Expressing The Amount Of A Substance In The Atmosphere

The SI unit for the amount of a substance is the mole (mol). The number of atoms or molecules in 1 mol is Avogadro's number, Na = 6.022 x 1023 moi-1. Concentration is the amount (or mass) of a substance in a given volume divided by that volume. Mixing ratio in atmospheric chemistry is defined as the ratio of the amount {or mass) of the substance in a given volume to the total amount (or mass) of all constituents in that volume. In this definition for a gaseous substance the sum of all constituents includes all gaseous substances, including water vapor, but not including particulate matter or condensed phase water. Thus mixing ratio is just the fraction of the total amount (or mass) contributed by the substancc of interest.

The volume mixing ratio for a species i is



where c, is the molar concentration of i and ctotal is the total molar concentration of air. From the ideal-gas law the total molar concentration at any point in the atmosphere is

Thus the mixing ratio ^ and the molar concentration are related by p/RT

p/RT ' p where p, is the partial pressure of i.

Concentration (mol m3) depends on pressure and temperature through the ideal-gas law. Mixing ratios, which are just mole fractions, are therefore better suited than concentrations to describe abundances of species in air, particularly when spatiotemporal variation is involved. The inclusion of water vapor in the totality of gaseous substances in a volume of air means that mixing ratio will vary with humidity. The variation can amount to several percent. Sometimes, as a result, mixing ratios are defined with respect to dry air.

It has become common use in atmospheric chemistry to describe mixing ratios by the following units:

parts per million (ppm) 10" 6 (^mol moF1

parts per billion (ppb) 10"9 nmol mol-1

parts per trillion (ppt) 10-12 pmol mol-1

These quantities are sometimes distinguished by an added v (for volume) and m (for mass), that is, ppmv parts per million by volume ppmm parts per million by mass

Unless noted otherwise, we will always use mixing ratios by volume and not use the added v. The parts per million, parts per billion, and parts per trillion measures are not SI units; the SI versions are, as given above, pmol mol1, nmol mol"-1, and pmol mol-1.

Water vapor occupies an especially important role in atmospheric science. The water vapor content of the atmosphere is expressed in several ways:

1. Volume mixing ratio, ppm

2. Ratio of mass of water vapor to mass of dry air, g H20 (kg dry air)-1

3. Specific humidity - ratio of mass of water vapor to mass of total air, g H20 (kg air)"1

4. Mass concentration, g H20 (m3 air)"1

6. Relative humidity - ratio of partial pressure of H20 vapor to the saturation vapor pressure of H20 at that temperature, Ph2o/Ph2o-

Relative humidity (RH) is usually expressed in percent:

Relative humidity (RH) is usually expressed in percent:

Number Concentration of Water Vapor The vapor pressure of pure water as a function of temperature can be calculated with the following correlation:

p°Hi0(T) = 1013.25 exp[13.3185a — 1.97a2 - 0.6445a3 - 0.1299a4] (1.10) where


(An alternate correlation is given in Table 17.2.)

Let us calculate the number concentration of water vapor /¡h,o (molecules cm-5) at RH = 50% and T = 298 K:

PH:0 — «IIjO RT From the correlation above, at 298 K, we obtain


«¡1,0 = —---- ■ ■ ■—————r-—ss 3.81 x 10 moleculescm

H2U 8.314 x 298 x 10s

Figure 1.3 shows the U.S. Standard Atmosphere temperature profile at 45°N and that at the equator. Corresponding to each temperature profile is the vertical profile of P}bo/P> exPressed as mixing ratio. Note that in the equatorial tropopause region, the saturation mixing ratio of water vapor drops to about 4-5 ppm, whereas at the surface it is several percent. Air enters the stratosphere from the troposphere, and this occurs primarily in the tropical tropopause region, where rising air in towering cumulus clouds is injected into the stratosphere. Because this region is so cold, water vapor is frozen out of the air entering the stratosphere. This process is often referred to as "freeze drying" of the atmosphere. As a result, air entering the stratosphere has a water vapor mixing ratio of only 4-5 ppm, and the stratosphere is an extremely dry region of the atmosphere.

US Standard Atmosphere 45°N

US Standard Atmosphere 45°N

US Standard Atmosphere 45°N

200 220 240 260 280 300 10 10 5 10 4 10"3 10~2 10'

Temperature, K

H20 Saturation Mixing Ratio

Satellite Climatology Equator, Jan

Satellite Climatology Equator, Jan

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