Unit 1: Atmospheric Chemistry, Photochemical Smog & Acid Deposition

The terrestrial atmosphere is a dynamic, multi-component gaseous envelope governed by hydrostatic equilibrium, radiative transfer, and complex chemical feedback cycles. Understanding its behavior requires establishing its vertical thermal architecture and chemical composition.

1. Hydrostatic Equation and the Barometric Law

Consider a vertical fluid element of unit cross-sectional area $A = 1\text{ m}^2$, thickness $dz$, and density $\rho(z)$ at altitude $z$ in the gravitational field of Earth:

Applying the ideal gas equation of state:

where $M$ is the mean molecular mass of dry air ($M \approx 28.97\text{ g/mol} = 2.897 \times 10^{-2}\text{ kg/mol}$), $R = 8.3145\text{ J/(mol}\cdot\text{K)}$, and $T(z)$ is the absolute temperature. Substituting $\rho$ into the hydrostatic equation yields:

where $H_s(z) = \frac{R T(z)}{M g}$ is the local atmospheric scale height. For an isothermal atmosphere with effective temperature $T_0 = 250\text{ K}$ and $g = 9.807\text{ m/s}^2$:

Integrating yields the classical barometric profile:

2. Thermal Stratification and Atmospheric Nomenclature

The vertical profile of temperature divides the atmosphere into four discrete concentric shells separated by pauses:

1. Troposphere ($0$ to $\sim 11-18\text{ km}$): Characterized by strong convective overturning and a negative environmental lapse rate:

Heated from below via sensible heat and terrestrial thermal infrared re-radiation.

1. Stratosphere ($\sim 11$ to $\sim 50\text{ km}$): Inverted thermal gradient ($dT/dz > 0$), temperature rising from $\approx 215\text{ K}$ at the tropopause to $\approx 270\text{ K}$ at the stratopause. This stability is driven by exothermicity in ozone photolysis and recombination:

1. Mesosphere ($\sim 50$ to $\sim 85\text{ km}$): Decreasing temperature reaching the coldest region in the atmosphere ($\sim 140-180\text{ K}$) due to intense $\text{CO}_2$ infrared radiative cooling to space ($15\ \mu\text{m}$ band).
2. Thermosphere ($> 85\text{ km}$): High kinetic temperature ($> 1000\text{ K}$) driven by photodissociation and photoionization of $\text{O}_2$ and $\text{N}_2$ by extreme ultraviolet (EUV, $\lambda < 100\text{ nm}$) radiation.

3. Chemical Inventory of Dry Atmospheric Air

Dry air consists predominantly of chemically non-reactive or long-lived permanent species:

• Molecular Nitrogen ($\text{N}_2$): $78.084\% = 780,840\text{ ppmv}$
• Molecular Oxygen ($\text{O}_2$): $20.946\% = 209,460\text{ ppmv}$
• Argon ($\text{Ar}$): $0.934\% = 9,340\text{ ppmv}$
• Carbon Dioxide ($\text{CO}_2$): $\approx 425\text{ ppmv}$ (rapidly rising due to anthropogenic fossil combustion)
• Neon ($\text{Ne}$), Helium ($\text{He}$), Methane ($\text{CH}_4$, $\sim 1.9\text{ ppmv}$), Krypton ($\text{Kr}$), Hydrogen ($\text{H}_2$), and Nitrous Oxide ($\text{N}_2\text{O}$, $\sim 0.33\text{ ppmv}$).

The hydroxyl radical $(\cdot\text{OH})$ serves as the primary chemical scavenger and oxidative detergent of the troposphere, initiating the removal of virtually all reduced and partially oxidized trace gases.

1. Photochemical Generation of Hydroxyl Radicals

Because the direct bond dissociation energy of water is excessively high ($D_0(\text{H}-\text{OH}) = 497\text{ kJ/mol}$, requiring vacuum UV $\lambda < 240\text{ nm}$ that cannot penetrate the stratospheric ozone filter), tropospheric $\cdot\text{OH}$ is generated via a two-step photolytic sequence involving tropospheric ozone:

1. Photolysis of ozone by solar actinic UV-B radiation ($\lambda < 320\text{ nm}$):

1. Reaction of electronically excited singlet oxygen atoms $\text{O}(^1D)$ with ambient water vapor:

In competition with water reaction, the vast majority ($> 90\%$) of $\text{O}(^1D)$ undergoes collision-induced electronic quenching by inert atmospheric bath gas molecules $\text{M} = \text{N}_2, \text{O}_2$:

The resulting ground-state triplet oxygen atom $\text{O}(^3P)$ rapidly recombines with $\text{O}_2$:

yielding a null cycle.

