# 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 = Na k T/<mw> = Rg T
where, N is the number of molecules per unit volume, Boltzmann's constant k = 1.3806 · 10-16 erg/K, the gas constant
Rg = Na · k/<mw>, Avogadro's number, Na = 6.02 · 1023 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,
N0 = Pstp/(k · Tstp) = 2.687 · 1019 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

Z = (1/N0) Ni(z) · dz
Hydrostatic equilibrium relates the pressure and vertical coordinates
dP - g dz, or dz = -dP/( g),
and the number density, Ni can be written as a function of the density,
Ni = qi · Na/<mw>, molecules/cm3
where, qi is the volumetric fraction of species i.
Z = Na/(g N0) qi/<mw> · dP Na/(g N0) · ( qi/<mw>) · P = H0 · P
H0 = 10 · Na qi/(g N0 <mw>) Km-amagat/Bar

 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(H2) 1.00 1.00 0.90 0.96 1.00 0.85 0.85 28.97 44.01 2.22 2.14 28.00 2.30 2.30 gm/mole H0 7.88 13.61 37.45 100.50 58.85 94.08 74.56 Km-am/Bar 1000/H0 126.9 73.49 26.70 9.95 16.99 10.63 13.41 mB/Km-am