Partial Pressure
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We all know about pressure because we've all blown up a balloon but let me recap a bit so we are sure we are all speaking the same language. Consider my drawing. It is a cylinder with a piston in it (think steam trains) and to keep matters simple enough for me it has one, count it, one whole molecule of gas in it. Now if the temperature was absolute zero (the holy grail of cryogenics) then this molecule would be stationary and generally not getting involved in anything sordid like pressure. However in the real world it has a temperature and this implies it is moving. In fact at a reasonably brisk 0oC it is pounding along at about one thousand miles per hour and bouncing off the walls lots and lots of times a second.

This allows us to make some immediate deductions about one molecule situations.
  1. When the molecule hits the piston it tries to push it back. A force is being applied to it. It is doing the same to the other walls but we can get our fingers on the piston and feel the force for ourselves. This force is what we call pressure.
  2. If the piston was half the size the molecule would only hit it half as often so we would only get half the force. Hence it is easy to measure pressure in force divided by area units (pound per square inch, kilograms per square meter) so that we can work out what forces to expect if we know how big the piston is.
  3. The faster the molecule is going the more often it will bounce off the piston and when it does so it does it more vigorously. Hence hotter (read faster) molecules will impart more force on the piston hence more pressure.
  4. If we give it more volume to rush around in, it will spend more time rushing around and less time piston hitting so more volume implies less pressure.
Yeah. Just one molecule. Bit of a special case eh?
Well no. Molecules are stupid. Deep down stupid. What makes you think that one molecule knows or cares if there is another molecule in this universe? Put two molecules in our cylinder and sometimes they might bounce off one another snooker ball fashion but effectively they just carry on bouncing about. Put 20000000000000000000000 molecules in and you are getting realistic for a litre of air.(That was 22 zeros by the way, count them.) Now they spend a lot more time bouncing off one another but the pistons just gets hits 2000.... etc times as often.

OK so what do we now know about pressure?
More gas = more pressure
Less volume = more pressure
Hotter = more pressure

This takes us to the Ideal Universal Gas Law which tends to be written in diving books as PV/T is constant. i.e. Pressure times Volume divided by Absolute Temperature is a constant for any sample of gas so we can work out what happens if we heat, cool, compress or anything a constant amount of gas. So if you halve the volume something has to change to keep things constant so normally we assume the pressure has doubled although what tends to happen is the temperature goes up a bit so the pressure more than doubles. The new PV/T continuing to equal the old PV/T. When using it never forget that absolute temperature is degrees centigrade plus 273 or you get some very silly results.
Read the article on Van der Waals' work to get a more detailed explanation and where it is too simplistic.

What about different gases?
Well the molecules of different gases are heavier or lighter but the same general rules apply. Remember that our molecules continue to be stupid so they don't know that they are now in a mixed gas scenario. So if I have enough Oxygen molecules to give me 3 units of pressure on my piston if they were on their own and enough Nitrogen to give me 5 units of pressure again on their own and I stuff the lot into the cylinder together I get (dramatic pause) 8 units of pressure.

Physicists like to keep things complicated so we speak of having a partial pressure of 3 for Oxygen and 5 for Nitrogen and a total pressure of 8. That tells us how much Oxygen is contributing to the pressure and in effect how much oxygen there is in the mixed gas. Beware however. Having the same partial pressures does not mean you have the same quantity of gases, just that they are pressing as hard. Heavier gases play rougher when it comes to bouncing off pistons.
If we introduce a mouse to our cylinder (no, not a computer mouse, the whiskers and tail variety) and wait we will begin to observe a decrease in the oxygen partial pressure and an increase in the carbon dioxide partial pressure and if we leave it too long we will have an ex-mouse situation develop.

The wonderful discovery that partial pressures are independent and you can just add up them up is called Dalton's Law. It may be pretty obvious now but poor old Mr. Dalton had to work it out from scratch and that deserves serious credit.

So how do we calculate partial pressures and fractions? Because things just add up it is easy.
If, for example, Oxygen is 20% of the gas we are interested in then it contributes 20% of the pressure. Hence if we are at 15 meters depth which is 2.5 bar total pressure we multiply 2.5 by 20% (0.2) and we get 0.5 bar of oxygen partial pressure. Conversly if we want to have a maximum partial pressure of oxygen of 1.5 bar at 35 meters then, as 35m is 4.5 bar total pressure, the fraction of O2 in the gas must be 1.5/4.5 = 0.3333 so 33% max mix.

Dissolved gases

When a liquid and a gas are in contact two things happen. Some of the liquid molecules might become detached from the surface and rush about pretending to be a gas and some of the gas molecules steam into the liquid, forget to bounce off, and stooge around pretending to be liquid.
The first is called evaporation and the second is called dissolving. Now evaporation is a complex process that involves a liquid molecule scraping together enough energy (called latent heat) to actually break free of the embrace of all its fellow liquid molecules so I'm not going to worry about it here but dissolving of gases is a more interesting process (to divers).
Dissolving and undissolving is a two way process. Every time a molecule of gas meets the top of the liquid from either the inside or the outside there is a mathematically determined probability that it will swap sides. It is a two way stream with molecules dissolving and undissolving all the time and things generally tend toward a balanced situation.
Let's do some simple sums (or you can beep them out if maths is a dirty word to you).

Imagine I know the probability that any nitrogen atom hitting a water surface will dissolve (I don't) say it is 5% that is 0.05 as a fraction or something. Call this r1. Hence the number of Nitrogen atoms dissolving will be based on the partial pressure (p1) because that tells us how many atoms are hitting the surface multiplied by r1.
Inside the liquid we have the exact analogy of partial pressure for the dissolved gas molecules moving about, call this p2 and some probability that they will undissolve, call it r2.
If we leave it long enough to even out finally the number of molecules dissolving will equal the number undissolving so,
p1 * r1 = p2 * r2 (please excuse the computereese * for multiply as x just looks like a letter)
Now why have I gone to this length? Because you can now see that if I increase the partial pressure (p1) of the gas then, given time, the amount dissolved (represented by p2) will go up by exactly the same fraction so our equation stays balanced.

This time the honours go to a Mr. Henry. Henry's law is that the amount of gas that will dissolve in a fluid given time is directly proportional to the partial pressure of that gas over the fluid.

Interesting. Remember that all the gases act independently so from air the Oxygen dissolves according to its own partial pressure and Nitrogen according to its own, quite separate, partial pressure.


What do we measure pressures and partial pressures in?
Well the old classics were to use a mercury barometer and measure it in millimetres or inches of mercury but you had to convert these to something useful before doing any sums. Now we tend to use force per area methods so pounds per square inch or newtons per square meter (known as Pascals) or 106 dynes per sq. cm (known as Bar).
The unit Bar is rather handy as 1 bar is just about the pressure of the atmosphere at sea level so a tank at 200bar is roughly 200 times atmospheric pressure and contains about 200 times as much as it would at 1 bar.

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