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ppm ↔ mg/m³ ↔ mg/L converter

ppm by volume in air to mg/m³, ppm by mass in solution to mg/L, each with its own parameter.

Parameters

The pollutant’s: CO 28.01, CO₂ 44.01, NO₂ 46.01, benzene 78.11, SO₂ 64.06.
101,325 Pa = 1 atm (an exact value fixed by the 10th CGPM, 1954).

Result

Concentration

57.244 mg/m³

Calculation
C = ppm × M / Vm = 50 × 28.01 ÷ 24.465 = 57.244 mg/m³
In ppm
50
Molar volume Vm at the entered conditions
24.465 L/mol
Note

Molar volume 24.465 L/mol at the entered conditions: that is what carries the temperature and pressure dependence. The “÷ 24.45” of industrial-hygiene tables is this same formula frozen at 25 °C and 1 atm, inexact elsewhere.

Calculation, assumptions and sources

OverviewIn a gas, ppm is a volume fraction (hence molar); in a solution, a mass fraction.

In a gas, ppm is a volume fraction (hence molar); in a solution, a mass fraction. Air: C(mg/m³) = ppm × M / Vm, with Vm computed at the entered temperature and pressure. Solution: C(mg/L) = ppm × ρ. The “÷ 24.45” of hygiene tables is the same formula at 25 °C and 1 atm.

Method & formulasair: C(mg/m³) = ppm × M(g/mol) / Vm(L/mol)
air: C(mg/m³) = ppm × M(g/mol) / Vm(L/mol)molar volume: Vm = R·T / Psolution: C(mg/L) = ppm(mg/kg) × ρ(kg/L)R = 8.31446261815324 J·mol⁻¹·K⁻¹ (exact since the 2019 SI)

In a gas, a volume fraction is also a mole fraction (Avogadro’s law): the mass concentration is obtained by multiplying by the molar mass and dividing by the molar volume Vm, the only term that depends on temperature and pressure. In a solution, 1 ppm = 1 mg/kg and the density converts to mg/L.

ppm by volume (ppmv)
one volume of pollutant gas per million volumes of air, at the same T and P. The unit of occupational exposure limits and air-quality measurements.
ppm by mass (mg/kg)
one milligram of solute per kilogram of solution (not of solvent).
Molar volume (Vm)
24.465 L/mol at 25 °C and 1 atm; 22.414 L/mol at 0 °C.
Validity domainThe air calculation assumes an ideal gas mixture, valid for dilute pollutants at ambient conditions, less so at very high pressures.

The air calculation assumes an ideal gas mixture, valid for dilute pollutants at ambient conditions, less so at very high pressures. Mass ppm in a gas, a third convention, is treated as a solution, using the gas density. No exposure limit value is provided.

The “1 ppm = 1 mg/L” and “÷ 24.45” shortcuts“1 ppm = 1 mg/L” assumes a density of 1 kg/L: the error reaches 2.5% in seawater, more in brine or an organic solvent.

“1 ppm = 1 mg/L” assumes a density of 1 kg/L: the error reaches 2.5% in seawater, more in brine or an organic solvent. “ppm × M ÷ 24.45” assumes 25 °C and 1 atm: at 0 °C, Vm is 22.41 L/mol and the result is off by 9%; at altitude, pressure also changes Vm.