LECTURE 3
AOSC 637
Atmospheric Chemistry
Finlayson-Pitts Chapt. 1 & 14
Seinfeld Chapt. 1 & some of 16
Wayne Chapt. 5 & 9
Outline
ID. Biogeochemical Cycles and Atmospheric Budgets
Examples:
1. Water
2. Carbon
3. Oxygen
II. Thermodynamics
A. Enthalpies of formation and combustion
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ID. Biogeochemical Cycles and Atmospheric Budgets
Definitions:
Biogeochemical Cycle -The process by which an element or compound
passes through the atmosphere, biosphere, and geosphere (oceans and
crust).
Global Budget - The total atmospheric burden of a substance and the
rates of its production and destruction, or its source and sink strengths.
Steady State - The condition of constant concentration of a substance in
the atmosphere. Steady state implies that the sources and sinks are equal;
the lifetime, t (also called residence time) is the burden divided by
production (or destruction) rate.
t = Burden/Production
After time t (1 - e-1) of the material has been exchanged. We will derive
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this later.
Example 1 - Water
The atmosphere contains 0.48% water on average.
 Burden = grams water in the global atmosphere:
0.48 x 0.01 x 18/29 x (5.15x1021) = 1.5x1019 g H2O
(Note mass of atmosphere and surface area on table in syllabus.)
or
1.5x1019/5.13x1018 = 3 g/cm2
UNITS: mole fraction x Mwts x mass atmos. = mass water
 Source - evaporation - rate not easily measured
 Sink - precipitation - estimates range from 95 to 110 cm/yr. We will use 100
cm/yr or 100 grams per cm2 year. The strength of this sink is uncertain because of
limited observations over the oceans.
Assume steady state, i.e., sources = sinks
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Lifetime (t) = 3/100 years or 11 days
Does this tell us anything useful about water in the atmosphere?
1. t << transport time - more H2O in areas of strong sources. The fraction of
water in the atmosphere varies from a few percent near the surface to < 10
ppm at the tropopause.
2. Global budgets are best for compounds whose lifetimes are much longer
than the transport time of ca 1 year.
3. Absolutely absurd approach w.r.t. meteorology - tells us doodley squat
about the probability of rain.
4. A wide variety of units is possible
5. The longer the lifetime the more stable concentration in time and space.
NOTE: In general, the shorter the t the higher variation in time and space
(Junge, Tellus, 1974).
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EXAMPLE 2
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How much C is there in the
atmosphere? We will assume all
the carbon is CO2, and that the
mean concentration, [CO2], is
380 ppm.
 Burden
380 x 10-6 x 1.8 x 1020 x 12 =
8.2x 1017 gC (as CO2)
(350 ppm gives 7.5)
UNITS: [CO2] x moles air x
g/mole = gC
 Major source - Respiration
 Major sink - Photosynthesis
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But if the biosphere is in S.S. then the net is zero. The biosphere is
actually slight source of CO2 to the atmosphere because of forest
destruction. Story about Brazil with rainforest and U.N. speech.
 Other source - fossil fuels, volcano, oceans
 Other sink - oceans
Lifetime = burden / sources
t = 7.6x1017 / {(1.5 + 0.05 + 0.05 + 0.0007) x 1017}  5 yr
Can man make much of a change in the burden?
Total reduced (fossil and living) carbon = 142 x 10 17 g
[CO2] = (142 /7.6) x 350 ppm = 6500 ppm!
Yes, we can make a big increase.
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EXAMPLE 3 OXYGEN
R. R. Dickerson
2011
Can fossil fuel ©burning
affect atmospheric
oxygen?
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Where is the oxygen?
 Burden: In the atmosphere: 32/29 x 0.21 x 5.15 x
1021 = 1.2x 1021 g O as O2
UNITS: mwt's [O2] x mass atmosphere = grams O2
In the oceans as H2O: (16/18) x (1.6x1024) =
1.4x1024 g O
UNITS: mwt's x mass seas x mass O in seas
The crust doesn't count, because the exchange is
very slow but we can calculate the burden anyway.
