The Physical Chemistry of SCUBA Diving with Compressed Air

 

Derrik Peterson

Chemistry 405 – Project Report

 

 

 

 

 

 

 

 

 

 

 

Going up and down through water is not like riding an elevator.  When riding an elevator you’re in your natural element, a gaseous atmosphere made up of about 78% nitrogen, N2, a do nothing inert gas, and 21% oxygen, O2, a big time combustion supporter, combined they are called air.  The more O2 the hotter and faster things burn.  A very fast hot burn is called an explosion.  You can explode going up or down too fast through water but it won’t be because your burning, water doesn’t support combustion, it’ll be the action of gases under pressure.

           

            So why is it so easy to move a 1,000 feet up or down through air and not water?  The answer is pressure. But doesn’t air have pressure?  Yes, an inch square column of air starting at sea level and going up to the end of the atmosphere weighs 14.7 pounds (1 atm).  This weight produces a force called pressure.  This force is described in pounds per square inch; so, the force of a one-inch square column of air from the sea, to as far as air extends, is 14.7 psi (pounds per square inch).

           

            Isn’t 14.7 psi a lot of force?  Yes it is.  Then why aren’t we flattened by it?   We would be if it weren’t for the pressure being exerted equally on every square inch of us.  This, everywhere found (ubiquitous) distribution of force, allows us to be as we are and move about freely.  If the force were applied only to the topside of us we would be squashed, with a vertical dimension of zero.                

 

            Great!  What’s the entire atmosphere (air) and weight of air  (pressure), got to do with scuba diving using compressed air?  The answer is simple, everything!  But, to get to the heart of the matter we need to dive into some physical chemistry, so here are the details.

           

            Here we go, physical chemistry made simple.  Let’s start with pressure.  Water like air has weight, but much more of it because water is more dense; heavier for a given amount (volume).  The pressure of air at sea level, 14.7 psi, can push a one-inch square column of water to a height of 33 feet.  The connection, for every 33 feet of water that is above you is equal to the weight of one atmosphere.  We call 14.7 psi 1 atmosphere (atm).  At a depth of 33 feet you are now being pressured by the weight of the air, 1 atm, and the weight of 33 feet of water, another 1 atm, combined, 2 atms, 29.4 psi.  For divers, adding the weight x space of the air plus the weight of the water is a unit called “ata”, atmosphere absolute.  For each 33 feet of water one descends another atm of pressure is exerted.

 

            Back to the equal distribution of air pressure, the 14.7 psi everywhere.  If this held true in water, all you would need to stay alive is a snorkel.  If breathing under water worked the same as breathing air you wouldn’t need to know about Boyle’s law, Charles’ law, Dalton’s law, Henry’s law, along with a myriad of other things.  But under water the laws of physical chemistry are working against you, not for you, as they do in air. In water you’re outside your natural element unless you plan to breathe water. 

 

            The difference is water pressure vs. air pressure.  On land, air pressure is equal all around you.  In water, the pressure outside of you is always going to be greater than the pressure inside of you unless we can equalize them. 

 

Water pressure is trying to make of you a two dimensional creature.   This pressure makes breathing under water more difficult than on land.  It’s the pressure, the weight of the water, it exerts (pushes) against your lungs trying to flatten them.  This one of the reasons just simply using a snorkel won’t work much below 3 meters, you don’t have the power to pull air in.  Nor have you the power to push out the CO2.  Just a few feet below the surface and you’ll encounter great difficulty breathing using a snorkel. 

 

The force exerted by that amount of water has already put enough force against your lungs to severely curtail breathing.  Things are copasetic when the pressure is equal on every inch2.  But even a small pressure difference can produce an enormous force.  Just a one-psi difference between the inside and outside of your house, whichever is the greater, the house will either explode or collapse.  When diving, water pressure is trying to do the same things to your lungs.  Holding your breath while descending deeper in water increases the pressure on the outside of the lung and decreases on the inside trying to collapse them. 

 

Ascending is exactly opposite.  Holding your breath while ascending decreases the pressure on the outside of the lung while increasing the pressure inside your lung, trying to get it to explode. This is where the golden rule of diving comes into play, “never hold your breath”. 

 

            To balance the pressure outside your lungs as you dive requires an increase the pressure inside your lungs by forcing in air under at increasing pressure.  To balance the pressure inside your lungs while ascending calls for decreasing the pressure that’s pushing air into your lungs.

 

            So lets look at how compressed air (a gas under pressure) aids breathing, and its detriments.  What we need to understand is how gases behave under pressure.  How much space (volume) they occupy as pressure changes and how pressure changes as a gas occupies more or less volume.  The best way to describe these variations is to think of your lungs as balloons.

 

            When inhaling, air is going into your lungs (expanding the balloon).  When you exhale, the balloon gets smaller (collapses).  Let’s see what happens to the air inside the balloon when exposed to different pressures.  We fill the balloon at sea level with an amount of air; the exact amount is of no importance.  The balloon expands to some size S, and contains a specific number of many molecules of N2 and O2.  Now we’re going to drag the balloon under water and observe the effect of pressure on volume.   The greater the depth we drag the

balloon down the more it will shrink.  This shrinkage is due to pressure.  At the surface the force on the outside of the balloon was 1 atm and the balloon had a certain size S.  At 33 feet below the surface the balloon is exposed to 2 atms (1 atm from the air, 1 atm from the water) or 1 ata (atmosphere absolute) and will be one-half its original size, S/2.  At 66 feet, 3 atms it will be one-third its original size, S/3.  At 99 feet, 4 atms, one-fourth original size, S/4.  This relationship will continue in an approximate linear proportion for every 33 feet of decent.  Water is slightly compressible, so the relationship is not perfectly linear, but for our purpose it‘s inconsequential.

