Conversion between ppm and mg/m³
While working on the Air Quality post I came accross the following complication:
Complication: The O₃ values are reported in ppm (parts per million) in North America while in Europe they are usually expressed in mg/m³ (micrograms per cubic meter).
To compare the values, I can convert the ppm values to mg/m³ using the following formula:
$$ \text{mg/m}^3 = \text{ppm} \times \frac{\text{Molar mass of } \mathrm{O}_3 \times 1000}{\text{Molar volume (L)}} $$
At standard temperature and pressure (STP: 25°C, 1 atm), molar volume = 24.45 L/mol, and ozone's molar mass = 48.00 g/mol:
$$ \text{mg/m}^3 = \text{ppm} \times \frac{48.00 \times 1000}{24.45} \approx \text{ppm} \times 1963 $$
Note: The factor 1963 assumes 25°C and 1 atm. If temperature or pressure varies significantly, the molar volume changes slightly, and the conversion factor must be adjusted.