Mass concentration in mg per cubic metre equals ppm times molar mass divided by molar volume, and the molar volume depends on temperature and pressure. Normal conditions are usually 0 C and 1013.25 hPa, standard conditions 25 C or 15 C. Always state the reference conditions, and whether the gas is dry, and at what oxygen level.
- Convert ppm to mg/Nm3 and back for a given gas
- Name the usual normal and standard reference conditions
- Explain why a limit must state temperature, pressure, moisture basis and oxygen level
From ppm to mg/m3
A cubic metre holds a number of moles that depends on temperature and pressure. Each mole of a gas has a known mass, its molar mass. So to turn a volume fraction into mass per volume, multiply by molar mass and divide by the volume of a mole.
mg/m3 = ppm x M / Vm Vm = 22.414 L/mol at 0 C and 1013.25 hPa
50 ppm of carbon monoxide (M = 28.01): 50 x 28.01 / 22.414 = 62.5 mg/Nm3. For carbon monoxide, 1 ppm is about 1.25 mg/Nm3.
Normal, standard and actual
- Normal conditions (Nm3): usually 0 C and 1013.25 hPa. Used widely in Europe and in gas industry.
- Standard conditions (Sm3): often 15 C or 25 C and 1013.25 hPa. Definitions differ by industry and country.
- Actual conditions: the real temperature and pressure of the gas at the measurement point.
The same gas in the same duct gives different mg per cubic metre under each. At 25 C the molar volume is about 9 % larger than at 0 C, so the mg/m3 figure is about 9 % smaller.
A mass limit has four hidden conditions
- Temperature, for example 0 C or 25 C.
- Pressure, usually 1013.25 hPa.
- Moisture basis: dry or wet. Environmental limits are normally dry.
- Reference oxygen for combustion gases: the value is restated to a stated oxygen level. See Emission correction to reference oxygen.
Comparing a reading with a limit without checking all four. A value that looks compliant can fail once it is dried and corrected to the reference oxygen.
Why analysers report ppm
The sensor responds to molecules, so the natural unit is a volume fraction. The analyser or the control system then converts to mg/Nm3 using the gas, temperature, pressure and oxygen reading. For stack monitoring that conversion, and the oxygen channel it needs, are part of the system design; see Emission monitoring (CEMS) basics: what a system does.
- mg/m3 = ppm x molar mass / molar volume.
- Molar volume is 22.414 L/mol at 0 C and 1013.25 hPa and grows with temperature.
- State temperature, pressure, dry or wet basis and reference oxygen with every mass limit.
- Analysers measure volume fractions; conversion to mass is arithmetic.
Check your understanding
Answer in your head or on paper first, then open the answer. Recalling an answer teaches more than rereading.
What is the molar volume of an ideal gas at 0 C and 1013.25 hPa?
22.414 litres per mole.
Why is a limit in mg/Nm3 at 25 C lower numerically than the same limit at 0 C?
At 25 C a cubic metre holds fewer molecules, so the same ppm corresponds to fewer mg per cubic metre.
List the four conditions that a combustion emission limit must state.
Temperature, pressure, dry or wet basis, and the reference oxygen level.
Key terms
Frequently asked questions
How do I convert ppm to mg/Nm3?
Multiply by the molar mass and divide by 22.414, for 0 C and 1013.25 hPa.
What is the difference between Nm3 and Sm3?
Nm3 refers to normal conditions, usually 0 C; Sm3 to standard conditions, often 15 or 25 C. Always check the definition in the document.
Is a wet or dry basis used for emission limits?
Usually dry, but the permit or standard decides.
Does temperature change ppm?
No. ppm is a volume fraction. It changes mg/m3.