molar mass derivations
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.
\[M_{air} = 10^{3}\frac{\rho N_{A}}{n}\]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.
\[M_{air} = \frac{M_{H_{2}O}M_{dry\_air}}{\left(1-q_{H_{2}O}\right)M_{H_{2}O} + q_{H_{2}O}M_{dry\_air}}\]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.
\[M_{air} = M_{dry\_air}\left(1 - \nu_{H_{2}O}\right) + M_{H_{2}O}\nu_{H_{2}O}\]