Structure and Composition of the Atmosphere

Introduction

The atmosphere is a thin envelope of gas: half of its mass lies below about 5.5 km, a height less than one-thousandth of the Earth's radius. Yet within this shell the temperature rises and falls in distinct layers, the pressure drops by a factor of a million, and gases present at a few parts per billion control ozone, climate and air quality. Before studying atmospheric reactions we need a clear picture of the stage on which they happen and of the units chemists use to describe atmospheric composition.

Core explanation

Temperature layers. The atmosphere is divided according to how temperature changes with altitude.

Layer Approximate altitude Temperature trend Cause --- --- --- --- Troposphere 0 to 10–16 km Falls, about 6.5 K per km Heated from the ground; rising air expands and cools Stratosphere Tropopause to about 50 km Rises Ozone absorbs solar ultraviolet Mesosphere 50 to about 85 km Falls Little ozone; radiative cooling by CO₂ Thermosphere Above 85 km Rises sharply Absorption of very short-wavelength UV by O₂ and N₂

The tropopause is higher over the tropics (about 16 km) than over the poles (about 8–10 km). Because temperature increases with height in the stratosphere, warm air lies over cool air; this temperature inversion makes the stratosphere very stable, so vertical mixing there is slow. By contrast the troposphere is turbulent and well stirred, mixing vertically in days to weeks.

Pressure profile. Each layer of air supports the weight of the air above it. Combining this hydrostatic balance with the ideal gas law gives the barometric equation:

p(z) = p₀ exp(−z/H)

where p₀ ≈ 1013 hPa at sea level and H = RT/(Mg) is the scale height . For air (M = 0.029 kg mol⁻¹) at 250 K, H ≈ 7.3 km. Pressure therefore halves roughly every 5.5 km. At the top of Everest the pressure is about one-third of that at sea level; at 50 km it is roughly one-thousandth.

Composition. Dry air is dominated by nitrogen (78.08%), oxygen (20.95%) and argon (0.93%). These major gases have long lifetimes and constant mixing ratios up to about 100 km. Water vapour is highly variable (up to about 4% near the tropical surface). Carbon dioxide is about 420 ppm, and a long list of trace gases — methane (about 1.9 ppm), nitrous oxide (about 0.34 ppm), ozone (tens of ppb near the surface, up to about 10 ppm in the stratosphere), carbon monoxide, nitrogen oxides and halocarbons — are present at parts per million to parts per trillion. Despite their tiny amounts, trace gases drive most atmospheric chemistry.

Concentration units. Atmospheric chemists use the mixing ratio (mole fraction), expressed as ppm (10⁻⁶), ppb (10⁻⁹) or ppt (10⁻¹²). A mixing ratio does not change when air is compressed or expanded, which makes it ideal for comparing air masses. For kinetics we need number density , n (molecules cm⁻³). At the surface the total air number density is about 2.5 × 10¹⁹ molecules cm⁻³, so 1 ppb corresponds to roughly 2.5 × 10¹⁰ molecules cm⁻³.

Formulae

Barometric equation: p(z) = p₀ e^(−z/H), with scale height H = RT/(Mg). Total number density: n = p/(k B T). Number density of a trace gas = mixing ratio × n.

Step-by-step reasoning

To convert a mixing ratio into a number density:

1. Find the total air number density from n = p/(k B T), using p in Pa and T in K; divide by 10⁶ to convert m⁻³ into cm⁻³. 2. Multiply by the mixing ratio as a pure fraction (e.g. 40 ppb = 40 × 10⁻⁹). 3. Report the answer in molecules cm⁻³. 4. At altitude, recalculate n with the local pressure and temperature, since the mixing ratio alone does not give the concentration.

Visual explanation

Sketch a graph with altitude on the vertical axis and temperature on the horizontal. The line zigzags: leaning left through the troposphere, bending right through the stratosphere, left again through the mesosphere and sharply right in the thermosphere. Beside it, a pressure curve falls smoothly and exponentially.

Real-world analogy

A stack of mattresses is squashed most at the bottom, where it carries the weight of all the mattresses above. The atmosphere behaves the same way: air near the ground is compressed by the air above it, so density and pressure are greatest at the surface.

Real-world example

Passenger aircraft cruise at about 10–12 km, near the tropopause. At mid-latitudes they sometimes fly in the lowest stratosphere, where the stable air gives a smooth ride. The cabin must be pressurised because outside pressure is only about a quarter of sea-level pressure.

Why?

Why does temperature rise through the stratosphere? Ozone molecules absorb ultraviolet photons and pass that energy to surrounding molecules as heat. The heating is strongest near 50 km, where sunlight is intense and ozone still plentiful, producing the warm stratopause.

Common misconception

"The ozone layer is a layer of pure ozone." Even at its peak ozone makes up only about 10 ppm of stratospheric air. If all atmospheric ozone were brought to surface pressure it would form a layer only about 3 mm thick.

Worked example

Question: Surface air at 1013 hPa and 288 K contains 40 ppb of ozone. Calculate the ozone number density.

Reasoning: n = p/(k B T) = 101300 ÷ (1.381 × 10⁻²³ × 288) = 2.55 × 10²⁵ m⁻³ = 2.55 × 10¹⁹ cm⁻³. Ozone = 40 × 10⁻⁹ × 2.55 × 10¹⁹.

Answer: About 1.0 × 10¹² molecules cm⁻³.

Quick check

1. Why is the stratosphere much more stable to vertical mixing than the troposphere? Answer: Temperature increases with height in the stratosphere, so warm light air lies above cooler denser air and there is no tendency for convection.

Exam focus

Be able to name the layers, give approximate altitudes and explain the cause of each temperature trend. Practise converting mixing ratios into number densities with n = p/(k B T), keeping careful track of m³ and cm³.

Advanced insight

Above about 100 km, the homopause , turbulent mixing gives way to molecular diffusion, and each gas settles according to its own molar mass, so lighter gases such as helium and atomic hydrogen become relatively enriched. Below it, all long-lived gases share the same scale height and keep constant mixing ratios.

Summary

The atmosphere is layered by temperature: troposphere, stratosphere, mesosphere and thermosphere. Pressure falls exponentially with a scale height of about 7 km. Dry air is mostly N₂, O₂ and Ar, but trace gases at ppm to ppt levels drive the chemistry. Mixing ratios compare air masses; number densities are needed for reaction rates.

Practice questions

1. Explain why temperature falls with height in the troposphere. Answer: The troposphere is heated from the ground, and rising air expands into lower pressure and cools adiabatically. 2. Using a scale height of 7.5 km, estimate the pressure at 15 km as a fraction of the surface pressure. Answer: e^(−15/7.5) = e^(−2) ≈ 0.14 of the surface value. 3. Convert a CO₂ mixing ratio of 420 ppm into a percentage by volume. Answer: 420 × 10⁻⁶ = 4.2 × 10⁻⁴ = 0.042%. 4. Why are mixing ratios preferred to number densities for comparing air at different altitudes? Answer: Mixing ratios do not change when air expands or is compressed, whereas number densities fall with pressure even if the composition is the same.