Atmospheric Chemistry

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Atmospheric Composition

Atmospheric Gases

Name

Formula

Concentration

Lifetime

Nitrogen N2 78.1%
Oxygen O2 20.9%
Argon Ar 0.9%
Carbon Dioxide CO2 394 ppm 30-100 years
Water Vapor H2O 5-50,000 10 days
Neon Ne 18
Helium He 5
Methane CH4 1.7 10 years
Krypton Kr 1.1
Stratospheric Ozone O3 500 ppb
Hydrogen H2 500 5 years
Nitrous Oxide N2O 300 100 years
Xenon Xe 90
Carbon Monoxide CO 50 3 months
Tropospheric Ozone O3 10 20 days
CFC-12 CF2Cl2 500 ppt 150 years
Carbonyl Sulfide OCS 500 2 years
CFC-11 CFCl3 250 75 years
Hydrogen Peroxide H2O2 100 1 day
Formaldehyde CH2O 100 10 days
Terpene C10H16 100 10 hours
Isoprene C5H8 100 5 hours
Carbon Tetrachloride CCl4 100 30 years
Methylchloroform CH3CCl3 65 7 years
Nitrogen Oxides NOx 10 1 day
Ammonia NH3 10 5 days
Sulfur Dioxide SO2 10 5 days
Dimethyl Sulfide CH3SCH3 10 1 day
Carbon Disulfide CS2 1 1 month
Hydrogen Sulfide CS2 1 5 days
Hydroperoxyl Radical HO2 1 1 second
Hydroxyl Radical OH- 0.1 1 second

Residence Time

\[ \tau = \frac{A}{F} \ \left[ \frac{Capacity}{Flux} \right] \]

Mixing Ratio (ppb)

\[ MR = \frac{n_i}{n_{tot}-n_i} \ \frac{mol}{mol} \]

Volume Mixing Ratio (ppbv)

\[ VR = \frac{V_i}{V_{tot}-V_i} \ \frac{m^3}{m^3} \]

Gas Laws

Dalton's Law

\[ p_{tot} = p_1 + p_1 + p_1 + \cdots + p_n \equiv \sum_{i=1}^{n} p_i \]

Boyle's Law

\[ p_1V_1 = p_2V_2 \]

Charles's Law

\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]

Gay-Lussac's Law

\[ \frac{p_1}{T_1} = \frac{p_2}{T_2} \]

Avogadro's Law

\[ \frac{V_1}{n_1} = \frac{V_2}{n_2} \]

Ideal Gas Law

\[ pV = nR^*T \] \[ pV = Nk_BT \]

Chemical Reactions

Reaction Types

\[ \Delta H_{reaction}^{\ominus} > 0 \ \ \ (Endothermic) \] \[ \Delta H_{reaction}^{\ominus} < 0 \ \ \ (Exothermic) \]

Hess's Law

\[ \Delta H_{reaction}^{\ominus} = \sum \Delta H_{f\ (products)}^{\ominus} - \sum \Delta H_{f\ (reactants)}^{\ominus} \]

Arrhenius Equation

\[ k_b = A \exp \left( \frac{-E_a}{RT} \right) \]

Unimolecular Reaction

Example

Rate

Lifetime

A → B+C \[ r = -\frac{d[A]}{dt} = k_u[A] \] \[ \tau_u = \frac{1}{k_u} \]

Bimolecular Reaction

Example

Rate

Lifetime

A+B → C+D \[ r = -\frac{d[A]}{dt} = k_b[A][B] \] \[ \tau_b = \frac{1}{k_b[B]_0} \]

Termolecular Reaction

Example

Rate

Lifetime

A+B+m → C+D+m \[ r = -\frac{d[A]}{dt} = k_b[A][B][m] \] \[ \tau_t = \frac{1}{k_t[B]_0[m]} \]

General Reaction

Example

Rate

Lifetime

aA + bB → cC + dD \[ r = -\frac{1}{a} \frac{d[A]}{dt} = k[A]^a[B]^b \] \[ \tau = \frac{1}{k[B]_0^b} \]

Steady State

\[ \frac{d[A]}{dt} = 0 \]

Photochemistry

Photochemical Processes

Reaction

Example

Luminescence

\[ A^* \to A + h\nu \] Bleach

Non-Radiative Deactivation

\[ A^* \to A + \Delta H \] Sunscreen

Ionization

\[ A^* \to A^+ + e^- \] Scanner

Energy Transfer

\[ A^* + B \to A + B^* \] Plastics

Isomerization

\[ A^* \to B \] Vitamin D Synthesis

Addition

\[ A^* + B \to A + B^* \] Fungicide

Photodissociation

\[ AB^* \to A + B \] Ozone

Tropospheric Ozone

\[ NO_2 + h\nu \xrightarrow{\lambda<420} NO + O\left( ^3P \right) \] \[ O_2 + O\left( ^3P \right) \xrightarrow{M} O_3 \]

