Mixing Gases to a Precise Contentration

Mixing a tank of gas of known composition is no more difficult than mixing a liquid solution of known concentration. It does have it's own rules, however, since you cannot see the gas directly and must physically contain the gas at all times. Familiarity with the physical and chemical properties of the gases involved is also needed.


DALTON'S LAW OF PARTIAL PRESSURE:

The fundamental principle that allows us to calculate gas mixtures of known concentration is "Dalton's law of partial pressures" This states that;

The pressure in a container exerted by a particular species of gas molecule depends only on the temperature of the gas and the number of gas molecules present. It is independent of other species of gas molecules present.

In a tank of mixed gases the temperature is the same for all components so each component exerts a pressure proportional to the number of molecules present.

Ptotal = P1 + P2 ... + Pn where:
Ptotal = The total absolute tank pressure
P1 = Pressure of component #1
etc.

From this we can see that to construct a known gas mixture all we must do is add individual components so that the ratio of the pressures of the various components is the same as the ratio of the concentrations desired.

EXAMPLE #1:

 Create a gas mixture containing;
78% - N2
21% - O2
1% - Ar

To accomplish this we must fill our tank so that 78% of the final pressure is from N2, 21% of the final pressure is from O2 and 1% of the final pressure is from Ar. Please note that we can choose any final pressure we like within the safe limits of our hardware. Also note that the pressures here are ABSOLUTE PRESSURES. The fact that we live at the bottom of an ocean of air with an average pressure of 15 psi is irrelevant to this calculation. It is, however, important when we go to measure these pressures.

To return to our example. The small Aluminum tanks used to mix gases have a safety release set to 300 psi. The highest pressure precision gauge we have is 200 psig, so it looks like 200 psig is a good final pressure to assume. Since when a standard type pressure gauge reads "0 psi" the gas pressure is 15 psi ABSOLUTE our final pressure for calculation purposes is 215 psia. Hence:

1.0% of 215 psi = 2.15 psi delta P Ar
21% of 215 psi = 45.15 psi delta P O2
Balance (78%) to 215 psia => 200 psig

Notice that what we are calculating is a DELTA P or change in pressure. We can add the gases to the tank in any order that is convenient as long as we increase the pressure by 2.15 psi when adding Argon, 45.15 psi when adding Oxygen and end up with 200 psig (215 psia) total pressure. This is really all the fundamental calculation necessary for mixing gases. Everything else is to increase precision or to account for the physical properties of the gas involved.

INCREASING PRECISION:

An "empty" gas tank is not empty; it has 15 psia of whatever was in the tank last still in it. To remove this we must pump the tank out with a vacuum pump and preferably flush it a few times with the "balance" gas of our new mixture. In the above example Nitrogen.

The vacuum gauge used to monitor this gives us an opportunity to increase the precision of the minor components in the mix. The 2.15 psi delta P for Argon in example #1 would be a small deflection on a 0 -> 200 psi gauge. The vacuum gauge's 0 -> "-"15 psi range would give us a much larger deflection. Vacuum gauges, however, are usually calibrated in mmHg (760 -> 0 mmHg) rather than psi so we must convert as follows:

      2.15 psi       1 mmHg
                 X  -----------   =  111.23 mmHg
                    0.01933 psi

Since our ability to read the gauge's pointer position is independent of the range of the gauge we can gain precision by always using the lowest pressure range gauge possible.

DILUTION:

It is worth mentioning that gas mixtures can be diluted just like liquid solutions. Indeed for extremely low level components this is the only practical technique. In example #1 if we had wanted to include 330 ppm CO2 in the mix we would have had a very low delta P for CO2.

330 ppm = 0.033%

0.033% of 215 = 0.071 psi delta P CO2

0.071 psi     1 mmHg
          X ----------- = 3.67 mm Hg delta P CO2
            0.01933 psi

Even with the larger deflection on the vacuum gauge this would be a marginal technique at best.

A better approach is to make a more concentrated temporary mix in the balance gas (Nitrogen). If we make a more reasonable 1% CO2 in N2 mix we can then use this instead of pure CO2 to add this component. Since only one part in 100 of our temporary mix is CO2, we must add 100 times as much. Hence the delta P for CO2 using a 1% mix is 7.1 psi or 367 mmHg. A much easier delta P to measure.