3 x 106 x 17 x 103 x 5.1 x 1014 x .47 = 1.2 x 1025g O
UNITS: density x depth x area x O by wt x O in
crust.
UNITS: g/m3 x m x m2 = g
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 Biomass: 0.015 x 1021 grams C
 Organic sediments: 45 x 1021 grams C
Take all of organic C and make CO2 out of it you produce:
142x1017 x 32/12 = 380 x 1017 g O as CO2
UNITS: mass C X mwt's = mass O2 consumed.
380x1017 /1.2 x 1021 = 3.2%
Problem for students: At what altitude is the oxygen partial pressure reduced by
3.2%?
PO2 = 3.2%
ans. about 250 m
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Thermodynamics
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FORMATION AND COMBUSTION
(In search of the Criterion of Feasibility)
1. First Law of Thermodynamics (Joule 1843 - 48)
dE = đQ – đW
(In AOSC 620 E = U)
The energy of a system is equal to the sum of the heat and the work.
Explain eq. of state and exact differentials. 1. Define Enthalpy (H)
dH = dE + d(PV)
dH = đQ - đW + PdV + VdP
At constant pressure and if the only work is done against the atmosphere i.e. PdV work, then: đW
= PdV
dHp = DQp
and đQ is now an exact differential, that is independent of path.
Note that you can do the same thing at constant volume except the result is:
dQv = dEv
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For example, the burning of graphitic carbon might proceed through CO:
H
Cgraph. + O2 → CO2
-94.0 kcal/mole
Cgraph + 1/2 O2 → CO
-26.4
CO + 1/2 O2 → CO2
-67.6
___________________________________
NET Cgraph + O2 → CO2
-94.0 kcal/mole
This is Hess' law. There is a table of Hfo in Finlayson-Pitts & Pitts,
Appendix I, p. 943. The units of kcal are commonly used because Hfo is
usually measured with Dewars and change in water temperature.
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2. Heat capacity:
The amount of heat required to produce a one degree change in temp in a given
substance.
C = đQ/dT
Cp = (∂Q/∂T)p = (∂H/∂T)p
Cv = (∂Q/∂T)v = (∂E/∂T)v
Because đQp = dH and đQv = dE
For an ideal gas PV = nRT
Cp = Cv + R
Where R = 2.0 cal/moleK
The heat capacity depends on degrees of freedom.
Translation = ½ R each; every gas has 3 translational degrees of freedom.
Rotation = ½ R
Vibration = R
For a gas with N atoms you see 3N total degrees of freedom and 3N - 3 internal (rot +
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vib) degrees of freedom.
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Equipartition principle: As a gas on warming takes up energy in all its
available degrees of freedom.
Measured Heat Capacities
Cv
Cp
He
3.0
5.0
Ar
3.0
5.0
O2
5.0
7.0
N2
4.95
6.9
CO
5.0
6.9
CO2
6.9
9.0
SO2
7.3
9.3
H2O
6.0
8.0
Cv = R/2 x (T.D.F.) + R/2 x (R.D.F.) + R x (V.D.F.)
Cp = Cv + R
Translational degrees of freedom - always 3.
Internal degrees of freedom = 3N - 3
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Where N is the number of atoms in the molecule
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Check Cv(He): 3 x R/2 = 3.0 cal/(mole K)
Cv(O2): 3 x R/2 + 2(R/2) + 1(R) = (7/2) R = 7.0 cal/(mole K)?
What's wrong?
Not all energy levels are populated at 300 K
Not all the degrees of freedom are active (vibration)
O2 vibration occurs only with high energy; vacuum uv
radiation.
at 2000K Cv (O2) approx 7.0 cal/mole K
Students: show that on the primordial Earth the dry adiabatic lapse
rate was about 12.6 K/km.
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IIA. Enthalpy (Heat)
1. Formation
Definition: The enthalpy of formation. Hfo is the amount of heat
produced or required to form a substance from its elemental
constituents.
