QUESTIONSQUESTIONS

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 / KINETICS2. PHYSICAL CHEMISTRY BASICS / KINETICS(CHAPTER 9 +)(CHAPTER 9 +)

THE PERIODIC TABLETHE PERIODIC TABLE

First drafts of Mendeleev’s periodic table, 1869photos from Mendeleev museum, St. Petersburg, 2007

Convalent bonds: sharing of paired electrons

Polar convalent bonds: When 2 atoms from different elements share e- unequally

CHEMICAL BONDSCHEMICAL BONDSBond 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

OXIDATION STATEOXIDATION 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 ionexample: Na+1Cl-1 Ca+2Br2

-1

Note: sum of oxidation numbers must equal zero

Covalent Molecules: more arbitrary, based on electronegativity scaleexample:

CO2: C+4O2

-2

oxidation: C oxidation state has increased from

-IV to +IV (the opposite would be reduction)

Atmosphere is generally an oxidizing medium.

Alkanes (C-C single bonds) Alkenes (C-C double bonds)

etheneethane

Alkynes (C-C triple bonds)

ethyne Benzene

Aromatic compounds

Oxygenated hydrocarbons:Aldehydes, alcohols, ketones, etc…

CnH2n+2 CnH2n

CnH2n-2 CnH2n-6

ORGANIC MOLECULAR NOMENCLATUREORGANIC MOLECULAR NOMENCLATURE

methanol Acetic acid acetaldehyde

COMMON IONSCOMMON IONS

Ammonium NH4+

Acetate CH3COO-

Nitrate NO3-

Nitrite NO2-

Hydroxide OH-

Hypochlorite ClO-

Chlorite ClO2-

Chlorate ClO3-

Perchlorate ClO4-

Permanganate MnO4-

Carbonate CO32-

Sulfate SO42-

Sulfite SO32-

Peroxide O22-

Silicate SiO32-

Phosphate PO43-

CHEMICAL THERMODYNAMICSCHEMICAL THERMODYNAMICS

Enthalpy: Thermodynamic potential of the system Heat of reaction (ΔHrxn)= change of enthalpy

depends on T, is independent of path

, ,rxn f products f reactantsH H H ΔHf = heat of formation (per mole)by definition = 0 for elements

Exothermic Endothermic

Gibbs Free Energy:

calculated ΔG in same way as enthalpy changeΔG < 0 forward reaction spontaneous ΔG > 0 reverse reaction spontaneous ΔG = 0 reaction is at equilibrium

G H TS

G H T S

S = entropy

REACTION RATES: BASICSREACTION RATES: BASICS

A balanced chemical reaction does not represent the actual steps of the reaction pathway or mechanismRate-determining step: the slowest step which determines the max rate of overall rxn

Rate of an elementary reaction: A + B CReaction Rate = k [A][B]

Rate of reactions generally increase with temperature:

Catalysts decrease the energy of activation increases the rate of forward and reverse reactions

/( ) ( ) E RTk T A T e If A ≠ f(T) = Arrhenius formE = activation energy

k=rate constant

General Reaction Rates: aA + bB + … gG + hH …. , k

Reaction Rate = k[A]a[B]b…

1 1 1 1[ ] [ ] [ ] [ ]

d d d dA B G H

a dt b dt g dt h dt

a,b correspond to reaction order

CHEMICAL KINETICSCHEMICAL KINETICS

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)

Reaction Rate:

Special Case: Self Reaction: A + A B + C

[ ] [ ] [ ] [ ] [ ][ ]d d d d

A B C D k A Bdt dt dt dt

21[ ] [ ] [ ] [ ]

2

d d dA B C k A

dt dt dt

k: unit here [cm3/molecule/s]

For multi-step reactions, need to sum the individual reaction rates:A + B C k1

A + D B k2

1 2

[ ][ ][ ] [ ][ ]

d Bk A B k A D

dt

Rate of formation from 3rd rxn:

But assume AB* short lifetime, can use steady state approximationformation rate = loss rate

Re-arrange:

