# Units of Concentrations and Conversions

A number of different units are used in expressing the concentrations of various species in the atmosphere; we shall review these here. For a review of IUPAC recommendations, see Schwartz and Warneck (1995).

a. Parts per Million, Parts per Hundred Million, Parts per Billion, and Parts per Trillion

For gas-phase species, the most commonly used units are parts per million (ppm), parts per hundred million (pphm), parts per billion (ppb), and parts per trillion (ppt). These units express the number of molecules of pollutant found in a million (106), a hundred million (10x), a billion (an American billion (109)), or a trillion (1012) molecules of air, respectively. It should be noted that, although these are commonly used, confusion may arise in that in some European countries a billion means 1012 and a trillion means 1018. As a result, in some journals when these units are used, they are accompanied by a definition, e.g., ppb (parts in 109). Care must also be taken to ensure that ppt means parts per trillion and not parts per thousand. The latter unit is often used in isotope studies and is denoted parts per mille, or %c.

Alternatively, because numbers of molecules (or moles) are proportional to their volumes according to the ideal gas law (PV = nRT), these units may be thought of as the number of volumes of the pollutant found in 106, 10x, 109, or 1012 volumes of air, respectively.

This ratio of moles, molecules, or volumes of the species to the number of moles, molecules, or volumes of dry air is more commonly known as the mixing ratio. The use of mixing ratios is widespread for expressing the relative amounts of a species at various altitudes throughout the atmosphere. Since the total air pressure and hence total concentration of air decreases with altitude, a constant mixing ratio does not imply a constant concentration (i.e., as expressed in moles or molecules per unit volume). Although not expressly stated in most cases, mixing ratios are usually referenced to dry air. If water vapor is included, the mixing ratio would vary with humidity, which could induce a variation of a few percent. Although we shall use the term concentration frequently, if the units are ppm, ppb, or ppt, it should be understood that this is really a mixing ratio. Some journals emphasize this by writing these units as ppm (v:v), etc.

For example, a background concentration of 03 may be 0.04 ppm; this is 4 pphm, 40 ppb, or 40,000 ppt. Thus in 108 molecules of air, only 4 are 03; alternatively, in every 10x volumes of air, only 4 volumes are due to 03. While it is most convenient to express the concentration of 03 in ppm, pphm, or ppb, other important atmospheric species can be present in much smaller concentrations. For example, the hydroxyl free radical (OH), which, as we saw, drives the daytime chemistry of both the clean and polluted troposphere, is believed to have typical concentrations of only <0.1 ppt. Hence either ppt or an alternate unit discussed in the next section (number per cm3) is used.

Concentrations of pollutants in ambient air are normally sufficiently small that ppm is the largest unit in use. However, pollutant concentrations in stacks or exhaust trains prior to mixing and dilution with air are much higher, and percent (i.e., parts per hundred) is sometimes used in this case. For example, carbon monoxide concentrations in automobile exhaust are measured in percentages, reflecting the numbers of CO molecules (or volumes) per 100 molecules (or volumes) of exhaust.

Finally, it is important to remember that the number of molecules, or volumes, of a given gaseous species forms the basis of units in atmospheric chemistry; in water chemistry, mass rather than volume is used as the basis for expressing concentrations in ppm, and so on.

b. Number per Cubic Centimeter

A second type of concentration unit is generally used for species such as free radicals (e.g., OH) present at sub-ppt levels. It is the number of molecules, atoms, or free radicals present in a given volume of air, usually a cubic centimeter (cm3). One can convert from units of ppm, pphm, ppb, or ppt to units of number per cm3 using the ideal gas law. Thus the number of moles per L in air at 1 atm pressure and 25°C (298 K) is given by n/V= P/RT

= 1 atm/[0.08206 (L atm/K mol) x 298 K] = 0.0409 mol/L

Converting to units of molecules per cm3, one obtains n/V= 0.0409 mol/L x 10"3 (L/cm3) x 6.02 x 1023 molecules/mol = 2.46 x 1019 molecules cm"3

From the definition of ppm as the number of pollutant molecules per 106 molecules of air, 1 ppm corresponds to 2.46 x 1019 x 10"6 = 2.46 x 1013 molecules per cm3 at 25°C and 1 atm total pressure. It follows that a concentration of the OH radical in polluted air

 Parts per Unit Molecules, atoms, or radicals per cm5 106 f ppm 2.46 X f013 10« 1 pphm 2.46 x 10" 10" f ppb 2.46 x fO1" 1012 lppt 2.46 x 107

" 1 ppm in units of mass per cubic meter = 40.9 X (MW) /¿g

" 1 ppm in units of mass per cubic meter = 40.9 X (MW) /¿g of 0.1 ppt is 2.46 x 1019 x 10"12 x 0.1 = 2.46 x 106 molecules per cm3. As we shall see, the peak OH concentration is much smaller so the use of fractional ppt units becomes inconvenient. Units of number per cm3 are more commonly used in such cases.

Table 2.5 summarizes the relationship between these units at 1 atm pressure and 25°C. Of course, corrections must be made if the temperature or pressure differs significantly.

c. Micrograms per Cubic Meter

A third unit of measurement for gaseous species is mass per unit volume, usually 10~6 g per cubic meter (fig m~3). Since 1 atm at 25°C contains 4.09 x 10~2 mol L"1, 1 ppm must contain (4.09 x 10~2) x 10"h or 4.09 x 10~8 mol L_1 or 4.09 x 10"5 mol m"3. If the molecular weight of the pollutant is MW grams per mole, then 1 ppm in units of mass per m3 is (4.09 x 10"5) x (MW) g m"3 or (40.9) x (MW) fig m"3.

Returning to the example of a background 03 of 0.04 ppm, this concentration in fig m 3 is 40.9 x 48 x 0.04 (where 48 g mol-1 is the molecular weight of 03), or 79 fig m~3. If the pollutant were 0.04 ppm S02 (MW = 64) rather than 03, the concentration of S02 would be (40.9 x 64) x 0.04, or 105 fig m"3.

The conversion between fig m~3 and ppm, pphm, ppb, and ppt can be summarized as follows:

fig m~3 = ppm x 40.9(MW) = pphm x 0.409(MW) = ppb x 0.0409(MW) = ppt x (4.09 x 10~5)(MW)

For atmospheric particulate matter, concentrations are expressed in mass per unit volume, commonly ¡ig m~3, or in the number of particles per unit volume, for example, per cm3.

 Pollutant 