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The conversion equations depend on the temperature at which the conversion is wanted (usually about 20 to 25 °C). At an ambient sea level atmospheric pressure of 1 atm (101.325 kPa or 1.01325 bar), the general equation is:

{\displaystyle \mathrm {ppmv} =\mathrm {mg} /\mathrm {m} ^{3}\cdot {\frac {(0.082057338\cdot T)}{M}}}{\displaystyle \mathrm {ppmv} =\mathrm {mg} /\mathrm {m} ^{3}\cdot {\frac {(0.082057338\cdot T)}{M}}}

and for the reverse conversion:

{\displaystyle \mathrm {mg} /\mathrm {m} ^{3}=\mathrm {ppmv} \cdot {\frac {M}{(0.082057338\cdot T)}}}{\displaystyle \mathrm {mg} /\mathrm {m} ^{3}=\mathrm {ppmv} \cdot {\frac {M}{(0.082057338\cdot T)}}}

where:

mg/m3 = milligrams of pollutant per cubic meter of air at sea level atmospheric pressure and T

ppmv = air pollutant concentration, in parts per million by volume

T = ambient temperature in K = 273. + °C

0.082057338 = Universal gas constant in L atm mol⁻¹ K⁻¹

M = molecular mass (or molecular weight) of the air pollutant

Notes:

1 atm = absolute pressure of 101.325 kPa or 1.01325 bar

mol = gram mole and kmol = 1000 gram moles

Pollution regulations in the United States typically reference their pollutant limits to an ambient temperature of 20 to 25 °C as noted above. In most other nations, the reference ambient temperature for pollutant limits may be 0 °C or other values.

Although ppmv and mg/m3 have been used for the examples in all of the following sections, concentrations such as ppbv (i.e., parts per billion by volume), volume percent, mole percent and many others may also be used for gaseous pollutants.

Particulate matter (PM) in the atmospheric air or in any other gas cannot be expressed in terms of ppmv, ppbv, volume percent or mole percent. PM is most usually (but not always) expressed as mg/m3 of air or other gas at a specified temperature and pressure.

For gases, volume percent = mole percent

1 volume percent = 10,000 ppmv (i.e., parts per million by volume) with a million being defined as 106.

Care must be taken with the concentrations expressed as ppbv to differentiate between the British billion which is 1012 and the USA billion which is 109 (also referred to as the long scale and short scale billion, respectively).

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