Gas concentration from ppm to mg/m³ and vice versa
This online calculator converts the gas concentration value from ppm to mass concentration and back taking into account temperature and pressure
The calculator below converts between volume concentration of gas, i.e. the ratio of the gas volume to the total volume, and mass concentration of gas, i.e. the ratio of the mass of the gas to the total volume. Most of such calculators perform calculations for standard temperature and pressure (0°C, 100.00 kPa), but this calculator allows you to set your own temperature and pressure values. A detailed description of the calculation can be found under the calculator.
Conversion from mass concentration to volume concentration and vice versa
As mentioned above, the volume concentration of gas is defined as the ratio of the gas volume to the total volume. It is a dimensionless value, for convenience expressed in percent (%), permille (parts per thousand, ‰), or ppm (parts per million). Sometimes, to emphasize that we are talking about volume concentration, you can see %vol. or ppmv (parts per million by volume), although IUPAC recommends avoiding such notation^{1}.
Ppm is often used for low concentration values, typical for air pollution. By definition, it is the number of gas particles per million air particles, 1 ppm = 1/1000000 = 0.0001% = 0.001‰.
Sometimes, however, the gas concentration is expressed as the mass concentration in milligrams per cubic meter (mg/m3). For example, permissible exposure limits (PEL or OSHA PEL) are expressed both in ppm and in mg/m³.
The conversion from one unit to another is based on the Law of Avogadro's, according to which equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. According to the first corollary from Avogadro's law, one mole of any gas under the same  isobaric and isothermal  conditions occupies the same volume.
You can find the molar volume for a given temperature and pressure using the Clapeyron equation:
,
where the universal gas constant R ≈ 8.314 J / (mol K)
Conversion from ppm to mass concentration
Knowing ppm, we can find how many liters of gas are contained in one cubic meter of total volume. By dividing this number by the molar volume of the gas (for a given temperature and pressure), we can get the number of moles of gas in one cubic meter of total volume. Finally, by multiplying the number of moles of gas by the molar mass of gas, we can obtain the mass of gas in one cubic meter of total volume or mass concentration.
Conversion from mass concentration to ppm
By dividing the mass of gas in a cubic meter by the molar mass of gas, we can get the number of moles of gas in a cubic meter. Multiplying the number of moles of gas by the molar volume of gas (for a given temperature and pressure), we get the volume of gas in liters per cubic meter of total volume. Now we only need to express this volume in parts per million, thus obtaining the ppm value.

Quantities, Units and Symbols in Physical Chemistry. INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY, PHYSICAL CHEMISTRY DIVISION ↩
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