CHEMICAL KINETICS: THREE-BODY REACTIONSCHEMICAL KINETICS: THREE-BODY REACTIONSA + B AB* 3AB* A + B 4AB* + M AB + M* 5M* M + heat 6A + B + M AB + M 7

M = third body (usually inert: O2, N2) stabilizes the excited products AB*

5[ ] [ *][ ]d

AB k AB Mdt

3 4 5[ ][ ] [ *] [ *][ ]k A B k AB k AB M

3 5

4 5

[ ][ ][ ][ ] [ ] [ ]

[ ]

k k A B Md d dA B AB

dt dt dt k k M

In the atmosphere, take [M]=na

3 5

4

[ ] [ ] [ ] [ ][ ][ ]k kd d d

A B AB A B Mdt dt dt k

3[ ] [ ] [ ] [ ][ ]d d d

A B AB k A Bdt dt dt

Low-pressure limit [M] << k4/k5:

rate depends linearly on [M]High-pressure limit [M] >> k4/k5

rate independent of [M] (all AB* will stabilize)R3 is the rate-limiting step

CHEMICAL EQUILIBRIACHEMICAL EQUILIBRIA

A + B C + D, kf A + B ↔ C + DC + D A + B, kr

At equilibria (or ss) : [ ][ ] [ ][ ]

[ ][ ]

[ ][ ]

f r

feq

r

k A B k C D

k C DK

k A B

[ ][ ]

[ ][ ]

C DQ

A B

Notation: also see kr=k-f

Reaction Quotient (not in equilibrium):

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

Defining the photolytic rate constant:

For polycromatic radiation:

PHOTOLYSISPHOTOLYSIS

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 ABdt dt dt

j = photolytic rate constant [s-1]h = Planck constantν = frequencyJ = actinic flux [photons/cm2/s]σx = absorption cross-section

[cm2/molecule]φx = quantum yield (probability

photon abs causes photolysis) [molecules/photon]

x xj J

( ) ( )

x xj J d

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 CHAINSRADICAL-ASSISTED REACTION CHAINS

Radical: chemical species with an unpaired electron in the valence shellexample: 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 initiationradical + nonradical radical + nonradical propogation….radical + radical nonradical + nonradical termination( OR: radical + radical + M nonradical + M)

Example: Hydrogen & Bromine: Br2+H22HBr

2

2

2

2

2

2ka

kb

kc

kd

ke

Br Br

Br H HBr H

H Br HBr Br

H HBr H Br

Br Br Br

2 2

22 2 2

2 2

1/21/2

2 2

2

[ ][ ][ ] [ ][ ] [ ][ ]

: 2 [ ] [ ][ ] [ ][ ] [ ][ ] 2 [ ]

: [ ][ ] [ ][ ] [ ][ ]

2 [ ][ ][ ]

[ ]1

[ ]

d HBrkb Br H kc H Br kd H HBr

dt

SS Br ka Br kc H Br kd H HBr kb Br H ke Br

SS H kb Br H kc H Br kd H HBr

kakb H Br

d HBr kcdt kd HBr

kc Br

ACIDS AND BASESACIDS AND BASES

pH = -log[H+] the activity of H+

< 7 = acidic> 7 = basic7 = neutral

Note: in atmosphere neutral pH=5-5.7 because pure water takes up CO2

Acid-Base Equilibrium: example ionization of acetic acid

3 3

3

3

[ ][ ]

[ ]a

CH COOH H CH COO

H CH COOK

CH COOH

H2O(l) ↔ H+(aq) + OH-(aq)

14 2[ ][ ] 10 (mol/L)wK H OH

NOTE: OH- (hydroxide ion) OH (hydroxyl radical)!

SOLUBILITY AND HENRY’S LAWSOLUBILITY AND HENRY’S LAW

( )

[ ][ ]sp

AgCl s

K Ag Cl Slightly soluble salt

Ksp = solubility product

Solubility Equilibria:

Henry’s Law: Distribution of species between aqueous and gas phases

2 2

2

( )

[ ]A A

A

A g H O A H O

A H OK H

p

HA = Henry’s Law ConstantUnits here are mol/L/atm(sometimes reciprocal – be careful!)

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