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