Earth and Planetary Sciences 5 Midterm Exam January 22, 2008 Name: Teaching Fellow: INSTRUCTIONS PUT YOUR NAME ON EACH PAGE. Complete the problems directly on the exam. Extra paper is available if needed. Please show ALL your work so partial credit can be given! Neatness is appreciated. Scoring: Problem Score 1. Multiple Choice /28 2. Short Answer /24 3. Atmospheric Carbon Dioxide /12 4. Carbon Chemistry in the Oceans /13 5. Stratospheric Ozone Chapman Mechanism /12 6. Stratospheric Ozone Radical-Catalyzed Ozone Loss /16 7. Tropospheric Smog /15 8. Tropospheric Chemistry /20 Total /140 There are 140 possible points, and the value for each problem indicates the approximate time allotted to solve the problem.
Section I: Multiple Choice. Circle the best answer (1 pt each) 1. As the air temperature increases, with no addition of water vapor, which of the following are true? a. The dew point will remain the same. b. The relative humidity will decrease. c. The vapor pressure will remain the same. d. All of the above. 2. If the radius of the Earth were to triple, the effective temperature of the Earth would: a. decrease by a factor of 3. b. decrease by a factor of. c. increase by a factor of 3. d. increase by a factor of 3. e. remain approximately the same. 3. The Earth primarily emits radiation in: a. the infrared spectrum. b. the UV spectrum. c. the visible spectrum. d. The Earth emits radiation evenly across all frequencies. 4. The Coriolis force is due to: a. gravity. b. geomagnetism. c. rotation of the earth. d. tilt of the earth s axis. 5. The geostrophic approximation most accurately represents the surface wind velocity: a. in the tropics over oceans. b. at mid-latitude, over mountains. c. at mid-latitude, over oceans. d. near areas of strong convection. 6. Outside of a factory, an observer views the shape of a plume from a smokestack as it drifts downwind, shown in the figure below. Which of the following statements are true:
a. The plume is likely flat on the top due to a temperature inversion in the atmosphere above the smokestack. b. The plume spreads downwind because the smokestack is emitting less over time. c. Pollutants in the plume are effectively trapped near the ground. d. a. and b. only e. a. and c. only. f. All of the above 7. Which of the following statements is NOT true of the biological pump? a. The biological pump is limited by the supply of nutrients in surface waters. b. The biological pump is the only mechanism by which carbon can be transported to the deep ocean. c. The biological pump depends on photosynthesis of plankton. d. The biological pump carries carbon incorporated in the bodies of organisms to the deep ocean. 8. The Redfield ratio is: a. C:N:P = 105:15:1 b. C:N:P = 1:15:105 c. C:H:O = 105:15:1 d. C:H:O = 1:15:105 9. Which statement below does NOT contribute to the ocean s finite capacity for absorbing CO 2? a. The ocean is a limited volume of water. b. The decay of organic matter in the deep ocean releases CO 2. c. Dissolution of CO 2 in ocean water depends on temperature. d. Dissolution of CO 2 in ocean water depends on alkalinity. 10. The effectiveness of a greenhouse gas depends on all of the answers below, EXCEPT: a. How long it lasts the atmosphere, i.e., its chemical lifetime. b. Where in the IR spectrum it absorbs in a window region or not. c. Its circulation patterns in the atmosphere. d. Its radiation-absorbing ability. 11. In the thermohaline circulation, deep water formation depends on: a. The movement of carbon into deep water via the biological pump. b. Higher salinity in the North Atlantic relative to the North Pacific. c. The warming of surface waters at the equator. d. All of the above 12. Which of the following is NOT true of an El Niño Event: a. One important trigger is the slackening of the Trade Winds. b. The pool of warm water in the ocean s surface shift eastward in the equatorial Pacific. c. Indonesia experiences higher-than normal rainfall. d. In a strong or protracted El Niño Event, effects of the weather can be felt worldwide. 13. Which of the following statements about N 2 O is NOT true? a. It is an important greenhouse gas. b. It is inert in the troposphere.
