Molar volume of gas under pressure

[WFvolc]

Hi,

I would like to know the number of moles of argon gas that are in a known volume at a known pressure and the method for arriving at the answer.

I have tried to use the ideal gas law but I am not sure that my answers make sense.

For example, how many moles of Argon are in a cyclinder that is 5cm in diameter and 12 cm long that is under an equilibrium pressure of 100 bars?

I really look forward to your help!

Best regards.

[deleted-93346]

This site is for help in science fair projects. Your question is more in the nature of a homework problem. You are on the right track using the ideal gas law, but in addition to knowing the volume and the pressure you will need to specify the temperature (the absolute temperature to be precise). I'm sure your textbook has worked examples showing the application of the ideal gas law. The Wikipedia article is also fairly helpful, albeit not very tutorial. If you put the search string "ideal gas law examples" into Google (without the ""), you will find many worked examples showing the use of the ideal gas law.

[WFvolc]

Thanks for your help.
This isn't for homework - this is for an experiment.

I know the temperature and have used that as per the ideal gas law. Do you know whether the gas species I use makes a difference? I.e. if I use argon or helium, will it make a difference to the moles in the cylinder? Those atoms are different sizes, right??

Also, if I allow a certain controlled rate of gas release (and measure the resultant pressure drop), am I right in thinking that I only need the temperature at the start of the experiment because the number of moles left in the cylinder will not be affected by the ideal gas law anymore, but by my valve control??

Thanks again.

[deleted-93346]

"Do you know whether the gas species I use makes a difference? I.e. if I use argon or helium, will it make a difference to the moles in the cylinder? Those atoms are different sizes, right??"

The ideal gas law applies to an ideal gas; most gases are approximately described by this law, especially the nobel gases such as argon or helium. Part of the idealization is to neglect things like the sizes of the molecules -- in deriving the ideal gas law the molecules are treated as if they were like tiny billiard balls undergoing purely elastic and isotropic scattering.

"am I right in thinking that I only need the temperature at the start of the experiment because the number of moles left in the cylinder will not be affected by the ideal gas law anymore, but by my valve control?? "

I don't understand what you mean. The ideal gas law will apply all the time, and the temperature will always matter. For the rules of equilibrium thermodynamics to hold ou would need to add gas at exactly the temperature and pressure of the gas already in the cylinder; if you don't, the problem becomes one of non-equilibrium gas dynamics, which is hard to deal with. You would need to add a little gas, then wait for the system to reach a new equilibrium temperature and pressure (and volume unless your container can be approximated as rigid).

[WFvolc]

Hi again,

Thanks so much for your help yet again.

Right. I have another problem related to the above problems.

If I have my pressure container half filled with a liquid and half filled with a gas which is pressurised, and if I know the temperature and the pressure, can I calculate the diffusion of the gas into the liquid? I have found Henry's Law but I can't work out how to adapt it to this situation. I would like to know the theoretical amount of the gas that is in the liquid at a given time after the pressure is applied.

And what is molarity?

Any ideas?

Much appreciated.

[deleted-93346]

Are the liquid and the gas both the same molecule, for example water and water vapor?

[deleted-71882]

WFvolc,

As John Deher noted, you have to specify what the gas and liquid are. Some gasses will dissolve in some liquids well and others not so well. Once you specify the molecules, you can look up the partial pressure used in Henry's law and solve for the dissolved gas.

Henry's law tells you how much gas will dissolve at equilibrium. It does not tell you how fast the gas will diffuse into the liquid.

Molarity - http://en.wikipedia.org/wiki/Molar_concentration

WW

[WFvolc]

Hi all,

This is such a fantastic help.

I have a couple of liquids I could use, but the one that I think would be most interesting is an industrial oil which has a diffusivity of different gases written on the info-sheet that accompanies the product. The gas might be helium.

In Henry's Law, is the partial pressure anything to do with the pressure I set the system at? I.e. I pressurize the gas above the liquid (assume incompressible).

Thanks again,

[deleted-71882]

WFvolc,

Partial pressure is defined and discussed here: http://en.wikipedia.org/wiki/Partial_pressure.

If the only gas present is He, then the partial pressure is the total pressure.

WW

[deleted-71588]

I pressurize the gas above the liquid (assume incompressible).

Gases are definitely compressible so I hope your incompressible assumption is for the liquid.

[WFvolc]

Yep. I assume the liquid is incompressible... but in fact the compressibility of the liquid is noted on the manufacturer's leaflet but it's very small, of course.

So how do I calculate the Henry's Constant used in Henry's Law? If it dependents on the solvent (a type of oil) and the solute (helium)? I don't think I can look up anywhere the Henry's Constant for this particular oil for helium. Is there a way to derive it?

I have a "Diffusion Rate" of helium in this oil for a given pressure and temperature; is that the same thing? Probably not, right?

Cheers,

[deleted-71588]

You maybe able to calculate some bounds on the Henry's Law constant from the "Diffusion Rate" of helium into your oil at standard temperature and partial pressure assuming the published diffusion rate applies only when the oil starts with no disolved helium. The problem comes that you have to make assumptions on the rate of change of the net diffusion rate as the oil has more and more disolved helium.

The Henry's Law and the associated constant applies to the end point where the disolved mass and partial pressure reaches an equilibrium where the amount "leaving" equals the amoung "entering".

To assume that the Diffusion Rate is fairly constant and the net disolving rate only diminishes because the partial pressure diminishes, you would have to have some other gas present that has a significantly lower Diffusion Rate.

You also have to make an assumption on the rate at which helium leaves the oil. With no contrary evidence, the best assumption is that the Diffusion Rate applies to both directions equally.

This is one of those situations where experimentation would be appropriate. Design an experiment to measure the Henry's Law constant.