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Environmental Engineering DISCUSSION
Air quality limits are sometimes given in ppm or ppb and sometimes in µg/m³ or mg/m³, and my gas analyser reads in ppm. I have found the conversion factor 24.45 in one reference and 22.4 in another, and the results differ by almost 10 percent.
What is the correct way to convert, for example, 0.5 ppm of SO2 or 100 ppb of NO2 to mass concentration, which factor applies when, and is the ppm used for water samples the same kind of unit?
For a gas, ppm means parts per million by volume, which for ideal gases is the same as a mole ratio. To get mass per volume you need the molar mass of the pollutant and the volume that one mole of gas occupies at the stated conditions: C (mg/m³) = C (ppm) × M / V_m, with M in g/mol and V_m in L/mol.
V_m is where the two factors come from. At 0 °C and 101.325 kPa it is 22.41 L/mol; at 25 °C and the same pressure it is 24.45 L/mol; at 20 °C it is 24.06 L/mol. None of them is wrong. The ppm value does not change with temperature, but the mass per cubic metre does, because the same cubic metre holds fewer moles when it is warmer.
Worked examples at 25 °C. SO2 has M = 64.07, so 0.5 ppm = 0.5 × 64.07 / 24.45 = 1.31 mg/m³, or 1310 µg/m³. NO2 has M = 46.01, so 100 ppb = 0.1 ppm = 0.1 × 46.01 / 24.45 = 0.188 mg/m³, or 188 µg/m³. CO with M = 28.01 at 9 ppm is 9 × 28.01 / 24.45 = 10.3 mg/m³.
For any other condition, V_m = 22.414 × (T / 273.15) × (101.325 / P), with T in kelvin and P in kPa. At 35 °C and 95 kPa, for instance, V_m = 22.414 × 1.128 × 1.067 = 26.97 L/mol, and the same 0.5 ppm of SO2 is only 1.19 mg/m³ of actual air.
Which factor to use is set by the regulation, not by the weather on the day. Each standard defines its reference conditions, and the mass concentration must be expressed at those conditions even if the sample was taken at a different temperature. Ambient air standards in different jurisdictions use 25 °C, 20 °C or 0 °C, so check the definition before comparing a measurement with a limit, and state the reference conditions whenever you report mg/m³.
Going the other way is the same formula rearranged: ppm = mg/m³ × V_m / M. An analyser reading in ppm needs no temperature correction itself, which is one reason instruments and calibration gases are specified in volume units.
Stack emissions add two more normalisations. Limits are usually in mg per normal cubic metre of dry gas, so the measured value is corrected to the reference temperature and pressure and the water vapour is removed from the volume. Then it is corrected to a reference oxygen content, so that diluting the flue gas with extra air cannot make the figure look better: C_ref = C_measured × (20.9 - O2_ref) / (20.9 - O2_measured).
Example: 200 mg/Nm³ measured at 11 percent O2, reported at a 6 percent reference, becomes 200 × (20.9 - 6) / (20.9 - 11) = 200 × 14.9 / 9.9 = 301 mg/Nm³. The reference oxygen level depends on the fuel and plant type in the applicable regulation.
No, ppm in water is a different unit. There it is a mass ratio, milligrams of substance per kilogram of solution, and because a litre of dilute water solution has a mass of almost exactly one kilogram, 1 ppm is taken as 1 mg/L. Molar mass and temperature do not enter.
Two related points: particulate matter (PM10, PM2.5) can only be expressed as mass per volume, since particles are not a gas and have no volume fraction in this sense; and when writing reports it is clearer to use ppmv or ppbv for gases so that nobody reads the value as a mass ratio.
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