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

Copyright © 1997-2010 by Fred Senese
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Last Revised 02/23/18.URL: http://antoine.frostburg.edu/chem/senese/101/solutions/faq/converting-ppm-to-micrograms-per-cubic-meter.shtml