We could even save a step by making the concentrated CO2 mix in Argon rather than Nitrogen. We would then be able to add both these components at once. The calculation is left as an exercise for the reader.

LIQUIDS:

It is sometimes necessary to make a gas mixture that has components that are normally liquids. This is easily done but the maximum delta P will be limited by the vapor pressure of the liquid at room temperature.

The vapor pressure of many organic compounds are listed in the "Handbook of Chemistry and Physics" and the "Merk Index". It is not a good idea to try and make use of the maximum vapor pressure available for two reasons. First, if the temperature drops you will condense this component of your mix and change the vapor phase concentration. Second, it can take a very long time to reach the maximum vapor pressure in a system of useful size since the pressure rise will follow an exponential curve. A good rule of thumb is to only make use of 80% of the vapor pressure available to you.

EXAMPLE #2:
Create a gas mix containing;
0.5% Methanol (MeOH)
Balance N2
0.5% of 215 psi = 1.075 psi = 55.61 mmHg MeOH
Vapor Pressure of Methanol = 100 mmHg at 21.2 Deg. C

Since the required delta P of methanol is well below its vapor pressure at room temperature this is a very straightforward mix to make.

The liquid Methanol can be treated like a tank of gas with a pressure of 100 mmHg absolute. A closed container of methanol is connected to the mixing manifold and arranged so the liquid will NOT enter the manifold. The vacuum pump is used to eliminate the air originally in the headspace and to purge the container till only Methanol vapor and liquid remain.

The vacuum gauge attached to the manifold lets us monitor this process. When the pressure in the manifold (vacuum pump off) will only rise to approximately the vapor pressure of methanol (100 mmHg) we know that only methanol vapor and liquid remain. Note, however, that as liquid evaporates its temperature will drop and so will its vapor pressure. Warming the container back to room temperature will remedy this. For the same reason, when adding a liquid component to a tank, it may be necessary to warm the liquid container since large amounts of liquid may have to evaporate. Do not, however, warm the container much above room temperature as you may then condense liquid in another part of the system.

EXAMPLE #3:
Create a gas mix containing;
1.0% Methanol
Balance N2
1% of 215 psia = 2.15 psi = 111.23 mmHg delta P MeOH
Vapor Pressure of Methanol = 100 mmHg at 21.2 Deg. C

Obviously this will not work. Even if we had a puddle of methanol in the bottom of the tank, at room temperature, the partial pressure would never exceed 100 mmHg or 0.9% of the total pressure. The easy solution is to reduce the total pressure in the tank. If we assume a final tank pressure of 100 psig (115 psia) the calculation becomes;

1.0% of 115 psia = 1.15 psi = 59.49 mmHg delta P MeOH

This is well below the 100 mmHg vapor pressure limit and we can proceed as before.

FLAMMABLE GAS MIXTURES:

When making mixtures that contain flammable gases as well as Oxygen you must be aware of and respect the limits of flammability. The mixture will not necessarily spontaneously ignite but the potential amount of damage is large. The amounts of energy released compares with some explosives. Commercial gas companies will not even attempt mixtures within the flammability limits and will often come no closer than a factor of two.

OTHER SAFETY CONSIDERATIONS:

Pressurized gases probably have more different ways of killing you than anything else you are likely to come across in the laboratory.

First of all the tanks are heavy and unstable. A "T" size tank weighs about 150 lb and can do immense damage if it falls over on you. Skinned and crushed fingers are also a possibility when handling tanks.

Commercial gas tanks are often pressurized to over 2000 psi. At that high of a pressure escaping gas acts almost like a solid object moving at the speed of sound. All gas handling equipment has pressure limitations that MUST be respected. At all times you should be aware of the pressure in your system. Pressurized plumbing looks just like unpressurized plumbing. Every time you touch a valve or loosen a fitting you should KNOW what the system reaction will be.

Many gases are flammable or poisonous. Even such seemingly innocuous things as Nitrogen can displace the Oxygen in a confined space. When at all possible vent gases to an exhaust system or a suitable neutralization system.

Not all materials are compatible with all gases. When in doubt consult the compatible materials listed in most gas suppliers catalog.


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