet we know that ozone production really comes   from the reaction of NO with HO2 and RO2.  How are VOCs and NOx related to ozone production?  (Or put           another way, what other information do we need to know to get quantitative numbers of ozone production from VOC          oxidation?)

(b) Briefly explain why the EPA has been regulating only VOC emissions in an effort to reduce O3 in urban areas. 

 

 

(Super Bonus - 30 pts )  Variation of ozone production with [NO].  HOx, the sum of OH+HO2, has the rate equation:

 

d[HOx]/dt = P(HOx) – {2kHO2+HO2[HO2 ][HO2] + 2kOH+HO2[OH][HO2] + kOH+NO2+M [M][NO2][OH]}

 

where P(HOx) is the production rate (molecules cm-3 s-1) of HOx, OH or HO2 and the three expressions in brackets are three loss mechanisms for HOx.   HO2+HO2 -->HOOH+O 2 dominates when NO is low, OH+HO2 -->H2O+O2 dominates when NO is about 100 pptv, and OH+NO2+M --> HNO3+M dominates when NO is greater than a few hundred ppt.  In each one of these three NO regimes, we can assume that only the dominant HOx loss reaction is occurring.

 

Using the equations in 2.d) to help relate OH to HO2 and the assumption that [HOx] ~ [HO2}, determine the analytical expressions for [OH], [HO2], and P(O3) in terms of   P(HOx), [NO], [CO], [O3], and rate coefficients for the three NO regimes.  For this problem, P(O3) = kNO+HO2 [NO] [HO2].