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QUESTIONS
1.
Oxygen has a constant mixing ratio in the atmosphere. How would
you expect its number density in surface air to vary between day and
night?
2.
Give a rough order of magnitude for the number of molecules present
in a typical 1 micrometer aerosol particle.
3.
Does it make sense to talk about the mixing ratio of aerosol particles in
air? To express the concentration of soot aerosol in units of ppbv?
2. PHYSICAL CHEMISTRY BASICS / KINETICS
(CHAPTER 9 +)
THE PERIODIC TABLE
First drafts of Mendeleev’s periodic table, 1869
photos from Mendeleev museum, St. Petersburg, 2007
CHEMICAL BONDS
Bond formation involves the electrons (e-) in the outermost (valence) shell. A
complete outer shell consists of 8 valence electrons (except H and He which have 2)
Destruction of a bond corresponds to a release of energy.
Generally double or triple bond energies are higher than for single bonds.
Ionic bonds: electron attraction between positive and negative ions  e- transfer
Convalent bonds: sharing of paired electrons
Polar convalent bonds: When 2 atoms
from different elements share e- unequally
OXIDATION STATE
Oxidation State describes positive or negative character of atoms, or degree of
oxidation
Ionic Molecules: oxidation state is the same as the charge on the ion
example: Na+1Cl-1 Ca+2Br2-1
Note: sum of oxidation numbers must equal zero
Covalent Molecules: more arbitrary, based on electronegativity scale
example:
 oxidation: C oxidation
state has increased from
-IV to +IV (the opposite
would be reduction)
Atmosphere is generally
an oxidizing medium.
CO2: C+4O2-2
ORGANIC MOLECULAR NOMENCLATURE
Alkanes (C-C single bonds)
CnH2n+2
Alkenes (C-C double bonds)
CnH2n
ethane
ethene
Alkynes (C-C triple bonds)
CnH2n-2
Aromatic compounds
CnH2n-6
ethyne
Benzene
Oxygenated hydrocarbons:
Aldehydes, alcohols, ketones, etc…
methanol
Acetic acid
acetaldehyde
COMMON IONS
Ammonium
Acetate
Nitrate
Nitrite
Hydroxide
Hypochlorite
Chlorite
Chlorate
Perchlorate
Permanganate
Carbonate
Sulfate
Sulfite
Peroxide
Silicate
Phosphate
NH4+
CH3COONO3NO2OHClOClO2ClO3ClO4MnO4CO32SO42SO32O22SiO32PO43-
CHEMICAL THERMODYNAMICS
Enthalpy: Thermodynamic potential of the system
Heat of reaction (ΔHrxn)= change of enthalpy
 depends on T, is independent of path
ΔHf = heat of formation (per mole)
Hrxn   H f , products   H f ,reactants
by definition = 0 for elements
Exothermic
Gibbs Free Energy:
G  H  TS
G  H  T S
Endothermic
 calculated ΔG in same way as enthalpy change
ΔG < 0  forward reaction spontaneous
ΔG > 0  reverse reaction spontaneous
ΔG = 0  reaction is at equilibrium
S = entropy
REACTION RATES: BASICS
A balanced chemical reaction does not represent the actual steps of the
reaction pathway or mechanism
Rate-determining step: the slowest step which determines the max rate of overall rxn
Rate of an elementary reaction:
k=rate constant
A+BC
Reaction Rate = k [A][B]
Rate of reactions generally increase with temperature:
k (T )  A(T )e  E / RT 
If A ≠ f(T) = Arrhenius form
E = activation energy
Catalysts decrease the energy of activation  increases the rate of forward and
reverse reactions
General Reaction Rates: aA + bB + …  gG + hH …. , k

a,b correspond to
reaction order
1 d
1 d
1 d
1 d
[ A]  
[ B] 
[G] 
[H ]
a dt
b dt
g dt
h dt
Reaction Rate = k[A]a[B]b…
CHEMICAL KINETICS
For multi-step reactions, need to sum the individual reaction rates:
A+BC
k1
A+DB
k2
d [ B]
 k1[ A][ B]  k2 [ A][ D]
dt
Biomolecular Reaction: A + B  C + D
Collision of 2 reactants (A and B) forms an activated complex (AB*) which
decomposes rapidly to the products (C and D)
k: unit here
d
d
d
d
Reaction Rate:  [ A]   [ B]  [C ]  [ D]  k[ A][ B]
[cm3/molecule/s]
dt
dt
dt
dt
Special Case: Self Reaction: A + A  B + C

1 d
d
d
[ A]  [ B]  [C ]  k[ A]2
2 dt
dt
dt
CHEMICAL KINETICS: THREE-BODY REACTIONS
A + B  AB*
AB*  A + B
AB* + M  AB + M*
M*  M + heat
A + B + M  AB + M
3
4
5
6
7
Rate of formation from 3rd rxn:
M = third body (usually inert: O2, N2)
 stabilizes the excited products AB*
In the atmosphere, take [M]=na
d
[ AB]  k5 [ AB*][ M ]
dt
But assume AB* short lifetime, can use steady state approximation
formation rate = loss rate
k3[ A][ B]  k4 [ AB*]  k5[ AB*][ M ]
k k [ A][ B][ M ]
d
d
d
[ A]   [ B]  [ AB]  3 5
dt
dt
dt
k 4  k5 [ M ]
k3 k5
d
d
d