Stratospheric Ozone

\[ O_2 + h\nu \xrightarrow{\lambda<240} 2O\left( ^3P \right) \] \[ O_2 + O\left( ^3P \right) \xrightarrow{M} O_3 \]

Gas Constants

Universal Gas Constant

\[ R^* = 8.314 \ \frac{J}{mol\ K} \] \[ R^* = 0.082 \ \frac{L\ atm}{mol\ K} \]

Gas Constant (Dry)

\[ R_{d} = 287 \ \frac{J}{kg\ K} \]

Gas Constant (Moist)

\[ R_{v} = 461.5 \ \frac{J}{kg\ K} \]

Physical Constants

Avogadro's Number

\[ N_A = 6.022\times 10^{23} \ \frac{molec}{mol} \]

Air Concentration

\[ n_{air} = 2.46\times 10^{25} \ \frac{molec}{m^3} \]

Density of Air

\[ \rho_{air} = 1.2 \ \frac{kg}{m^3} \]

Density of Fresh Water

\[ \rho_{fresh} = 1000 \ \frac{kg}{m^3} \]

Density of Seawater

\[ \rho_{sea} = 1025 \ \frac{kg}{m^3} \]

Density of Ice

\[ \rho_{ice} = 917 \ \frac{kg}{m^3} \]

Boltzmann's Constant

\[ k_{B} = 1.381\times 10^{-23} \ \frac{J}{K} \]

Molecular Weight of Air

\[ M_{d} = 28.97 \ \frac{g}{mol} \]

Molecular Weight of Water

\[ M_{v} = 18.02 \ \frac{g}{mol} \]

Specific Heat Capacity

\[ c_{v} = 717 \ \frac{J}{kg\ K} \] \[ c_{p} = 1004 \ \frac{J}{kg\ K} \]

Latent Heat

Latent Heat of Vaporization

\[ L_{v} = 2.50\times 10^{6} \ \frac{J}{kg} \]

Latent Heat of Sublimation

\[ L_{s} = 2.83\times 10^{6} \ \frac{J}{kg} \]

Latent Heat of Fusion

\[ L_{f} = 0.33\times 10^{6} \ \frac{J}{kg} \]

Solubility

pH Equation

\[ pH = -log_{10} \left[ H^+ \right] \]

Henry's Law

\[ \frac{\left[ A\left(l\right) \right]}{\left[ A\left(g\right) \right]} = H_A^*RTL \]

Air Quality

Air Quality Index

Color

Condition

8-hr O3
(ppb)

24-hr PM2.5
(μg/m3)

24-hr CO
(ppm)

Good     0 - 59     0.0 - 15.4   0.0 - 4.4
Moderate   60 - 75   15.5 - 35.4   4.5 - 9.4
USG   76 - 95   35.5 - 65.4   9.5 - 12.4
Unhealthy   96 - 115   65.5 - 150.4 12.5 - 15.4
Very Unhealthy 116 - 374 150.5 - 250.4 15.5 - 30.4
Hazardous N/A 250.5+ 30.5+

Sources of OH-

Photolysis of O3:

\[ \begin{aligned} &O_3 + h\nu \xrightarrow{\lambda<320} O \left( ^1D \right) + O_2 \\ &O \left( ^1D \right) + H_2O \to 2OH^- \end{aligned} \]

Photolysis of CH2O:

\[ \begin{aligned} &CH_2O + h\nu \xrightarrow{\lambda<330} O H^- + HCO^- \\ &HCO^- + O_2 \to CO + HO_2^- \\ &H^- + O_2 \to HO_2^- \\ &HO_2^- + NO \to NO_2 + OH^- \end{aligned} \]

Photolysis of H2O2:

\[ H_2O_2 + h\nu \xrightarrow{\lambda<360} 2OH^- \]

Photolysis of HONO:

\[ HONO + h\nu \xrightarrow{\lambda<400} OH^- + NO \]

Stratospheric Reactions

Ox Cycle:
(Chapman Cycle)

\[ \begin{aligned} &O_2 + h\nu \xrightarrow{\lambda<240} 2O\left( ^3P \right) \\ &O_2 + O\left( ^3P \right) \xrightarrow{M} O_3 \\ &O_3 + h\nu \xrightarrow{\lambda<320} O_2 + O\left( ^1D \right) \\ &O_3 + O\left( ^3P \right) \to 2O_2 \end{aligned} \]

HOx Cycle:

\[ \begin{aligned} &H_2O + O\left( ^1D \right) \to 2OH^- \\ &O_3 + OH^- \to HO_2 + O_2 \\ &O_3 + HO_2 \to OH^- + 2O_2 \\ &HO_2 + OH^- \to H_2O + 2O_2 \end{aligned} \]

NOx Cycle:

\[ \begin{aligned} &N_2O + O\left( ^1D \right) \to 2NO \\ &NO + O_3 \to NO_2 + O_2 \\ &NO_2 + h\nu \xrightarrow{\lambda<420} NO + O\left( ^3P \right) \\ &NO_2 + O\left( ^3P \right) \to NO + 2O_2 \end{aligned} \]

