How does it work?
Air is a mixture of gases
Dry air is 78% nitrogen, 21% oxygen and almost 1% argon. The rest are trace gases, measured in ppm (parts per million) and ppb (parts per billion): 1 ppm is one molecule in a million. The ideal gas equation gives the number of molecules in a given volume:
N = p · VR · T · NA 0.5 L at 37 °C → about 1.2·1022 molecules
Smog and inversion
Dust concentration in a city depends on how much of it we release and on how many cubic meters of air it gets diluted in. In a simple “box” model:
C ≈ Cbg + Eu · H · W E — emissions, u — wind, H — mixing-layer height, W — valley width
During an inversion the mixing layer shrinks from several hundred meters to about 100–200 m, and in calm weather the wind carries almost nothing away. The same emissions then give a concentration several times higher.
Acids, bases and pH
pH = −log10[H+] Δ pH = −1 → 10 times more H+; Δ pH = −0.1 → 26% more
A gas dissolves in water in proportion to its partial pressure (Henry's law: c = KH · p). That's why more CO₂ in the air means more carbonic acid in raindrops and in the ocean.
Catalysts: in the car and in the stratosphere
A catalyst speeds up a reaction without being used up. In a car it's our ally: on platinum, palladium and rhodium, poisonous CO and NOₓ turn into CO₂ and N₂. In the stratosphere, the chlorine atom from CFCs turned out to be a catalyst too — except that it destroys ozone. It leaves every cycle unchanged, so it can repeat it thousands of times.
Simplifications: all simulations are models with approximate numbers. The town is a “box” with a single layer of air, photochemical smog is a few reactions instead of hundreds, and the stratosphere has sped-up chemistry. Measured numbers are labeled with their source and year.