molar mass derivations

  1. molar mass of total air from density and number density

    symbol description unit variable name
    \(M_{air}\) molar mass of total air \(\frac{g}{mol}\) molar_mass {:}
    \(n\) number density \(\frac{molec}{m^3}\) number_density {:}
    \(N_A\) Avogadro constant \(\frac{1}{mol}\)  
    \(\rho\) mass density \(\frac{kg}{m^3}\) density {:}

    The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

    \[M_{air} = 10^{3}\frac{\rho N_{A}}{n}\]

  2. molar mass of total air from H2O mass mixing ratio

    symbol description unit variable name
    \(M_{air}\) molar mass of total air \(\frac{g}{mol}\) molar_mass {:}
    \(M_{dry\_air}\) molar mass of dry air \(\frac{g}{mol}\)  
    \(M_{H_{2}O}\) molar mass of H2O \(\frac{g}{mol}\)  
    \(q_{H_{2}O}\) mass mixing ratio of H2O \(\frac{kg}{kg}\) H2O_mass_mixing_ratio {:}

    The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

    \[M_{air} = \frac{M_{H_{2}O}M_{dry\_air}}{\left(1-q_{H_{2}O}\right)M_{H_{2}O} + q_{H_{2}O}M_{dry\_air}}\]

  3. molar mass of total air from H2O volume mixing ratio

    symbol description unit variable name
    \(M_{air}\) molar mass of total air \(\frac{g}{mol}\) molar_mass {:}
    \(M_{dry\_air}\) molar mass of dry air \(\frac{g}{mol}\)  
    \(M_{H_{2}O}\) molar mass of H2O \(\frac{g}{mol}\)  
    \(\nu_{H_{2}O}\) mass mixing ratio of H2O \(ppv\) H2O_volume_mixing_ratio {:}

    The pattern : for the dimensions can represent {vertical}, {latitude,longitude}, {latitude,longitude,vertical}, {time}, {time,vertical}, {time,latitude,longitude}, {time,latitude,longitude,vertical}, or no dimensions at all.

    \[M_{air} = M_{dry\_air}\left(1 - \nu_{H_{2}O}\right) + M_{H_{2}O}\nu_{H_{2}O}\]