How can ppm be converted to µg/m3?

I have two datasets of SO2 concentrations. One is in ppm while the other is in µg/m3. Is there a way to convert one to the other?
Jeff Borland 04/23/00

Vocabulary
atm*
ideal gas law*
ideal gas law constant*
kelvin*
micro*
moles*
parts per million*
It's easy to convert parts per million into other concentrations if you know what sort of "parts" you have. "1 ppm SO2 in air" could mean any of the following:
  • 1 gram of SO2 for every million grams of air (parts per million by mass);
  • 1 mL of SO2 for every million mL of air (parts per million by volume);
  • 1 gram of SO2 for every million mL of air (parts per million by mass per volume).
The three are not equivalent. Parts per million by volume is most convenient for gaseous concentrations, so that's what I'll assume you have.

  1. Write "ppm" in terms of cubic meters. There are a million cubic centimeters in a cubic meter (1 cm3 = (10-2)3 m3 = 10-6 m3) so one part per million of SO2 by volume in air is actually 1 cm3 SO2/ 1 m3 of air.
  2. Convert cm3 of SO2 gas to µg SO2. You'll need the density of the gas at the appropriate temperature and pressure. If you don't have the density you can estimate it using the ideal gas law:

    PV = nRT

    where P is the pressure, V is the volume, n is moles of gas, R is the ideal gas law constant (82.06 atm cm3/mol K) and T is the temperature in kelvins. Since density is mass per unit volume and the mass of the gas is moles of gas times molecular weight M,

    d = g/V = M (n/V) = MP/RT

    For example, at 25°C and 1.00 atm, the density of SO2 gas is approximately MP/RT = (64 g/mol)(1 atm)/(82.06 atm cm3/mol K)(298 K) = 0.00262 g/cm3 = 2620 µg/cm3.

    Multiplying parts per million SO2 by volume by the density of SO2 in µg/cm3 gives you µg/m3.

Author: Fred Senese senese@antoine.frostburg.edu


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