c. It is the main source of NO x in the stratosphere. d. It is produced as a by-product during denitrification but not during nitrification e. Its main sink is photodissociation in the stratosphere. 14. Which of the species listed below are NOT fixed forms of nitrogen? a. NO 2 b. N 2 O c. NO 3 - d. All of the above 15. The following figure represents the relationship between CO 2 and O 2 in a given year. If segment AD represents the net relationship, what can you say about the ocean during this time period? a. The ocean was a net SINK for O 2 and a net SOURCE for CO 2 b. The ocean was a net SINK for O 2 and had NO EFFECT on CO 2 c. The ocean was a net SOURCE for O 2 and had NO EFFECT on CO 2 d. The ocean had NO EFFECT on O 2 and was a net SINK for CO 2 e. The ocean had NO EFFECT on O 2 and was a net SOURCE for CO 2 16. Polar stratospheric clouds that are important in Antarctic stratospheric ozone loss are mainly composed of: a. condensed sulfuric acid. b. small droplets of liquid water. c. a combination of nitric acid and water. d. aerosols of volcanic origin. 17. Which of the following statements about the Chapman mechanism is NOT true? a. In an idealized O 2 -N 2 atmosphere, the Chapman mechanism is responsible for chemical production and loss of O 3. b. Odd oxygen (O 3 +O) concentration is approximately equal to the concentration of O 3. c. The lifetime of odd oxygen is short at low altitude and long at high altitude. d. The Chapman mechanism explains the occurrence of ozone layer at an intermediate altitude in the atmosphere. 18. Which of the following statements regarding NO x is NOT true? a. It acts as a catalyst for ozone production in the troposphere. b. It can be formed by natural processes. c. Mass destruction of ozone in the Arctic stratosphere during early spring is inhibited by NO x. d. Ozone production always increases as NO x increases.
e. It is released by cars. 19. The Chapman cycle reactions maintain the steady-state concentration of ozone in the stratosphere. Which of the following reactions is NOT part of the Chapman cycle? a. O + O 3 O 2 + O 2 b. hv + O 2 O + O c. hv + O 3 O + O 2 d. O 2 + O 2 O + O 3 e. O + O 2 + M O 3 + M 20. The amount of ozone in the stratosphere is controlled by: a. the rate at which O 2 is photolyzed. b. the rate of O 3 + O 2O 2. c. the rate at which O 3 is catalytically lost. d. all of the above 21. All of the following molecules are free radicals except: a. H 2 O b. OH c. NO d. ClO 22. Consider the chemical reaction A + B 2C with rate constant k. Which of the following statements is NOT true? a. The rate of the forward reaction is R = k[a][b]. b. The equilibrium constant for the reaction is K = [C] 2 /[A][B]. c. d[b]/dt = k[a][b]. d. d[c]/dt = 2k[A][B]. 23. Which of the following best describes rainwater in the U.S.? a. Rainwater is naturally basic due to the presence of ammonium in the atmosphere. b. Rainwater is naturally basic due to the presence of cations such as calcium in the atmosphere. c. Rainwater is naturally neutral. d. Rainwater is naturally acidic due to the presence of carbon dioxide in the atmosphere. e. Rainwater is naturally acidic due to the presence of carbon monoxide in the atmosphere. 24. What is a catalyst? a. A species that undergoes photolysis b. A species that is only found in the stratosphere c. A species that is only found in the troposphere d. A species that slows down a reaction, but does not get used up in the process e. A species that speeds up a reaction, but does not get used up in the process 25. Using the figure below, which of the following statements is true?
