Is nitrogen at 27˚C and 100 kPa an ideal gas?

[tommyninetwo]

Hello everyone. I stumbled across a problem while studying for my exam that I cannot confidently answer.

Can we assume nitrogen at the temperature of 27˚C and the pressure of 100 kPa an ideal gas? Justify your answer.

The definition of an ideal gas is "...a gas whose molecules are spaced far apart that the behavior of a molecule is not influenced by the presence of other molecules-a situation encountered at low densities."

I know that we can use the compressibility factor to find out if its not an idea gas or not but I am missing the specific volume.

z=Pν/RT

where z is the compressibility factor and ν is the specific volume.

I checked the ideal gas properties of nitrogen table in my book but it doesn't include specific volume.

How am I supposed to know if nitrogen at this temperature and pressure is an ideal gas or not?

 

[kuruman]

This might help
https://en.wikipedia.org/wiki/Expansion_ratio

 

[tommyninetwo]

This might help
https://en.wikipedia.org/wiki/Expansion_ratio

I don't understand ideal gases conceptually well enough to get any useful information out of that. I already looked at that before I posted here.

But I believe I might have an answer for it. Since we need two independent properties to identify the state of the system, and pressure and temperature is dependent, I cannot assume that this nitrogen gas will be an ideal gas. Does this seem correct?

 

[gneill]

I know that we can use the compressibility factor to find out if its not an idea gas or not but I am missing the specific volume.

z=Pν/RT

where z is the compressibility factor and ν is the specific volume.

This is not an area in which I have much experience, but it seems to me that if you're lacking the specific volume you should be able to calculate it, no? A web search turns up a Wikipedia entry for it and provides an equation that can be used to calculate it for an ideal gas. It also has a table entry for Nitrogen (although it's for Nitrogen at STP).

 

[Chestermiller]

Have you ever heard of the principle of corresponding states? What is the value of the reduced pressure and the reduced temperature of N2 in your example? From the graph in your textbook, what is the value of the compressibility factor z?

 

[tommyninetwo]

This is not an area in which I have much experience, but it seems to me that if you're lacking the specific volume you should be able to calculate it, no? A web search turns up a Wikipedia entry for it and provides an equation that can be used to calculate it for an ideal gas. It also has a table entry for Nitrogen (although it's for Nitrogen at STP).

Specific volume is the inverse of density. However, as you know, density changes with temperature. So I would need the density or specific volume at 27°C but I cannot find it in my ideal-gas properties for nitrogen table and cannot find it online.

 

[Chestermiller]

Specific volume is the inverse of density. However, as you know, density changes with temperature. So I would need the density or specific volume at 27°C but I cannot find it in my ideal-gas properties for nitrogen table and cannot find it online.

What if I told you that you don't need to know the specific volume to answer this question.

 

[tommyninetwo]

Have you ever heard of the principle of corresponding states? What is the value of the reduced pressure and the reduced temperature of N2 in your example? From the graph in your textbook, what is the value of the compressibility factor z?

If fluids compared at reduced pressure and reduced temperature have about the same compressibility factor. I would have to find the actual pressure and actual temperature of the fluid (lets say He) I am comparing it to, then find out if helium at that pressure and temperature is an ideal-gas or not. Wouldn't I be at where I started from but now I'm seeing if helium is ideal-gas or not using the same properties instead of nitrogen?

In summary, If I'm not able to find the compressiblity factor of nitrogen given the properties, how can I find the compressibility factor of helium?

 

[tommyninetwo]

What if I told you that you don't need to know the specific volume to answer this question.

I would love to know how else to solve this problem.

 

[Chestermiller]

If fluids compared at reduced pressure and reduced temperature have about the same compressibility factor. I would have to find the actual pressure and actual temperature of the fluid (lets say He) I am comparing it to, then find out if helium at that pressure and temperature is an ideal-gas or not. Wouldn't I be at where I started from but now I'm seeing if helium is ideal-gas or not using the same properties instead of nitrogen?