2. Steady-State Hydroxyl Radical Concentration

Applying the steady-state approximation to $[ ext{O}(^1D)]$:

The gross production rate of $\cdot\text{OH}$ is therefore:

Because $k_{\text{M}}[\text{M}] \gg k_{\text{H}_2\text{O}}[\text{H}_2\text{O}]$, this simplifies to:

Typical daytime boundary-layer steady-state concentrations of $\cdot\text{OH}$ are on the order of $10^6\text{ molecules/cm}^3$ ($~10^{-18}\text{ atm}$ or $~0.04\text{ pptv}$), resulting in a photochemical lifetime of less than 1 second.

3. Hydrocarbon and VOC Oxidation Mechanism

The oxidation of methane (and non-methane volatile organic compounds, NMVOCs) proceeds via hydrogen atom abstraction:

The methyl radical reacts instantaneously with $\text{O}_2$ to form a methylperoxy radical:

In the presence of nitrogen oxides ($\text{NO}_x$), $\text{CH}_3\text{O}_2\cdot$ oxidizes nitric oxide ($\text{NO}$) to nitrogen dioxide ($\text{NO}_2$):

The methoxy radical then reacts with oxygen to generate formaldehyde and a hydroperoxyl radical:

Finally, $\text{HO}_2\cdot$ completes the catalytic chain by oxidizing another molecule of $\text{NO}$ and regenerating $\cdot\text{OH}$:

Tropospheric ozone is not emitted directly by anthropogenic sources; it is an entirely secondary pollutant formed from the photolysis of nitrogen dioxide.

1. The Classical Leighton Photostationary Cycle

In unpolluted air containing nitrogen oxides but devoid of reactive organic radicals, the interconversion of $\text{NO}$, $\text{NO}_2$, and $\text{O}_3$ is governed by a triad of fast reactions known as the Leighton cycle:

1. Photolysis of $\text{NO}_2$:

1. Rapid combination of triplet oxygen with $\text{O}_2$:

1. Titration of ozone by nitric oxide:

2. The Leighton Relationship

Because reaction (2) is extremely rapid ($k_2[\text{O}_2][\text{M}] \approx 10^5\text{ s}^{-1}$), every oxygen atom generated in reaction (1) produces an ozone molecule immediately. Therefore:

Under photostationary steady-state conditions ($d[\text{O}_3]/dt = 0$):

At $298\text{ K}$, $k_3 \approx 1.8 \times 10^{-14}\text{ cm}^3\text{molecule}^{-1}\text{s}^{-1}$. At solar noon with clear skies, $J_{\text{NO}_2} \approx 8.0 \times 10^{-3}\text{ s}^{-1}$. Thus:

In clean pristine air where $[ ext{NO}_2]/[ ext{NO}] \sim 1$, the Leighton relationship predicts an ozone concentration of only $\approx 18-35\text{ ppbv}$.

3. Net Ozone Accumulation via VOC Coupling

The fundamental paradox of photochemical smog is that urban areas frequently exhibit ozone concentrations exceeding $150-300\text{ ppbv}$, despite high $[ ext{NO}]$. The resolution is provided by peroxy radicals ($\text{RO}_2\cdot$ and $\text{HO}_2\cdot$) produced during VOC oxidation:

These reactions bypass the ozone titration pathway (Reaction 3). They convert $\text{NO}$ to $\text{NO}_2$ without consuming ozone. When this newly formed $\text{NO}_2$ subsequently photolyzes:

a net molecule of ozone is produced for every peroxy radical oxidation step.

Photochemical smog is an oxidizing atmospheric pollution regime resulting from the solar radiation-driven interaction of hydrocarbons and nitrogen oxides in stagnant air masses.

