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.
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