a. Increasing NO x at point B would initially decrease ozone concentrations. b. Increasing NO x at point A would initially decrease ozone concentrations. c. Both points A and B are hydrocarbon limited. d. Both points A and B are NO x limited. e. Ozone concentrations are higher at point B than point A. 26. What is the first step in OH production? a. hv + O 2 O + O b. O( 1 D) + O 2 O( 3 P) + O 2 c. hv + O3 O(1D) + O2 d. hv + NO 2 O( 3 P) + NO 27. HO x and NO x catalyze O 3 in the troposphere and O 3 in the stratosphere. a. production, production b. destruction, destruction c. production, destruction d. destruction, production 28. Which of the following statements about chemical steady state is NOT true? a. A species is in chemical steady state when its chemical production and chemical loss are equal. b. Chemical steady state only occurs when the lifetime of a chemical species is very long. c. In chemical steady state, non-chemical influences on the concentration such as transport and deposition are insignificant. d. If a species X is in chemical state, d[x]/dt = 0. Section II: Short Questions
1. Energy Balance of the Earth a. Discuss how the water cycle on the earth could serve as a POSTIVE and NEGATIVE feedback with respect to global warming. (3 points) b. Discuss what is meant by the concept of an atmospheric window in the energy budget of the earth. Explain why compounds such a N 2 O and SF 6 that can absorb energy in the atmospheric window are potentially very harmful to our environment? (3 points) 2. Geostrophic wind a. The diagram below shows a hypothetical high pressure system in the southern hemisphere. On the diagram, draw vectors showing the following at point A: wind velocity, pressure gradient-force, Coriolis force, and frictional force. (4 points) A B 1000 mb 1020 mb b. Would the wind likely higher at point A or point B? Why? (2 points)
3. Atmospheric Stability Imagine the temperature profile of an atmosphere below 3 km is described by the following figure. The dry adiabatic lapse rate is 10 K/km and the moist adiabatic lapse rate is 6 K/km. a. Is this atmosphere stable or unstable? (2 points) b. If a dry air parcel at the surface has a temperature of 12 C, it will be warmer than the atmosphere and therefore buoyant. How high will it rise? (2 points) c. Another air parcel at the surface has a temperature of 14 C and contains water vapor. Its dew point is 10 C and does not change with altitude. As this air parcel is initially warmer than the atmosphere, it will rise. At what altitude do we expect the base of the cloud to form? (2 points)
4. Winds and Ocean Currents at the Equator (a) Surface Winds (b) Bulk Transport 30º N Equator 30º S a. In the diagram above, draw arrows to indicate (a) the predominant direction of surface winds between 30 º and the equator in both the northern and southern hemispheres. (Remember the Hadley circulation), and (b) the direction of Ekman/ bulk transport of ocean waters under these conditions. (1 point each) b. Is the bulk flow divergent or convergent? What phenomenon is the result of the bulk flow at the equator? (i.e., what are the consequences for vertical motion in the ocean?) (2 points) Section II: Problems Show ALL your work so partial credit can be given! 3. Atmospheric Carbon Dioxide (12 points) In your homework, we looked at fossil-fuel emissions and atmospheric carbon dioxide between 1959 and 1982. We found that during this time period about half of the total carbon emitted (91.2 10 9 metric tons) remained in the atmosphere, raising the mixing ratio of CO 2 from 315 ppm in 1959 to 339 ppm in 1982. In 2007, the atmospheric mixing ratio of CO 2 reached roughly 380 ppm. (a) How many molecules of CO 2 were added to the atmosphere between 1982 and 2007? The total mass of the atmosphere is 5 10 15 metric tons (1 metric ton = 1000kg), the
