ppm to mg/m³ Conversion

A part per million by volume is a mole fraction, and a milligram per cubic metre is a mass per volume, so converting between them needs two pieces of information: the molar mass of the gas and the volume one mole occupies. The second comes from the ideal gas law, $V_m = RT/P$, which at 25 °C and 101.325 kPa gives 24.45 L/mol. From there the conversion is just bookkeeping: $C = ppm \times M/24.45$ with M in g/mol and C in mg/m³. One ppm of sulphur dioxide, molar mass 64.06, is $64.06/24.45 = 2.62$ mg/m³; one ppm of carbon monoxide is 1.15 mg/m³; one ppm of nitrogen dioxide is 1.88 mg/m³. Those three numbers appear on wall charts everywhere and this is where they come from.

The reference state is the thing to be careful about, because 24.45 is a choice rather than a constant. At 25 °C the molar volume is 24.45 L/mol, at 20 °C it is 24.06, and at 0 °C it is 22.414 — the number from first-year chemistry. US and industrial-hygiene practice standardises on 25 °C; European emission limits are stated at 0 °C, and the same physical gas therefore converts to a mg/m³ figure 9.1 % higher under the European convention than the American one. That is larger than most compliance margins. A mg/m³ value with no stated reference temperature is an incomplete number, and the correct response to receiving one is to ask rather than to assume.

The other trap is which molar mass to use, and nitrogen oxides are the standing example. Flue gas NOx is mostly nitric oxide, NO, with a molar mass of 30.01, but essentially every regulation requires it to be REPORTED as nitrogen dioxide, molar mass 46.01, on the reasoning that the NO oxidises to NO₂ in the atmosphere within hours. So a NOx concentration in ppm converts with 46.01 regardless of what the analyser is actually seeing, and using 30.01 under-states the mass by a third. Sulphur oxides carry a similar convention, reported as SO₂, and total hydrocarbons are usually reported as methane or as propane depending on the rule, which changes the molar mass by a factor of nearly three.

Two smaller points, both of which cause arguments. Parts per million by volume and parts per million by mass are different quantities for a gas and coincide only when the molar mass of the contaminant equals that of air, 28.96 g/mol; for a gas analyser, ppm always means by volume unless it explicitly says otherwise, while for a liquid or a solid ppm almost always means by mass. And this conversion assumes ideal-gas behaviour, which for trace contaminants in flue gas at atmospheric pressure is accurate to well under a percent — a rare case where the assumption everyone worries about is the one that does not matter.