Duke University Nicholas School of the Environment Honor C.docx

Duke University Nicholas School of the Environment
Honor Code Cover Sheet for Exams
Student Name:
_____________________________________________________
(Please Print)
STATEMENT FOR EXAMS
Duke University is a community dedicated to scholarship,
leadership, and service
and to the principles of honesty, fairness, respect, and
accountability. Citizens of
this community commit to reflect upon and uphold these
principles in all
academic and nonacademic endeavors, and to protect and
promote a culture of
integrity.
The Pledge
Students affirm their commitment to uphold the values of the
Duke University
community by signing a pledge that states:
To uphold the Duke Community Standard:
I will not lie, cheat, or steal in my academic endeavors;

I will conduct myself responsibly in all my endeavors; and
I will act if the Standard is compromised.
I have adhered to the Duke Community Standard in completing
this exam.
________________________________________
_______________________
(Student Signature) Today’s Date
ENVIRON 239/EOS 239 FINAL EXAM
40 points
DUE BY: 5 pm, Thu May 2
IMPORTANT
1. Read the questions carefully.
2. Make sure that your answers precisely address the question -
no credit will be given for
material that does not address the question.

3. Write clearly, and do not clutter up the page. The progression
of your answer should be
self-evident. If I cannot figure out what you write, you will not
get credit for your answer.
4. The exam is open-book – you may consult your class notes,
the lecture slides, and the
readings. You are not allowed to consult any other sources or
search the web for answers.
5. Late exams will be penalized 8 points (20% of total) for each
day or part of day late.
SUBMISSION INSTRUCTIONS
Upload your completed final exam in electronic form to Sakai
Drop Box – name the file
Final_LastName.pdf or Final_LastName.docx. Or slide a hard
copy under my office
door. Also note that you should upload to Sakai Drop Box or
email to me your PLAS
program for Question 8.
Question 1 (3 points)
Briefly describe the two specific reasons that we discussed in
class as to why HOx and

NOx destroy O3 chemically in the stratosphere, but generally
produce O3 chemically in
the troposphere.
Briefly explain why anthropogenic VOC emissions control
measures in the 1990s did not
significantly reduce regional surface ozone pollution in the U.S.

There is evidence that surface NOx emissions from the
industrialized midlatitudes of the
Northern Hemisphere occasionally contribute to elevated levels
of NOx at the surface at
high northern latitudes. Given the relatively short chemical
lifetime of NOx (1-2 days),
this seems surprising till one considers organic nitrates. Using
PAN (peroxyacetyl nitrate)
as an example of a typical organic nitrate, explain how surface
NOx emissions from the
industrialized midlatitudes of the Northern Hemisphere can
occasionally lead to high
NOx concentrations at the surface at high northern latitudes.

Briefly summarize how humans have modified the global carbon
cycle. What is the main
gap in terms of our understanding of how humans have modified
the global carbon cycle?
Briefly explain how anthropogenic aerosols have directly and

indirectly counteracted
some of the warming from anthropogenic greenhouse gases?
We have covered a variety of topics over the course of the
semester. From your
perspective, what is one overarching thing that you learned
about atmospheric chemistry?
Give some details and explain why you consider it important.

Assuming a globally uniform atmospheric mixing ratio of 100
ppb CO, calculate the
column density of CO in units of molecules cm-2. Assume that
the total moles of air in the
atmosphere is 1.8 x 1020 moles, and that the radius of the Earth
is 6400 km.

Consider the elementary reaction NO3 + NO3 à 2NO2 + O2,
with a rate constant k.
(a) Assuming that the temperature dependence of k for this

reaction is given by the
Arrhenius expression, with the activation energy equal to 20360
J mole-1 and the pre-
exponential factor equal to 8.5 x 10-13 cm3 molecule-1 s-1,
what is the value of k (make
sure you specify units) at a temperature of 298K for this
reaction? (1 point)
(b) Assuming atmospheric pressure = 1000 hPa, temperature
=298K, and the following
initial mixing ratios at time t=0: NO3 = 1 ppb, NO2 = 0,
calculate and plot the mixing ratios of NO3 and NO2 (make sure
you specify units) as
function of time over 5 days using PLAS. (1 points)
NOTE: Upload your PLAS program to Sakai Drop Box or email
it to me. Include
the plot as part of your written exam.
(c) At the end of 5 days, what is the chemical lifetime of NO3
(make sure you specify
units)? (1 point)

Using the simple 1-layer greenhouse model equations we
considered in class (and
assuming as we did in class that incoming shortwave radiation
is 342 W m-2 and that the
albedo is 0.3), calculate the temperature of the surface and the
atmospheric layer if 100%
of outgoing longwave radiation emitted from the surface of the
earth is absorbed by the
atmosphere? Draw a figure (like the one we discussed in class)
showing quantitatively
all relevant energy fluxes for the earth’s surface, for the
atmospheric layer, and for the
earth/atmosphere system as a whole.

It has been proposed that ship emissions can contribute
significantly to NOx in the marine
boundary layer. Consider the following idealized scenario:
• Emissions from ship per unit surface area in the marine
boundary layer = 10-10 moles
m-2 s-1
• A uniformly mixed (i.e. no vertical gradient in NOx mixing
ratio) marine boundary
layer with a height of 1 km
• Constant NOx chemical lifetime of 1.5 days
• Constant number concentration of air throughout the marine
boundary layer = 2.5 x
1019 molecules cm-3
For this idealized scenario, calculate the steady-state NOx
mixing ratio (in ppb) in the
marine boundary layer by assuming that NOx emissions from
ships is balanced by NOx
chemical loss.

NOTE: THIS PROBLEM DOES NOT REQUIRE PLAS – YOU
SHOULD SHOW
ALL THE STEPS IN YOUR CALCULATIONS
Consider a parcel of air in the troposphere (number density of
air = 2.5 x 1019 molecules
cm-3) containing the following constant mixing ratios: 30 ppb
of O3, 70 ppb CO, and 30
ppt NOx (note NOx = NO + NO2). Assume that the following
simplified set of reactions
occurs in this air parcel:
Reaction Rate Constant

1. O3 + hν à 2OH j1 = 1 x 10
-6 s-1
2. CO + OH --> CO2 + HO2 k2 = 1 x 10
-13 cm3 molecule-1 s-1
3. HO2 + HO2 --> H2O2 + O2 k3 = 5 x 10
4. HO2 + NO --> OH + NO2 k4 = 8 x 10
5. NO + O3 --> NO2 + O2 k5 = 2 x 10
6. NO2 + hν --> NO + O3 j6 = 1 x 10
-3 s-1
NOTE: Some reactions are not balanced stoichiometrically. Do
not worry about this. The
additional species required to balance these reactions do not
affect the rates of these
reactions and hence can be ignored in this calculation.
(a) Assuming that HOx (note HOx = HO + HO2) is in steady-
state, calculate the number
concentration of HO2 in units of molecules cm-3. (2 points)
(b) Assuming that NO is in steady state, and noting that NOx =
30 ppt, calculate the
number concentration of NO and NO2 in units of molecules cm-
3. (2 points)
(c) Assuming that the partitioning between the HOx species (i.e.

the OH/HO2 ratio) is
controlled only by the fast reactions 2 and 4, calculate the
number concentration of
OH in units of molecules cm-3. (2 points)
(d) Assuming that the parcel is representative of the whole
troposphere, calculate the net
O3 chemical tendency (i.e. O3 chemical production rate - O3
chemical destruction
rate) in the troposphere in units of moles year-1. Assume that
the total moles of air in
the troposphere is 1.6 x 1020 moles. (2 points)

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