average molecular weight of air is 29 g/mol, and Avogadro s number is 6.022 10 23 /mol. (5 points) (b) Assuming that only half of total fossil fuel emissions remained in the atmosphere, how much carbon (in tons) was emitted between 1982 and 2007? (4 points) (c) If emissions rates continued at 1982-2007 levels, how long would it take for atmospheric CO2 to reach 500 ppm? What about if emissions were reduced to 1959-1982 levels? (We assume the Keeling fraction will remain the same.) (3 points) 4. Carbon Chemistry in the Oceans (13 points) Let s look at the uptake of atmospheric carbon in the oceans. (a) First, express the equilibrium constant (α, K 1, K 2 ) for each of the chemical reactions below in terms of the concentrations of the species: (3 points) CO2 ( g) CO2 ( aq), α CO 3 + 2 ( aq) + H 2O HCO + H, K 1 2 + HCO3 CO3 + H, K 2 (b) Calculate the concentration of total inorganic carbon (CO 2 (aq) + HCO 3 - + CO 3 2- ) at the ocean surface at a temperature of 10 C. Use an ocean ph of 8.2 and a partial pressure for atmospheric CO 2 of 380x10-6 atm. Your answer should be in mol/l. (4 points) Table: Values of equilibrium constants as a function of temperature
(c) Given the HCO 3 - and CO 3 2- concentrations you calculated above, calculate the alkalinity. (2 points) (d) If this water were 20ºC, with ph and CO 2 partial pressure remaining constant, concentration of total inorganic carbon would be 2.04 10-3 mole/l. Given this value and your answer to part (b), discuss the possible role of the ocean as a positive/negative feedback mechanism for global warming. (2 points) (e) How would dissolution of CaCO 3 affect the capacity of the ocean to take up atmospheric CO 2? (2 points) 5. Stratospheric Ozone - Chapman Mechanism (12 points) Here are the four Chapman reactions for stratospheric ozone:
(1) (2) (3) (4) O 2 + hv O + O J 1 = 6.0 x 10-10 s -1 O 2 + O +M O 3 + M k 2 = 7.6 x10-34 cm 6 molec -2 s -1 O 3 + hv O 2 +O J 3 = 5.1 x10-3 s -1 O 3 + O O 2 + O 2 k 4 = 3.4 x10-15 cm 3 molec -1 s -1 The J and k values provided are valid for an altitude of 44 km at 30 latitude. The number density of air at this location is 5.1 x 10 16 molec.cm -3, and the mixing ratio of O 3 is 3.9 ppm. You may assume that the mixing ratio of O 2 is 0.20 by volume. (a) Reactions (2) and (3) proceed much more rapidly than (1) and (4). Use that information to derive an expression for [O]/[O 3 ]. Explain your reasoning. (2 points) (b) Using the observed value of [O 3 ], calculate [O]. Express your answer in units of molecules.cm -3. (2 points) (c) Is J 1 higher or lower at 25km than at 44km? How about J 3? (1 point) (d) Calculate the rate for removal of odd oxygen (O x ). Express your answer in units of molecules cm -3 s -1. (2 points) (e) Calculate the production rate of O x. Express answer in units of molecules cm -3 s -1. (2 points) (f) Are the removal and production rates the same? If not, please explain why they are not. (Remember that transport of O x is important in determining [O x ] only at altitudes below about 30 km.) (3 points)
6. Stratospheric Ozone - Radical-Catalyzed Ozone Loss (16 points) Here is a list of chemical reactions that are important for ozone in the polar stratosphere. (1) Cl + O 3 ClO + O 2 (2) Cl + CH 4 HCl + CH 3 (3) ClO + O Cl + O2 (4) NO 2 + hv NO + O (5) ClO + NO Cl + NO 2 (6) ClO + HO 2 HOCl + O 2 (7) ClO + NO 2 + M ClNO 3 + M (8) HOCl + hv OH + Cl (9) OH + O 3 HO 2 + O 2 (10) NO + O 3 NO 2 + O 2 (11) NO 2 + O NO + O 2 (12) HCl + ClNO 3 Cl 2 + HNO 3 (a) For the reactions listed above, are there any heterogeneous reactions? Which one(s)? (2 points) (b) Write expressions for the chemical lifetimes of Cl and ClO. (3 points) (c) Using the reactions listed above, identify a catalytic cycle for ozone loss that includes NO (i.e. reaction 10 above). Include the net reaction. (3 points) (d) Using the reactions listed above, identify a catalytic cycle for ozone loss that includes HOCl (i.e. reaction 6 above). Include the net reaction. (5 points) (e) Identify the reactions that are sinks for ClO x ([ClO x ] = [Cl] + [ClO]). (3 points
7. Tropospheric Smog (15 points) The little-known city of Smogville, CA is heavily polluted, with ozone levels consistently above the federal standard of 80 ppb. Use the figure above, showing the midday peak concentration of ozone (ppb) in Smogville on a typical summer day, to answer the following questions about Smogville s pollution problem. (a) Explain briefly the difference between hydrocarbon and NO x limited ozone production. How are these regimes related to the heavy line shown in the figure? (3 points) (b) Current weekday emissions of hydrocarbons are 3.0x10 11 atoms C cm -2 s -1 and NO x emissions are 12.0x10 11 molecules cm -2 s -1. What midday ozone peak concentrations would you expect from these emissions? Is ozone production in Smogville hydrocarbon-limited or NO x -limited? (2 points)