1. Peroxyacyl Nitrates (PAN): Synthesis and Thermal Equilibria

Peroxyacyl nitrates, most notably peroxyacetyl nitrate (PAN, $\text{CH}_3\text{C(O)OONO}_2$), are classic lachrymatory, phytotoxic indicators of photochemical smog:

1. Oxidation of acetaldehyde ($\text{CH}_3\text{CHO}$) by $\cdot\text{OH}$:

1. Addition of molecular oxygen to the acetyl radical to yield the peroxyacetyl radical:

1. Reversible combination with nitrogen dioxide:

The backward thermal unimolecular dissociation reaction has a steep activation energy ($E_a \approx 113\text{ kJ/mol}$):

At $T = 298\text{ K}$ ($25^\circ\text{C}$), the thermal lifetime of PAN is short ($\tau \approx 30\text{ minutes}$), leading to rapid dissociation. However, at upper-tropospheric temperatures ($T = 250\text{ K}$), the lifetime expands to several months:

Consequently, PAN acts as a long-range atmospheric reservoir and transport vehicle for $\text{NO}_x$, subsiding in remote regions and releasing $\text{NO}_x$ to generate tropospheric ozone far from urban emission sources.

2. Ozone Isopleths and the VOC-vs-NOx Limitation Matrix

The non-linear relationship between ozone production and its precursor concentrations is summarized by empirical and photochemical EKMA (Empirical Kinetic Modeling Approach) ozone isopleths:

• VOC-Limited (or $\text{NO}_x$-Saturated) Regime: Characteristic of dense urban cores where $[ ext{NO}_x]$ is high. Here, $\text{NO}_2$ acts as a radical chain terminator via the reaction $\cdot\text{OH} + \text{NO}_2 + \text{M} \rightarrow \text{HNO}_3 + \text{M}$. Reducing $\text{NO}_x$ actually increases ozone (the $\text{NO}_x$ disbenefit). Ozone mitigation requires reducing VOC emissions.
• $\text{NO}_x$-Limited Regime: Characteristic of rural and suburban downwind regions where $[ ext{VOC}]/[\text{NO}_x] > 8$. Here, peroxy radicals undergo self-reactions ($ ext{HO}_2\cdot + \text{HO}_2\cdot \rightarrow \text{H}_2\text{O}_2 + \text{O}_2$), and ozone production is strictly limited by the availability of $\text{NO}$. Reducing $\text{NO}_x$ is the only effective way to suppress ozone.

Atmospheric particulate matter (aerosols) consists of microscopic solid or liquid particles suspended in the gas phase, playing major roles in human respiratory pathology, cloud microphysics, and planetary radiative balance.

1. Particle Size Distributions and Inhalation Aerodynamics

Particulates are classified by their equivalent aerodynamic diameter $d_a$, defined as the diameter of a unit-density sphere ($ ho_0 = 1000\text{ kg/m}^3$) that exhibits the identical gravitational settling terminal velocity $v_{ts}$:

where $C_c(d_p) = 1 + \frac{2\lambda}{d_p}\left(1.257 + 0.400 \exp(-0.55 d_p / \lambda)\right)$ is the Cunningham slip correction factor for non-continuum gas dynamics ($\lambda \approx 66\text{ nm}$ is the mean free path of air).

• Coarse Particles ($ ext{PM}_{10}$, $2.5\ \mu\text{m} < d_a \le 10\ \mu\text{m}$): Generated mechanically by crustal windblown dust, road abrasions, and sea spray. Captured primarily in the nasopharyngeal and tracheobronchial regions of the respiratory tract.
• Fine Particles ($ ext{PM}_{2.5}$, $d_a \le 2.5\ \mu\text{m}$): Dominated by combustion soot, secondary sulfates, nitrates, and secondary organic aerosols (SOA). Capable of penetrating deeply into the pulmonary alveoli and translocating into the vascular circulatory system.
• Ultrafine Particles (Nanoparticles, $d_a \le 0.1\ \mu\text{m}$): Dominated by gas-to-particle nucleation modes with lifetimes controlled by Brownian coagulation.

2. Secondary Inorganic Aerosol (SIA) Thermodynamics

Fine inorganic aerosol mass is dominated by ammonium sulfate, ammonium bisulfate, and ammonium nitrate:

1. Gas-phase oxidation of $\text{SO}_2$:

Due to its ultra-low saturation vapor pressure ($P_{\text{vap}} < 10^{-11}\text{ atm}$), sulfuric acid condenses irreversibly onto preexisting aerosol surfaces or undergoes binary homogeneous nucleation with $\text{H}_2\text{O}$.

