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.

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