Modeling the concentration of gas constituents in a Force Field

[Anon42]

Say there is a gas made up of two gas molecules: Molecule A and Molecule B.

Molecule A has a mass: m_a and mole fraction: n_a.
Molecule B has a mass: m_b and mole fraction: n_b.

The gas is at thermal equilibrium and has a constant temperature throughout itself (T) everywhere. It is placed in a Rectangular container of width w and height h. There is a homogenous force field applied to the container of the gas along its height pointing downward. (Like gravity). This field, unlike gravity, does not affect all molecules. This field only exerts a force on Molecule A in the gas, and does not affect Molecule B.

If there were no field applied, concentrations of each molecule at a certain height would be the same throughout the container, and they would just be equal to their mole fraction. However with the applied field, that only affects one type of molecule, the concentrations would vary with respect to the height of the container. Is there an equation that models the concentration of gas constituents at equilibrium as a function of height in a field like this? Or better yet, is there one that models those concentrations as a function of height and time assuming the container starts with a perfectly mixed gas once the field is applied.

I know there is an equation to model concentrations of various gasses in a gravitational field as a function of height. However that equation does not apply to this case because it assumes the force field applies to all molecules in the gas equally.

This attached PNG shows a container filled with a gas comprised of two types of molecules. The large "g" I drew on the left with an arrow pointing down shows what direction that field would be. That field would only apply to either the red or the grey molecules in that gas, and leave the other species alone. n_a(z) is the mole fraction of Molecule A as a function of container height.

 

[BvU]

Hi,

I know there is an equation to model concentrations of various gasses in a gravitational field as a function of height. However that equation does not apply to this case because it assumes the force field applies to all molecules in the gas equally.

Would the zero gravity for one species make much difference in the case the molecular weights are very far apart (e.g. H₂ and Xe) ?

$\$

 

[Chestermiller]

Are you assuming that this is a mixture of ideal gases?

 

[Anon42]

Are you assuming that this is a mixture of ideal gases?

Yes I am. Nothing like the Van der Waals equation of state used to describe this gas, just the ideal gas law.

Hi,



Would the zero gravity for one species make much difference in the case the molecular weights are very far apart (e.g. H₂ and Xe) ?

$\$

I don't know that it would. I assume that it would if the molecular weights are far apart, but I do not know by how much, or how I would go about describing this mathematically.

 

[Chestermiller]

Yes I am. Nothing like the Van der Waals equation of state used to describe this gas, just the ideal gas law.


I don't know that it would. I assume that it would if the molecular weights are far apart, but I do not know by how much, or how I would go about describing this mathematically.

True or false: In an ideal gas mixture, each constituent behaves as if the other constituents are not even present.

 

[Anon42]

True or false: In an ideal gas mixture, each constituent behaves as if the other constituents are not even present.

I want to say True. Since there are no intermolecular forces the ideal gas law depends only on the amount of gas molecules that are in a gas, and not the properties of any of its constituent gases. This is where the partial pressure law comes from. If only the amount of gas influences the pressure and nothing else. Partial Pressures of various constituents can be calculated as if other constituents were not there, and then be summed together to get the total pressure.

In short, True: In an ideal gas mixture, each constituent does behave as if the other constituents are not even present.

 

[Chestermiller]

I want to say True. Since there are no intermolecular forces the ideal gas law depends only on the amount of gas molecules that are in a gas, and not the properties of any of its constituent gases. This is where the partial pressure law comes from. If only the amount of gas influences the pressure and nothing else. Partial Pressures of various constituents can be calculated as if other constituents were not there, and then be summed together to get the total pressure.

In short, True: In an ideal gas mixture, each constituent does behave as if the other constituents are not even present.

Then you should have no problem solving your problem.

Let z be the distance measured upward from the base of your container, and A be the cross sectional area of your container. According to the relationship between pressure and depth, how is the vertical partial pressure gradient related to the density of a species? From the ideal gas law, how is the partial pressure related to species density? How is the total mass of a species in the container related to its vertical density variation?