Calculating Gas Density

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This article assumes a basic understanding of the common gas law properties. See A Gas Law Primer for review of these concepts.

The change in density as a result of change in chemical composition of a gas mix can be estimated using well-established chemical principles. It is fact that 1 mole (the molecular mass of a substance expressed in grams) of any gas occupies 22.4 liters at STP (standard temperature and pressure: 0 ^oC (273 K); 1 ata pressure). Tables of molecular weights can be found in any elementary chemical text. These tables tell us that:

molecular mass of O_2: 31.998 amu (atomic mass units)

molecular mass of N₂: 28.014 amu

molecular mass of He: 4.00 amu

Density is defined as mass / volume. Since one mole of DRY gas at STP (Temperature = 0^o C ; 1 atm pressure) occupies 22.4 liters, the density of a dry gas can be estimated::

Density O₂ = 31.998 g/mole x 1 mole/22.4 L = 1.428 g/L

Density N₂ = 28.014 g/mole x 1 mole/22.4 L = 1.251 g/L

Density He = 4.00 g/mole x 1 mole/22.4 L = 0.178 g/L

Oxygen enriched air (Nitrox, Oxygen enriched air, or EAN_x) is a binary mixture of nitrogen and oxygen. Thus, the mass for a dry mix can be estimated by simply summing the masses of the individual

For Air

For NOAA I (32 % O₂)

For NOAA II (36 % O₂)

Oxygen mass in 1 L = 0.21 x (1.428 g/L) (1 L) = 0.2999 g

Nitrogen mass in 1 L = 0.79 x (1.251 g/L) (1 L) = 0.9883 g

Mass of Air in 1 L at STP 1.2882 g

Oxygen mass in 1 liter of mix: 0.32 (1.428 g/L) (1 L) = 0.4570 g

Nitrogen mass in 1 liter of mix:: 0.68 (1.251 g/L) (1 L) = 0.8507 g

Mass of NOAA I mix occupying 1 liter at STP: 1.3077 g

Oxygen mass in 1 liter of mix: 0.36 (1.428 g/L) (1 L) = 0.5141 g

Nitrogen mass in 1 liter of mix: 0.64 (1.251 g/L) (1 L) = 0.8006 g

Mass of NOAA II mix occupying 1 liter at STP: 1.3147 g

This method, as long as components are known, can be applied to any mixture of gases. For example, the density of Tri-mix 21/50 calculates to be 0.7520 g/L.

Summary of Dry Gas Estimations

Air:

NOAA I

NOAA II

Tri-mix 21/50

1.2882

1.3077

1.3147

0.75196

Since the pressure changes associated with scuba diving at recreational depths are relatively small, we may assume ideal gas behavior. With this assumption, the gases will behave according to Boyle's law and density will be directly proportional to absolute pressure. For the direct comparison of air with oxygen enriched air, let's examine a "worst case" scenario: diver breathing dry gas at 0 ^oC at 66 FSW. First. determine the absolute pressure at 66 fsw:

Density Estimates of Dry Gases At 66 fsw

Air:

NOAA I :

NOAA II :

Tri-mix 21/50

1.288 g/L x 3 = 3.864 g/L

1.308 g/L x 3 = 3.924 g/L

1.315 g/L x 3 = 3.945 g/L

0.752 g/L x 3 = 2.256 g/L

Although the density differences between compressed air and oxygen enriched air are slight, there is some evidence (Israeli Military Divers) that the slight increase in density at depth of the EAN_x mixtures may lead to CO₂ retention. So, divers doing physical labor while diving on EAN_x should pay particular attention to CO₂ buildup. (Note that metabolic CO2 (Molecular Mass ~ 44 amu) significantly adds to the respiratory work of the gas being ventilated.)

Assuming ideal gas behavior allows basic chemical principles to be used to estimate gas density of a dry gas at recreational depths. It should be noted that mixes with helium often do not display ideal gas behavior. Also, as depth (pressure) increases, gas behavior departs from predictions of ideal relationships and more complex real gas equations must be used. Although this simple method offers a reasonable estimate of gas densities, it should not be considered "gospel" (i.e. absolutely accurate) for all mixes at all depths. (This estimation is a reasonable method of comparisons, but ignores water vapor composition of gasses, percentage of CO₂ in exhalation, and diving conditions different from STP.)

Larry "Harris" Taylor, Ph.D. is a biochemist and Diving Safety Coordinator at the University of Michigan. He has authored more than 200 scuba related articles. His personal dive library (See Alert Diver, Mar/Apr, 1997, p. 54) is considered one of the best recreational sources of information In North America.

Use of these articles for personal or organizational profit is specifically denied.