Dalton's Law
Partial Pressures
Throughout our discussions thus far, we have been talking about the effect
of pressure on air. We have discussed air in balloons, air in a tank, and
air in a divers lungs. It is important to point out that air is a mixture
of many different gasses, but mainly nitrogen and oxygen.
The air mixture is approximately 78% nitrogen, and 21% oxygen with the
remaining 1% being a mix of argon, carbon dioxide, neon, helium and other
rare gases. While some recreational diving is done on special mixtures
like nitrox, most is done breathing plain air. While the fact that air is a
mixture of gases is important when we deal with the physiology of diving, we
will spend a few moments now to understand the physics of gas mixtures.
It was the English scientist John Dalton that studied the properties of gas
mixtures as they relate to pressure and developed Dalton's Law. Dalton's
Law states: The total pressure of a gasmixture equals the sum of the
partial pressures that make up the mixture.
To study this law as it relates to scuba divers, let's see how this law
affects air at different pressures. In order to make our numbers a little
more manageable, we will assume that air is a mixture of just two gases,
nitrogen and oxygen. We will also assume that the mixture is comprised of
80% nitrogen and20% oxygen.
If we then look at this mixture as it relates to Dalton's Law, we know that
80% of the pressure of the gas is due to the nitrogen in the mixture and
20% of the pressure is due to the oxygen in the mixture. We refer to these
as partial pressures. This means at the surface, the pressure exerted on us
by the nitrogen in the air mixture is 80% of 14.7, or 11.76 pounds per
square inch. The pressure from the oxygen is 2.94 psi. Together, these
account for the 14.7 psi of pressure at the surface.
If we look at pressures at varying depths, we get the following chart:
Partial Pressures of Compressed Air
(assuming air is 80% nitrogen, 20% oxygen)
Depth Atmosphere Absolute Pressure Oxygen Pressure Nitrogen Pressure
0 1 14.7 2.94 11.76 33
33 2 29.4 5.88 23.52 66
66 3 44.1 8.82 35.28 99
99 4 58.8 11.76 47.04132
132 5 73.5 14.70 58.80165
165 6 88.2 17.64 70.56198
198 7 102.9 20.58 82.32231
231 8 117.6 23.52 94.08264
264 9 132.3 26.46 105.84297
297 10 147.0 29.40 117.60
We see then that as we increase the pressure on us by descending, we are
dealing with increased pressure of both nitrogen and oxygen in a 80 - 20
ratio.
It is an easy task to determine the partial pressure of any gas at any
depth by using the formulas we have learned thus far. Let's try to
determine the partial pressure of oxygen at a depth of 50 feet insea water
assuming oxygen is 20% of the gas mixture.
The first thing we must do is determine the ambient pressure for this depth
(If unfamiliar with ambient pressure, refer to
Intro to Gas Laws).
We know that saltwater exerts .445 pounds of pressure per foot, so the
water pressure for this depth would be.445 x 50, or 22.25 psi. To this we
add the atmospheric pressure of 14.7 for an ambient pressure of 37.95. If
we take 20% of this, we have our answer. 37.95 x .20 = 7.39 Thus, the
partial pressure of oxygen at a depth of 50 feet in sea water would be
7.39psi.
Determine the partial pressure of nitrogen at a depth of 40 feet in fresh
water, while breathing a gas mixture that is 79% nitrogen.
Fresh water exerts .432 psi per foot of depth so we multiply .432 by 40 to
get 17.28. To this we add our atmosphere of air pressure, 14.7 to get an
ambient pressure of 31.98. If you take 79% of this number you get the
answer: 31.98 x .79 = 25.2642
Unlimited Sunshine & Blue Water,
Scubabuf
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