Partial Pressure Full screen 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 0^{o}C 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.
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?
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. 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. 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.
Dissolved gasesWhen 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 r_{1}. Hence the number of Nitrogen atoms dissolving will be
based on the partial pressure (p_{1}) because that tells us how many
atoms are hitting the surface multiplied by r_{1}. 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.
UnitsWhat 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 10^{6} 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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