Calculating Gas Density At Depth

by

Larry "Harris" Taylor, Ph.D.

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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.

Calculating Gas Density At STP

The change in density as a result of change in chemical composition of a gas mix can be easily determined 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). Tables of molecular weights can be found in any elementary chemical text. These tables tell us that:

 molecular mass of O2: 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 occupies 22.4 liters, the density of a pure substance is easily determined:

Density =       Mass

Volume

 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 (EANx or Nitrox)  is a binary mixture of nitrogen and oxygen. Thus, the mass for the mix can be determined by simply summing the masses of the individual

components. For example, by choosing a volume of 1 liter, the density, at STP, of 32 % oxygen containing mix (NOAA I) can be calculated:

Mass = Density x  Volume

 For NOAA I  (32 % O2 ) For NOAA II  (36 % O2 ) Oxygen mass in 1 liter  of mix:  0.32 (1.428 g/L) (1 L) = 0.4569 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:              1.3076 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) = 0.8507 g _____________________________________________________ Mass of NOAA II mix occupying 1 liter at STP:            1.3648 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 0.75196 g/L. This can be compared to the value of dry air at STP listed in the CRC HANDBOOK OF CHEMISTRY AND PHYSICS of 1.296 g/L.

 Density of Dry Gases At STP (g/L) Air:  NOAA I  NOAA II  Tri-mix 21/50 1.2960 1.3076 1.3648 0.75196

Calculating Gas Density at Depth

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 132 FSW. (Note that 132 FSW exceeds the recommended depth for NOAA II; also 0 oC is much colder than waters where divers normally play.) These values was chosen, as an illustration, to maximize the density differences observed.

First. determine the absolute pressure at 132 fsw:

Absolute Pressure = Water Column Pressure + Atmospheric Pressure

 water pressure     = 132 ft / 33 ft/atm = 4 atm  absolute pressure = 4 atm + 1 Atm   = 5 ata

Since density is directly proportional to absolute pressure:

 Density of Dry Gases At 132 fsw Air:  NOAA I :  NOAA II :  Tri-mix 21/50 1.296 g/L x 5 = 6.48 g/L 1.308 g/L x 5 = 6.54 g/L 1.315 g/L x 5 = 6.58 g/L 0.752 g/L x 5 = 3.76 g/L

Conclusion

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 increases well beyond the recreational limit, 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" for all mixes at all depths.

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