# Modeling the concentration of gas constituents in a Force Field

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• Anon42
Then you would not be able to calculate the partial pressure of any molecule in the gas as if it was not there.

#### Anon42

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

Molecule A has a mass: ma and mole fraction: na.
Molecule B has a mass: mb and mole fraction: nb.

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. na(z) is the mole fraction of Molecule A as a function of container height.

#### Attachments

• IdealGas.PNG
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Hi,

Anon42 said:
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) ?

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

Chestermiller said:
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.

BvU said:
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.

Anon42 said:
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.

Chestermiller said:
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.

Anon42 said:
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?

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## 1. What is the purpose of modeling the concentration of gas constituents in a force field?

The purpose of this type of modeling is to predict and understand the distribution and behavior of gas constituents in a particular environment. It can help in identifying potential sources of pollution, assessing air quality, and evaluating the effectiveness of mitigation strategies.

## 2. How is the concentration of gas constituents in a force field determined?

The concentration of gas constituents in a force field is determined through mathematical models that take into account factors such as wind speed, temperature, and chemical reactions. Data from monitoring stations and remote sensing techniques are also used to validate the models.

## 3. What types of gas constituents are typically modeled in a force field?

The types of gas constituents that are typically modeled include pollutants such as carbon monoxide, sulfur dioxide, and nitrogen oxides, as well as greenhouse gases like carbon dioxide and methane.

## 4. What are the limitations of modeling the concentration of gas constituents in a force field?

One major limitation is that the accuracy and reliability of the models depend on the quality and availability of data. Additionally, these models may not be able to capture the full complexity of atmospheric processes and may require simplifying assumptions.

## 5. How are these models used in real-world applications?

Models of gas constituent concentration in force fields are used in various applications, such as air quality management, climate change research, and emergency response planning. They can also aid in making policy decisions and informing the public about potential health risks.