1. Atmospheric neutralization by ammonia ($\text{NH}_3$):

1. When ambient $\text{NH}_3$ exceeds sulfate neutralization capacity, excess ammonia reacts with gas-phase nitric acid to form volatile ammonium nitrate in temperature- and humidity-dependent equilibrium:

3. Metallic Aerosols and Toxicological Speciation

Heavy metals emitted by industrial smelting, coal combustion, and vehicular friction brakes partition into particulate phases:

• Lead ($\text{Pb}$): Historically dominated by tetraethyllead fuel anti-knock additives; now dominated by battery recycling, coal combustion, and industrial paint manufacturing.
• Cadmium ($\text{Cd}$) and Arsenic ($\text{As}$): Emitted from metallurgical processing and coal fly ash; exist as fine submicron condensates with high bioavailability.
• Transition Metals ($\text{Fe, Cu, Mn, Cr}$): Catalyze in vivo and in-cloud Fenton chemistry:

generating intracellular Reactive Oxygen Species (ROS) that induce pulmonary lipid peroxidation and systemic oxidative stress.

Internal combustion engines operate under high-temperature, high-pressure hydrocarbon combustion, serving as major global mobile sources of carbon monoxide, unburned hydrocarbons, and nitrogen oxides.

1. Zeldovich Thermal NOx Mechanism

At peak flame combustion temperatures ($T > 1800\text{ K}$), molecular nitrogen is oxidized via the classical high-activation-energy Zeldovich mechanism:

1. $\text{O} + \text{N}_2 \xrightarrow{k_1} \text{NO} + \text{N} \quad (E_{a,1} \approx 314\text{ kJ/mol})$
2. $\text{N} + \text{O}_2 \xrightarrow{k_2} \text{NO} + \text{O} \quad (E_{a,2} \approx 26\text{ kJ/mol})$
3. $\text{N} + \cdot\text{OH} \xrightarrow{k_3} \text{NO} + \text{H} \quad (E_{a,3} \approx 0\text{ kJ/mol})$

Because Reaction 1 requires breaking the strong $\text{N}\equiv\text{N}$ triple bond ($945\text{ kJ/mol}$), thermal $\text{NO}$ production is exponentially sensitive to combustion temperature:

2. The Three-Way Catalytic Converter (TWC)

To abate vehicle emissions simultaneously, modern automotive exhaust systems employ Three-Way Catalytic Converters consisting of noble metal nanoparticles (Platinum $\text{Pt}$, Palladium $\text{Pd}$, and Rhodium $\text{Rh}$) dispersed onto a high-surface-area $\gamma-\text{Al}_2\text{O}_3$ washcoat supported on a cordierite ceramic honeycomb monolith. The converter carries out three simultaneous redox reactions:

1. Oxidation of Carbon Monoxide:

1. Oxidation of Unburned Hydrocarbons:

1. Reduction of Nitric Oxide:

3. The Stoichiometric Air-to-Fuel Window

Optimal conversion efficiency ($> 98\%$ for all three pollutants simultaneously) occurs only within an extremely narrow air-to-fuel mass ratio window centered at stoichiometry:

• Rich Mixture ($\lambda < 1.0$): Insufficient $\text{O}_2$; conversion efficiency of $\text{CO}$ and $\text{HC}$ drops precipitously.
• Lean Mixture ($\lambda > 1.0$): Excess $\text{O}_2$; surface oxygen coverage on Rh blocks $\text{NO}$ dissociation sites, collapsing $\text{NO}_x$ reduction efficiency.

Closed-loop control is maintained via a heated zirconium dioxide ($\text{ZrO}_2$) oxygen sensor ($\lambda$-sensor) that adjusts real-time fuel injection pulse width.

Acid deposition (acid rain) is the atmospheric deposition of strong mineral acids onto terrestrial and aquatic ecosystems via wet precipitation (rain, snow, fog) and dry aerosol/gas deposition.

1. Natural Rain pH and the Carbonic Acid Buffer

Pure, unpolluted rainwater in equilibrium with atmospheric carbon dioxide ($ ext{CO}_2 \approx 420\text{ ppmv}$) is naturally mildly acidic. The equilibrium is governed by Henry's law and carbonate equilibria:

1. Gas-liquid dissolution:

1. First dissociation of carbonic acid:

Assuming $[ ext{H}^+] \approx [ ext{HCO}_3^-]$ from charge balance:

Therefore, acid rain is formally defined as precipitation having a $\text{pH} < 5.60$, driven by anthropogenic emissions of sulfur dioxide ($\text{SO}_2$) and nitrogen oxides ($\text{NO}_x$).