[
A
]


[
B
]

[
AB
]

[ A][ B][ M ]
Low-pressure limit [M] << k4/k5: dt
dt
dt
k4
Re-arrange:

High-pressure limit [M] >> k4/k5
rate depends linearly on [M]
d
d
d
 [ A]   [ B]  [ AB]  k3[ A][ B]
dt
dt
dt
rate independent of [M] (all AB* will stabilize)
R3 is the rate-limiting step
CHEMICAL EQUILIBRIA
A + B  C + D, kf
C + D  A + B, kr
A+B↔C+D
Notation: also see kr=k-f
At equilibria (or ss) : k f [ A][ B]  kr [C ][ D]
kf
kr

[C ][ D]
 K eq
[ A][ B]
Reaction Quotient (not in equilibrium):
Q
[C ][ D]
[ A][ B]
if Q < Keq then rxn will shift to R (more products)
if Q > Keq then rxn will shift to L (more reactants)
Le Châtelier’s Principle: Perturbance of a system at equilibrium  system will
shift to minimize perturbance
PHOTOLYSIS
Breaking a chemical bond with an incident photon: AB + hν  A + B
AB + hν  AB* AB + hν
luminescence
 AB + M
quenching
A+B
photodissociation
d
d
d
 [ AB]  [ A]  [ B]  j[ AB]
dt
dt
dt
Defining the photolytic rate constant:
j  x x J
For polycromatic radiation:
j   x ( ) x ( ) J  d 

j = photolytic rate constant [s-1]
h = Planck constant
ν = frequency
J = actinic flux [photons/cm2/s]
σx = absorption cross-section
[cm2/molecule]
φx = quantum yield (probability
photon abs causes photolysis)
[molecules/photon]
A gas molecule will absorb radiation at a given wavelength only if the energy
can be used to increase the internal energy of a molecule
Rotational transitions  far IR radiation (> 20 µm)
Vibrational transitions  near IR radiation (0.7-20 µm)
Electronic transitions  UV radiation (< 0.4 µm)
RADICAL-ASSISTED REACTION CHAINS
Radical: chemical species with an unpaired electron in the valence shell
example: NO (7 + 8 = 15 e) = radical, HNO3 (1+7+24 = 32 e) = non-radical
 high free energies, more reactive
 nomenclature often denotes these with a dot, example: CH3●
Radical chain reactions (often called photochemical chain reactions):
nonradical + hν  radical + radical
initiation
radical + nonradical  radical + nonradical
propogation
….
radical + radical  nonradical + nonradical
termination
( OR: radical + radical + M  nonradical + M)
Example: Hydrogen & Bromine: Br2+H22HBr
ka
Br2 
 2 Br 
kb
Br   H 2 
 HBr  H 
d [ HBr ]
 kb[ Br ][ H 2 ]  kc[ H ][ Br2 ]  kd [ H ][ HBr ]
dt
SS Br : 2ka[ Br2 ]  kc[ H ][ Br2 ]  kd [ H ][ HBr ]  kb[ Br ][ H 2 ]  2ke[ Br ]2
kc
H   Br2 
 HBr  Br  SS H : kb[ Br ][ H 2 ]  kc[ H ][ Br2 ]  kd [ H ][ HBr ]
kd
H   HBr 
 H 2  Br 
ke
Br   Br  
 Br2
1/2
 ka 
2kb   [ H 2 ][ Br2 ]1/2
d [ HBr ]
 kc 

dt
 kd [ HBr ] 
1 

 kc[ Br2 ] 
ACIDS AND BASES
H2O(l) ↔ H+(aq) + OH-(aq)
NOTE:
OH- (hydroxide ion) 
OH (hydroxyl radical)!
K w  [ H  ][OH  ]  1014 (mol/L) 2
pH = -log[H+]  the activity of H+
< 7 = acidic
> 7 = basic
7 = neutral
Note: in atmosphere neutral pH=5-5.7 because pure water takes up CO2
Acid-Base Equilibrium: example ionization of acetic acid
CH 3COOH 
 H   CH 3COO 
[ H  ][CH 3COO  ]
Ka 
[CH 3COOH ]
SOLUBILITY AND HENRY’S LAW
Solubility Equilibria:
AgCl ( s)  Slightly soluble salt
K sp  [ Ag  ][Cl  ]
Ksp = solubility product
Henry’s Law: Distribution of species between aqueous and gas phases
A( g )  H 2O 
 A  H 2O
HA = Henry’s Law Constant
Units here are mol/L/atm
(sometimes reciprocal – be careful!)
[ A  H 2O ]
KA 
 HA
pA
Some Henry’s Law Constants of Atmospheric Relevance:
Chemical Species
Henry’s Law Constant @ 25C
(mol/L/atm)
HNO3
2.1x105
NH3
57.5
SO2
1.2
CO
9.6x10-4