The standard conditions, represented by a super “0”, are a little
different from those for the Ideal Gas Law: 25oC (not 0oC), 1.0 atm.
and the most stable form of elements. The standard heat of formation
is zero for elements. This quantity is very useful for calculating the
temperature dependence of equilibrium constants and maximum
allowed rate constants. It was thought for a long time that H was the
criterion of feasibility. Although H tends toward a minimum, it is not
the criterion. Things usually tend toward minimum in H, but not
always. Examples are the expansion of a gas into a vacuum, and the
mixing of two fluids.
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2. Enthalpy of Reactions
The heat of a reaction is the sum of the heats of formation of the
products minus the sum of the heats of formation of the reactants.
Hrxn =  Hfo(products) -  Hfo(reactants)
The change of enthalpy of a reaction is fairly independent of
temperature.
Problem for the student: Enthalpy calculation.
Which is hotter, an oxygen-acetylene flame or an oxygen-methane
flame?
REACTIONS
C2H2 + 2.5O2 → 2CO2 + H2O
CH4 + 2O2 → CO2 + 2H2O
Note: melting point iron = 1535°C.
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3. Bond Energies
See Appendix III of Pitts for a table of bond energies. The quantity is
actually heat not energy. Don’t confuse with free energy to follow.
Definitions:
Bond Dissociation Energy - The amount of energy required to break a
specific bond in a specific molecule.
Bond Energy - The average value for the amount of energy required to
break a certain type of bond in a number of species.
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Example: O-H in water
We want
H2O → 2H + O +221 kcal/mole
We add together the two steps:
H2O → OH + H +120
OH → O + H
+101
--------------------------------NET
+221
Bond energy (enthalpy) for the O-H bond is 110.5
kcal/mole, but this is not the b.d.e. for either O-H bond.
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Example: what is the C-H bond energy in methane?
We want Hfo for the reaction: CH4 → Cgas + 4H
any path will do (equation of state).
H (kcal/mole)
CH4 + 2 O2 → CO2 + 2H2O
-193
CO2 → Cgraph + O2
+94
2H2O → 2 H2 + O2
+116
2H2 → 4H
+208
Cgraph → Cgas
+171
------------------------------------------------NET CH4 → Cgas + 4H
+ 396 kcal/mole
The bond energy for C-H in methane is: +396/4 = +99 kcal/mole
Bond energies are very useful for "new" compounds and substances for which b.d.e.
can’t be directly measured such as radical.
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Why does your car get worse gas
mileage in winter?
Why do Europeans like diesel powered
cars?
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What is the energy density of common fuels?
ΔH
0
rxn
  ΔH f
0
products
  ΔH f
0
reactants
Consider the combustion of isooctane (C₈H₁₈), an approximation of gasoline.
Density = 0.67 g/cm3. Note that the ratio of N₂ to O₂ is 3.76.
C₈H₁₈ + 12.5 O₂ (+ 47N₂) → 8CO₂ + 9H₂O (+ 47N₂)
If we assume complete combustion, then CO₂ and H₂O will be the only products.
ΔH 0 rxn  8  94  9  58  (51)  1243 kcal/mole (5200 kJ/mole)
This is a lot of heat. The heat from 114 g of gasoline is sufficient to boil 15 L of
water if none of the heat escapes.
http://en.wikipedia.org/wiki/Standard_enthalpy_change_of_formation_%28data_table%
29#Miscellaneous_Compounds
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Ethanol: CH3CH2OH
Hf0 = -234.8 kJ mole-1
Density = 0.79 g/cm3
What is the heat of combustion?
CH3CH2OH + 7/2O2  2CO2 + 3H2O
H = – 2*94 – 3*58 –(– 234.8/4.18) = -305.8 kcal/mole
Diesel fuel: The average chemical formula for common diesel fuel is
C12H23, ranging approximately from C10H20 to C15H28. This is similar
to Jet-A of JP5. Density = 0.82 g/cm3
Hf0 ≈ - 70 kcal mole-1
C12H23 + 23.5O2  12CO2 + 11.5H2O
H = – 2*94 – 3*58 –(– 70) ≈ –1730 kcal/mole
Note these calculations use gaseous water; some use liquid.