2. Gas-Phase vs Aqueous-Phase Oxidation of SO2

While gas-phase oxidation by $\cdot\text{OH}$ occurs at moderate rates ($~1\%\text{ per hour}$):

the predominant mechanism responsible for severe acid deposition ($> 80\%$) takes place inside cloud droplets via aqueous-phase oxidation by dissolved hydrogen peroxide ($\text{H}_2\text{O}_2$) and ozone ($\text{O}_3$):

1. Aqueous dissolution and hydration:

1. Oxidation by dissolved $\text{H}_2\text{O}_2$:

The rate law for hydrogen peroxide oxidation is:

Because $[ ext{HSO}_3^-] \propto [\text{H}^+]^{-1}$, the $[ ext{H}^+]$ factors cancel, making the rate of $\text{H}_2\text{O}_2$ oxidation virtually independent of cloud pH down to $\text{pH} \approx 1.5$! Consequently, aqueous $\text{H}_2\text{O}_2$ rapidly converts dissolved $\text{SO}_2$ to sulfuric acid even in highly acidic droplet environments.

Environmental radioactivity originates from primordial terrestrial radionuclides, cosmogenic spallation products, and anthropogenic nuclear fission/activation byproducts.

1. Primordial Radionuclides and the Radon Hazard

Primordial radioisotopes formed during stellar nucleosynthesis before the condensation of the solar system include Potassium-40 ($^{40}\text{K}$, $t_{1/2} = 1.25 \times 10^9\text{ y}$), Thorium-232 ($^{232}\text{Th}$), and Uranium-238 ($^{238}\text{U}$, $t_{1/2} = 4.468 \times 10^9\text{ y}$). Within the $^{238}\text{U}$ decay series, Radium-226 ($^{226}\text{Ra}$, $t_{1/2} = 1600\text{ y}$) decays via alpha emission into Radon-222 ($^{222}\text{Rn}$):

As a noble gas with zero chemical reactivity, $^{222}\text{Rn}$ diffuses upward through porous soil minerals and cracks in building foundations into indoor environments. While $^{222}\text{Rn}$ is exhaled upon inhalation, its short-lived decay progeny:

are solid, chemically reactive heavy metal ions that attach to submicron aerosols ($d_p \approx 0.1-0.3\ \mu\text{m}$). Inhaled into the bronchial epithelium, the high-LET alpha particles from $^{218}\text{Po}$ ($E_\alpha = 6.00\text{ MeV}$) and $^{214}\text{Po}$ ($E_\alpha = 7.69\text{ MeV}$) deliver concentrated ionizing radiation directly to basal stem cell nuclei, representing the leading cause of lung cancer in non-smokers.

2. Cosmogenic Radionuclides: Carbon-14 and Tritium

Cosmic ray spallation of stratospheric and upper tropospheric nuclei produces cosmogenic isotopes:

1. Carbon-14 ($^{14}\text{C}$, $t_{1/2} = 5730\text{ y}$):

The nascent $^{14}\text{C}$ atom rapidly oxidizes to $^{14}\text{CO}_2$, entering the global photosynthetic carbon cycle.

1. Tritium ($^3\text{H}$, $t_{1/2} = 12.32\text{ y}$):

Tritium oxidizes to tritiated water ($\text{HTO}$) and enters the global hydrological cycle.

3. Anthropogenic Nuclear Fallout Radionuclides

Atmospheric nuclear weapons testing and major reactor accidents (Chernobyl, Fukushima) injected long-lived fission products into the atmosphere:

• Cesium-137 ($^{137}\text{Cs}$, $t_{1/2} = 30.17\text{ y}$): Alkali metal that mimics potassium ($K^+$), rapidly bioaccumulating in muscle tissues and soil clay mineral interlayers.
• Strontium-90 ($^{90}\text{Sr}$, $t_{1/2} = 28.9\text{ y}$): Alkaline earth metal that chemically mimics calcium ($Ca^{2+}$), depositing into human bone trabeculae and irradiating bone marrow.