Calculating Gas Volume with Pressure: Non-Ideal Gas Equation for Mixed Gases

[FishBlackpool]

Hi

I am trying to find a formula which can calculate the volume that gas X will decrease by when pressure Y is added to it. Now I have already been pointed to the Ideal Gas Equation, however I read that this is best suited when looking at a single volume of a monatomic gas eg. Argon.

However I wish to experiment (play about) after doing my calculations and instead of messing about with a monatomic gas I would much rather use air so my question is...

Does anyone know a formula I can use to calculate the change in volume of a mixed gas (air) with varying pressure.

PS. I guess a list of pressure volume ratios for air which I could extrapolate from would also be usefull if anyone has them?...but I'd rather do the calculations myself.

Thanks

 

[alxm]

Well, the next-simplest after the ideal gas law is the van der Waals gas law (which has a pair of parameters). There are some other theoretical models, but I'd suggest a Virial expansion. (I believe that's the mostly used in practice.) It depends really on what temperature/pressure range you're interested in as well.

Note that most equations of state (including the vdw) can get pretty bad results at or near a phase change point.

Hmm, annoyingly the CRC handbook I've got only lists vdW coefficients, and not for air. Shouldn't be hard to find though.

See also:
http://en.wikipedia.org/wiki/Equation_of_state

 

[quicknote]

for your question! The Ideal Gas Equation is indeed best suited for calculating the volume of a single monatomic gas, as it assumes that the gas particles do not interact with each other. However, for a mixed gas like air, the particles do interact and the Ideal Gas Equation may not give accurate results.

In this case, you can use the Non-Ideal Gas Equation, also known as the Van der Waals equation, which takes into account the interactions between gas particles. It is given by:

(P + an^2/V^2)(V - nb) = nRT

where P is the pressure, V is the volume, n is the number of moles, T is the temperature, and a and b are constants specific to the gas.

You can also use the Combined Gas Law, which relates the initial and final volumes of a gas at different pressures and temperatures:

(P1V1)/T1 = (P2V2)/T2

where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures.

As for pressure-volume ratios for air, these can be found in tables or calculated using the above equations. However, it is always best to calculate them yourself to ensure accuracy for your specific experiment.

I hope this helps and good luck with your experiment!