(c) If hydrocarbon emissions are reduced by 50% without changing NO x emissions, what is the percent change in ozone concentration? (2 points) (d) If instead NO x emissions are reduced by 50% without changing hydrocarbon emissions, what is the percent change in ozone concentration? (2 points) (e) If hydrocarbon and NO x emissions are instead each reduced by 25%, what is the percent change in ozone concentration? (2 points) (f) Which emission control strategy would you recommend? Why? (2 points) (g) On weekends, fewer cars and trucks drive though Smogville, resulting in a 25% decrease in NO x emissions. Assuming no emission controls have been implemented, what midday ozone peak concentrations would you expect on weekends? How does this compare (qualitatively) to the weekday value you found in part (b)? (2 points) 8. Tropospheric Chemistry (20 points) The following sequence of reactions describes the oxidation of a compound called acetaldehyde (CH 3 CHO). This process is similar to the oxidation of CO that we studied in class. (1) CH 3 CHO + OH CH 3 CO + H 2 O k 1 (2) CH 3 CO + O 2 CH 3 COOO k 2 (3) CH 3 COOO + NO CH 3 COO + NO 2 k 3 (4) CH 3 COO CO 2 + CH 3 k 4 (5) CH 3 + O 2 CH 3 OO k 5 (6) CH 3 OO + O 2 + NO CH 2 O + NO 2 + HO 2 k 6 (7) CH 2 O + OH CHO + H 2 O k 7 (8) CHO + O 2 CO + HO 2 k 8 (9) CO + OH CO 2 + H k 9 (10) H + O 2 + M M + HO 2 k 10
(a) Write the net reaction for the conversion of acetaldehyde to CO 2 and H 2 O in the above series. At this stage you will have net production or removal of some radicals. (4 points) (b) Use the following reactions to rewrite the net reaction so that there is no change in the concentrations of OH, HO 2, NO, and NO 2. (Some reactions occur multiple times.) (11) HO 2 + NO OH + NO 2 k 11 (12) NO 2 + hv NO + O k 12 (13) O + O 2 + M O 3 + M k 13 Your answer should have the form a CH 3 CHO + b O 2 + z O 3 x CO 2 + y H 2 O + z O 3. O 3 appears on both sides of the equation to allow for the fact that O 3 could be either produced or consumed. Find the correct values of a, b, c, x, y, and z. Is ozone produced or destroyed? (5 points) (c) If reaction 1 is the rate-limiting step, write an expression for the rate of ozone change: d[o 3 ]/dt. Think carefully about the sign of the rate! (2 points) (d) Reaction 11 competes for HO 2 radicals with the following reaction: (14) HO 2 + O 3 OH + 2O 2 k 14 If ALL HO 2 radicals react via reaction 14 rather than reaction 11, what will be the net reaction (i.e. find a, b, c, x, y, and z for the new reaction). (5 points)
(e) What atmospheric conditions would cause reaction 14 to be more important than reaction 11? What are the implications for ozone production/destruction? (4 points)
Appendix Ideal gas law: pv=nkt (k is Boltzmann's Constant = 1.38x10-23 J/K) p=rrt (R = k/m = 287.5 J kg -1 K -1 ) p=nkt Stefan-Boltzman Law: (energy flux integrated over all wavelengths for a blackbody)=σ T 4 Effective temperature: Surface Temperature: Barometric Law: 1/ 4 T eff F(1 A) = 4σ, σ = 5.67x10-8 Wm -2 K -4 T 1/ 4 = ( N +1) T g z H eff H P( z) P e or P( z) = P( z ) e or z = H ln(p0/p) = 0 0 ( z z0 ) RT kt Scale height: H = = g mg First Law of Thermodynamics: ΔQ = ΔE +W = ΔE + pδv Δ Q = C ΔT + pδv v, C v =717 J/(kg K) RT Δ Q = C pδt Δp, C p =1003 J/(kg K) p ΔT g 1 Dry Adiabatic Lapse Rate: = = 9.8K km Δz c Angular velocity: Rotational velocity: Relative velocity: Angular momentum: Coriolis Force: Geostrophic Velocity: Deflection associated with Coriolis Force: The Keeling fraction p 2π Ω =, for the Earth Ω = 7.3x10-5 rad/s t 2π r 2πR cos( λ) v r = = t t v = v a v 2 L = mrv = mr Ω F=2mv Ωsinϕ 1 ΔP v = 2Ωρ sin λ Δx r 2 Δx Ωsin( λ) Δy = v (P + CO2 0 2 V f atm = 1 [ CO3 ] 0 PCO M 2 0 Lifetime = (reservoir size) / (loss rate from reservoir) = (the total amount of a species) / the rate of removal ph = - log 10 [H + ] 2.12 Gtons of carbon burned is equivalent to 1ppm increase of CO 2 in the atmosphere ) 1