NOx Reservoir Species:

\[ \begin{aligned} &NO_2 + OH^- \to HNO_3 \ \ \ (day) \\ &NO_2 + O_3 \to NO_3 + O_2 \ \ \ (night) \\ &NO_2 + NO_3 \to N_2O_5 \end{aligned} \]

CFC Reactions

Gas-Phase Reactions:

\[ \begin{aligned} &CF_2Cl_2 + h\nu \xrightarrow{\lambda<260} Cl + CF_2Cl \\ &Cl + O_3 \to ClO + O_2 \\ &ClO + O\left( ^3P \right) \to Cl + O_2 \end{aligned} \]

Multi-Phase Reactions:

\[ \begin{aligned} &Cl + HO_2 \to HCl + O_2 \\ &ClO + OH^- \to HCl + O_2 \\ &ClO + NO_2 \to ClONO_2 \\ &ClONO_2 + HCl \xrightarrow{surface} Cl_2 + HNO_3 \\ &Cl_2 + h\nu \xrightarrow{\lambda<350} 2Cl \end{aligned} \]

Tropospheric Reactions

ROx Cycle:

\[ \begin{aligned} &RH + OH^- \to R + H_2O \\ &R + O_2 \xrightarrow{M} RO_2 \end{aligned} \]

HOx Cycle:

\[ \begin{aligned} &CO + OH^- \to H + CO_2 \\ &H + O_2 \xrightarrow{M} HO_2 \\ \\ &CH_4 + OH^- \to CH_3 + H_2O \\ &CH_3 + O_2 \xrightarrow{M} CH_3O_2 \\ &CH_3O_2 + NO \xrightarrow{M} CH_3O + NO_2 \\ &CH_3O + O_2 \xrightarrow{M} CH_2O + HO_2 \end{aligned} \]

NOx Cycle:

\[ \begin{aligned} &NO + RO_2 \to NO_2 + RO \ \ \ (day) \\ &NO_2 + h\nu \xrightarrow{\lambda<420} NO + O\left( ^3P \right) \\ &O_2 + O\left( ^3P \right) \xrightarrow{M} O_3 \\ \\ &NO + O_3 \to NO_2 + O_2 \ \ \ (night) \\ &NO_2 + h\nu \xrightarrow{\lambda<420} NO + O\left( ^3P \right) \\ &O_2 + O\left( ^3P \right) \xrightarrow{M} O_3 \end{aligned} \]

Combustion:

\[ \begin{aligned} &O_2 \xrightarrow{heat} 2O\left( ^3P \right) \\ &N_2 + O \xrightarrow{heat} NO + N \\ &N + O_2 \xrightarrow{heat} NO + O\left( ^3P \right) \end{aligned} \]

Volatile Organic Compounds

General Formula

Example

Alkane

\[ R-H \] \[ CH_4 \ \ (methane) \]

Alkene

\[ R_2C=CR_2 \] \[ C_2H_4 \ \ (ethylene) \]

Alkyne

\[ RC=CR \] \[ C_2H_2 \ \ (acetylene) \]

Aromatic

\[ C_6R_6 \] \[ C_6H_6 \ \ (benzene) \]

Alcohol

\[ R-OH \] \[ CH_3OH \ \ (methanol) \]

Aldehyde

\[ R-CHO \] \[ CH_2O \ \ (formaldehyde) \]

Ketone

\[ RCOR \] \[ (CH_3)_2CO \ \ (acetone) \]

Peroxides

\[ R-OOH \] \[ H_2O_2 \ \ (h.\ peroxide) \]

Organic Acid

\[ R-COOH \] \[ CH_2O_2 \ \ (formic\ acid) \]

Organic Nitrate

\[ R-ONO_2 \] \[ CH_3NO_3 \ \ (methyl\ nitrate) \]

Alkyl Peroxy Nitrate

\[ RO_2-NO_2 \] \[ CH_3O_2NO_2 \ \ (methyl\ p.) \]

Peroxy Acyl Nitrate

\[ RO_2-NO_2 \] \[ C_2H_3NO_5 \ \ (PAN) \]

Alkyl Radical

\[ R\cdot \] \[ CH_3\cdot \ \ (methyl\ r.) \]

Acyl Radical

\[ RC\cdot O \] \[ CH_3C\cdot=O \ \ (acetyl\ r.) \]

Alkoxy Radical

\[ RO\cdot \] \[ CH_3O\cdot \ \ (methoxy\ r.) \]

Peroxy Radical

\[ RO_2\cdot \] \[ CH_3O_2\cdot \ \ (methylperoxy\ r.) \]

Biogenic

\[ C_5H_8 \] \[ C_{10}H_{16} \ \ (\alpha -pinene) \]

Particle Sizes

Aitkin

Large

Giant

\[ r<0.1 \] \[ 0.1 < r < 1 \] \[ r>1 \]

Nuclei

Accumulation

Coarse

\[ r<0.1 \] \[ 0.1 < r < 2.5 \] \[ r>2.5 \]