Concentration conversion

Definitions

Concentration in parts per million (in volume)

LaTeX code: C(ppm_v)=10^6\frac{V_S}{V_A}

where LaTeX code: V_S is the volume of the specie LaTeX code: S and LaTeX code: V_A is the volume of the air. Using the perfct gas law:

LaTeX code: C(ppm_v)=10^6\frac{n_S}{n_A}

where LaTeX code: n_S is the number of moles of the specie LaTeX code: S and LaTeX code: n_A is the number of moles of air.

Conversions

from LaTeX code: ppm_v to LaTeX code: \mu mol m^{-3}

The conversion between LaTeX code: C(ppm_v) and LaTeX code: C(\mu mol\,m^{-3}) can be obtained invoking the he perfct gas law:

pV=LaTeX code: {n_A}RT

where R is the universal gas constant and thus:

LaTeX code: C(ppm_v)= C(\mu mol\,m^{-3})\frac{RT}{p}

Note that using LaTeX code: \mu mol eliminates the factor LaTeX code: 10^6.

from LaTeX code: \mu mol m^{-3} to LaTeX code: \mu g m^{-3}

It is sufficient to multiply LaTeX code: C(\mu mol\,m^{-3}) by the molecular weight (in LaTeX code: g\,mol^{-1}) of the chemical specie:

LaTeX code: C(\mu g m^{-3})= C(\mu mol\,m^{-3})P_m(g\,mol^{-1})

from LaTeX code: ppm_v to LaTeX code: \mu g m^{-3}

LaTeX code: C(\mu g m^{-3})=C(ppm_v)\frac{p}{RT}P_m(g\,mol^{-1})

practical formula using standard atmosphere

LaTeX code: C(ppm_v)=10^{-6} C(mol\,m^{-3}) \frac{P_{m_{air}}}{\rho_{0_{air}}}\frac{T_0}{T}\frac{p}{p_0}

where:

LaTeX code: R=8.314 J\,K^{-1}\,mol^{-1}

LaTeX code: T_0=273.15 K

LaTeX code: p_0=101325 Pa

LaTeX code: P_{m_{air}}=28.8 g\,mol^{-1}

LaTeX code: \rho_{0_{air}}=1 293 g\,m^{-3}