In summary, If I'm not able to find the compressiblity factor of nitrogen given the properties, how can I find the compressibility factor of helium?

The principle of corresponding states says the the compressibility factor z is a unique function of the reduced pressure (pressure divided by critical pressure) and reduced temperature (temperature divided by critical temperature), irrespective of what substance you are considering.

 

[Chestermiller]

 

[tommyninetwo]

The principle of corresponding states says the the compressibility factor z is a unique function of the reduced pressure (pressure divided by critical pressure) and reduced temperature (temperature divided by critical temperature), irrespective of what substance you are considering.

Since the compressibilty factor is a unique function of reduced pressure and reduced temperature, that is the only information required for me to find z. Correct?

 

[tommyninetwo]

View attachment 113812

I see it now, with Pr and Tr, I can find what z is. And I can find Pr and Tr with the given information.

Thank you for your help, I understand this much better now.

 

[kuruman]

Can we assume nitrogen at the temperature of 27˚C and the pressure of 100 kPa an ideal gas? Justify your answer.

Look, you are told you have nitrogen at room temperature and atmospheric pressure. It is about 80% of the air that you breathe with every breath. Its volume expands 700 times when it turns from liquid to gas at 77 K and more when it reaches room temperature. Do you or do you not think that it fulfills the condition of

"...a gas whose molecules are spaced far apart that the behavior of a molecule is not influenced by the presence of other molecules-a situation encountered at low densities." ...

?

 

[tommyninetwo]

Look, you are told you have nitrogen at room temperature and atmospheric pressure. It is about 80% of the air that you breathe with every breath. Its volume expands 700 times when it turns from liquid to gas at 77 K and more when it reaches room temperature. Do you or do you not think that it fulfills the condition of
?

I wanted to understand the general idea behind this question instead of finding the answer from a specific scenario if that makes sense.

 

[Chestermiller]

Since the compressibilty factor is a unique function of reduced pressure and reduced temperature, that is the only information required for me to find z. Correct?

Yes

 

[kuruman]

... but what if the numbers start to skew and I cannot easily determine it?

The ideal gas is just a model, an idealization, hence the name. If the numbers start to skew, this means you have measurements that are accurate enough to detect a breakdown of the ideal gas model. In that case you will have to come up with a more refined model. In short, if you have numbers telling you that the gas you are considering is not ideal, then it is not. If you have numbers that cannot tell otherwise, then the gas is ideal for all intents and purposes of interpreting your numbers.
The original question you posted asks whether it is a good assumption to treat nitrogen at room temperature as if it were an ideal gas and why. Concentrate on deciding whether it fulfills the criteria of the model.

On edit: It will probably be more comfortable for you to go the compressibility route, so I will butt out and let Chestermiller see you through.

 

[tommyninetwo]

The ideal gas is just a model, an idealization, hence the name. If the numbers start to skew, this means you have measurements that are accurate enough to detect a breakdown of the ideal gas model. In that case you will have to come up with a more refined model. In short, if you have numbers telling you that the gas you are considering is not ideal, then it is not. If you have numbers that cannot tell otherwise, then the gas is ideal for all intents and purposes of interpreting your numbers.
The original question you posted asks whether it is a good assumption to treat nitrogen at room temperature as if it were an ideal gas and why. Concentrate on deciding whether it fulfills the criteria of the model.

On edit: It will probably be more comfortable for you to go the compressibility route, so I will butt out and let Chestermiller see you through.

I understand that I could assume that nitrogen is an ideal gas at that temperature and pressure but I was having trouble understanding what makes a gas ideal in the first place. Only thing I knew that I could relate to this problem was that there is a range in the compressiblity factor where the gas is ideal. Your explanation also made sense to me and I appreciate you doing that for me. I now have a much better understanding of how to tackle a problem like this now.