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Energy density of common fuels
H * r / Mwt
Fuel
Approx.
formula
Molecular
Weight
(g/mole)
Heat of
Combustion
(kcal mole-1)
Density
(g cm-3)
Energy
(heat)
Density
Kcal cm-3
Gasoline
(iso-octane)
C8H18
114
-1243
0.67
7.31
Ethanol
C2H5OH
46
-306
0.79
5.26
167
-1730
0.82
8.49
Diesel and
Jet fuel
Appx C12H23
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The USEPA mandates more ethanol in gasoline in the
winter, to reduce CO emissions, although the benefits
are small. You get less energy per gallon in the winter.
Europeans like diesel fuel, even though it is more
expensive to build diesel engines, because it has more
energy per unit volume.
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• What is Biodiesel?
Biodiesel
– Vegetable Oil/ Animal Fat (triglyceride) derivative
• Rapeseed (canola) Oil common feed source in Europe
• Soybean Oil common feed source in United States
• How is it produced?
– Transesterification:
• 1 triglyceride substituted by 3 monohydric alcohol (methanol)
Environmental Problems see Crutzen et al. (2008) Atmospheric Chemistry and
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Physics.
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Organic Nomenclature worth remembering:
Alkanes CmHn
Examples: Methane, ethane, propane, butane...
Alkenes RC=CR’
Examples: ethene or ethylene H2C=CH2, a plant hormone and
isoprene C5H8 or (CH2=CH-C(CH3)=CH2, a diene.
Alkynes
Examples: Acetylene or ethyne HC≡CH
Aromatic Hydrocarbons
Based on the benzene ring
Example: Toluene
http://chemistry.boisestate.edu/people/richardbanks/organic/nomenclature/organic
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nomenclature1.htm
Organic Nomenclature worth remembering:
Alcohols R-CH2OH
Example ethanol CH2CH3OH
Ethers R-O-R’
Example diethyl ether CH3CH2OCH2CH3 (good night!)
Aldehydes R-CHO
Examples formaldehyde H2CO; acetaldehyde CH3CHO
Ketones R-C(O)-R’
Example Acetone
Carboxylic acids R-COOH
Examples Formic acid
Formate HCOO-
acetic acid
acetate CH3COO-
http://chemistry.boisestate.edu/people/richardbanks/organic
/nomenclature/organicnomenclature1.htm
More organic nomenclature worth remembering:
Organic Halides
Example
called 2-chloropropane, or 2-propyl chloride, or isopropyl chloride
*Freons
Examples: CFC-11, Trichlorofluoromethane, CFCl3
CFC-12, Dichlorodifluoromethane, CF2Cl2
Halons (used in fire extinguishers)
Example: Halon 1011 (bromochloromethane, CH2BrCl)
HCFC’s (Freon substitutes)
Example: HCFC-123, CF3CHCl2
Sulfur Compounds
Examples: CH3–SH, methanethiol.
CH3–S–CH3, dimethyl sulfide (DMS).
* See Finlayson-Pitts Chapt 13 or Seinfeld Chapt 2.
More organic nomenclature worth remembering: N compounds.
More details in the lecture on the biogeochemical cycles of Nr.
Amines, RNH2
Example CH3NH2, methylamine (a primary amine).
Nitriles, Nitro Compounds and Organic Nitrates
Examples acetonitrile
A nearly unique marker for biomass burning.
Alkyl nitrates, such as ethylnitrate
Methyl nitrite CH3ONO.
Nitryl Chloride ClNO2 (ClONO).
All NOx reservoirs.
Amides, RC(O)NH2
Example ethanamide
Amino acids, H2N-CH(R)-COOH building blocks of proteins and enzymes.
Urea, (NH2)2CO