 

This phenomenon of pressure and volume being inversely related, as one increases the other decreases, is described by Boyle’s Law: PxV/1=K, where v= absolute volume per unit, p=absolute pressure and the temperature, K, is kept constant. 

 

To illustrate, if a diver held his breath at 99 feet and surfaced, the volume of air in his lung would be 4 times greater at the surface than at 99 feet. The pressure at 99 feet is 4 atms and the volume of gas can be defined as 1.  At the surface the pressure goes to 1 atm, the weight of the air, and the volume of gas goes to 4, i.e. occupies 4 times the space at 1 atm than it did at 4 atms.  If the area containing the volume of gas is fixed, the pressure inside the container must increase to 4 atms.  If the container is a lung, the increase in pressure inside the lung may be more than the lung can withstand thus causing the lung to rupture (nice for explode).  The tear in the lung will allow gas bubbles to go directly into the blood; this is called an air embolism. An air embolism can cause paralysis or death.

           

            Let’s do the experiment going from the surface to 99 feet.  You take a breath at the surface and dive to 99 feet; the volume of air in your lungs now occupies only one-fourth the space it did on the surface.  Water pressure has pushed all the molecules of air closer together.  The pressure inside your lung is also one-fourth of what it was on the surface.  To equalize the pressure inside the lung, to that outside, we must put in 4 times more air.  To fill the void we force air into the lung under pressure (compressed) until the empty space is filled equal to what it was at 1 atm.  Now the volume of space occupied at 99 feet is the same as it was on the surface but the pressure has risen to 4 atms, is 4 times greater.  This is what Boyle’s law tells us, that volume and pressure are related inversely.  As pressure increases by a given factor, volume will decrease by one-fourth that factor.  In our example, from a pressure of 1 atm to 4 atms, the volume within a container will decrease from 1unit at 1 atm to1/4 unit at 4 atms.

           

            If we add the effects of heat to Boyle’s law we get Charles’ law.  Heating the air inside the balloon makes the air molecules move more quickly causing them to hit the sides more often and with more force (f).  Force equals mass times velocity (f=mv).  This force will cause the balloon to further expand at any given constant level of volume and pressure.  The opposite will occur if the temperature is lowered, again holding a given level of v and p constant.

           

            Combining the two laws, Boyle’s and Charles’, get us to the General Gas

 

 

 

Law:     P1xV1  =  P2xV2

                T1            T2

where P1, V1, T1 are initial pressure, volume, temperature, and

where P2, V2, T2 are final pressure, volume, temperature. 

 

            Now that we have some understanding of the relationship between pressure, volume, and temperature we can talk about partial pressure.  When breathing compressed air it’s useful to understand how the gases behave individually under pressure.  In this instance we are talking air, a gaseous mixture composed of 78% N2 and 21% O2.

Dalton’s law on partial pressure states: 

                        The total pressure exerted by a mixture of gases is the sum of

                        the  pressure that would be exerted by each of the gasses, if it

                        alone were present and occupied the total volume.

Therefore, a container of air at a total pressure of 1000 psi, the partial pressure of N2 is 800 psi and the partial pressure of O2 is 200 psi. The total pressure in the container is therefore the sum of partial pressure of each gas, or 800 psi + 200 psi = 1000 psi.

 

            The final concept we need to understand to fully appreciate the dangers and complexity of breathing compressed air is given in Henry’s law.  Henry’s law states:

            The amount of gas that will dissolve in a liquid at a

            given temperature is almost directly proportional to

            the partial pressure of the gas.

Henry’s law describes how much N2 and O2 will be present in our blood the deeper we go and the longer we stay.  On land an average man has around 1 quart of dissolved N2 in his body.  The N2 comes from the air he breathes.  If he dives to a depth of 5 atms and remains long enough, his body will now contain around 5 quarts of dissolved N2, or until equilibrium (the amount of N2 in the blood equals the amount of N2 in the lungs), is reached.

 

            If a diver breathes compressed air at greater depths, the diver may get decompression sickness (the bends).  If the excess nitrogen in the divers body is not given enough time to equilibrate as he/she rises, nitrogen bubbles can collect within the blood vessels and tissue.  These bubbles can lead to joint pain, blindness, convulsions, and/or paralysis.  To prevent decompression sickness, the diver may have to slow down, or even stop at various depths, during his/her ascend to make sure the body’s N2 levels in the blood and lungs stay at equilibrium.

 

            As shown, the depths a diver reaches has a lot to do with the variables of pressure, volume, and temperature.  Boyle’s law and Charles’ Law explain the effects of these variables while diving.  These two laws lead us to Dalton’s Law of partial pressures and Henry’s Law dealing with the ratios of the aqueous-phase of a chemical to it’s equilibrium partial pressure.  If these laws are not taken seriously when diving, many injuries can occur.  A few examples are air embolisms and decompression sickness.  The injuries can range from very minimal, like dizziness, to very serious, including paralysis and death.

 

 

 

 

 

 

 

 

 

 

 

 

Bibliography

 

1.   Atkins, Peter.   (2001).  The Elements of Physical Chemistry.  New      York:  W.H. Freeman and Company.

 

2.  http://www.bishopmuseum.org/bishop/treks/palautz97/phys.html

 

3.  http://www.bwl.unimannheim.de/Dekanat/homepages/alexv/physics.

          htm#Partial%20Pressure

 

4.  http://www.diveventures.com/fizzics.htm