# Amagats

From the ideal gas law we can define the number of particles
at standard temperature (273.15 K) and standard pressure (1 atm =
1013.25 milli-bars). The ideal gas law can be written many ways, here
we will adopt the notation(s)

*P*=

*N k T*=

*N*/<mw> =

_{a}k T*R*

_{g}Twhere,

*N*is the number of molecules per unit volume, Boltzmann's constant

*k*= 1.3806 · 10

^{-16}erg/K, the gas constant

*R*=

_{g}*N*/<mw>, Avogadro's number,

_{a}· k*N*= 6.02 · 10

_{a}^{23}particles per mole, <mw> is the molecular weight in grams/mole.

This number of molecules at STP is called Loschmidt's number and has the value,

*N*=

_{0}*P*

_{stp}/(

*k · T*

_{stp}) = 2.687 · 10

^{19}cm

^{-3}

The number of amagats of a gas is given as a ratio of the
actual number of particles at the given temperature and pressure to
Loschmidt's number. In planetary atmospheres the number density is a
function of height. We can calculate the thickness of an equivalent
atmospheric column at standard temperature and pressure. This is
denoted as cm-amagats or Km-amagats and is given by

*N*)

_{0}*N*(

_{i}*z*) ·

*dz*

Hydrostatic equilibrium relates the pressure and vertical coordinates

*dP*-

*g dz*,

**or**

*dz*= -

*dP*/(

*g*),

and the number density,

*N*can be written as a function of the density,

_{i}*N*=

_{i}*q*·

_{i}*N*/<mw>, molecules/cm

_{a}^{3}

where,

*q*is the volumetric fraction of species

_{i}*i*.

*N*/(

_{a}*g N*)

_{0}*q*/<mw> ·

_{i}*dP*

*N*/(

_{a}*g N*) · (

_{0}*q*/<mw>) ·

_{i}*P*=

*H*

_{0}· P*H*= 10 ·

_{0}*N*/(

_{a}q_{i}*g N*<mw>) Km-amagat/Bar

_{0}

Earth | Mars | Jupiter | Saturn | Titan | Uranus | Neptune | |

g | 981.0 | 374.1 | 2425.3 | 1000.0 | 136.0 | 880.1 | 1110.5 cm/s |

q(H_{2}) | 1.00 | 1.00 | 0.90 | 0.96 | 1.00 | 0.85 | 0.85 |

<mw> | 28.97 | 44.01 | 2.22 | 2.14 | 28.00 | 2.30 | 2.30 gm/mole |

H_{0} | 7.88 | 13.61 | 37.45 | 100.50 | 58.85 | 94.08 | 74.56 Km-am/Bar |

1000/H_{0} | 126.9 | 73.49 | 26.70 | 9.95 | 16.99 | 10.63 | 13.41 mB/Km-am |