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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+BC 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+BC k1 A+DB 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+H22HBr 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 ] 1014 (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