Are the gas laws compeletely true?

[Superhoben]

I've looked alittle at the gas laws and I get the feeling that they are simplified. From what I can see they don't take intermolecular forces into account. Will the intermolecular forces simply disappear or just get so weak that we don't take them into account?
The gas law I'm thinking about here is mainly p1*V1/T1=p2*V2/T2 (sorry, I don't know how to write math on computers).

 

[voko]

That law is called the ideal gas law. "Ideal" means "simplified". So you are correct. There are gas models that take the intermolecular forces into account. Perhaps the most famous (and historically first) of these is the van der Waals model. But that, too, is a simplification, there are more complex models, giving rise to equations of state of varying complexity.

 

[sophiecentaur]

I've looked alittle at the gas laws and I get the feeling that they are simplified. From what I can see they don't take intermolecular forces into account. Will the intermolecular forces simply disappear or just get so weak that we don't take them into account?
The gas law I'm thinking about here is mainly p1*V1/T1=p2*V2/T2 (sorry, I don't know how to write math on computers).

Look at the definition of the particles in an ideal gas - totally unreasonable if you're being really fussy.
The intermolecular forces correspond to changes in the Potential Energy between molecules as they her closer and closer together. So, if the total energy in the system is unchanged (it is), then the KE of the molecules (defining the Temperature) will not be what you might expect (from the gas laws) when a real gas is highly compressed. There is no end to how far you can refine these models but they are still useful within particular ranges of conditions.

 

[Chestermiller]

The ideal gas law accurately describes the behavior of real gases in the limit of low pressures. As a rule of thumb, this means pressures on the order of one atmosphere or less, give or take. For higher pressures, as Voko points out, more accurate mathematical approximations to real gas behavior are available.

 

[cjl]

The ideal gas law accurately describes the behavior of real gases in the limit of low pressures. As a rule of thumb, this means pressures on the order of one atmosphere or less, give or take. For higher pressures, as Voko points out, more accurate mathematical approximations to real gas behavior are available.

The ideal gas law can work fairly well to several tens of atmospheres of pressure - it isn't just limited to ~1atm or less. If you wanted to determine the mass of air in your bicycle tire, for example, it would work just fine.

 

[Superhoben]

Thanks a lot for your responses guys. Do anyone of you know some good site for more details about where and why this modell work (and for exampel why it differ more from reality at higher pressures) or some other model which give more accurate approximations?
I think that I start to understand how the volume of gases is connected with pressure and temprature (and vice versa).
Do you know anywhere to look up how much the intermolekylar forces affect the gases? Just a few graphs would be enough for me to get an slight understand though I would prefer a good modell (that's not way to advanced, I'm quite interested in physics but I know very little).

 

[Chestermiller]

Thanks a lot for your responses guys. Do anyone of you know some good site for more details about where and why this modell work (and for exampel why it differ more from reality at higher pressures) or some other model which give more accurate approximations?
I think that I start to understand how the volume of gases is connected with pressure and temprature (and vice versa).
Do you know anywhere to look up how much the intermolekylar forces affect the gases? Just a few graphs would be enough for me to get an slight understand though I would prefer a good modell (that's not way to advanced, I'm quite interested in physics but I know very little).

Check out this web site: http://en.wikipedia.org/wiki/Equation_of_state

Also, look up "law of corresponding states", which says that all materials behave roughly the same when their compressability factor z is expressed in terms of reduced temperature and reduced pressure. Reduced pressure is the actual pressure divided by the critical pressure, and reduced temperature is the actual temperature divided by the critical temperature.

For more details, see Smith and Van Ness, Introduction to Chemical Engineering Thermodynamics.

Chet

 

[wreckemtech]

Try this too: http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/deviation5.html

In layman's terms:

Basically, the larger and more "sticky" the molecules are, the more the collisions between them deviate from being perfectly elastic. The "stickyness" can be there for a variety of reasons including the individual molecules having strong dipole moments or geometry that lends itself to "catching" on other molecules rather than bouncing straight off, or just being large as far as gas molecules go.

 

[klimatos]

Most gas laws require that conditions of equilibrium exist (if not throughout the process, then at least at the beginning and end of it). Since the Earth's atmosphere in never even close to a condition of equilibrium, one must be very, very cautious in trying to apply laboratory-valid gas laws to the free atmosphere.

 

[dauto]

Most gas laws require that conditions of equilibrium exist (if not throughout the process, then at least at the beginning and end of it). Since the Earth's atmosphere in never even close to a condition of equilibrium, one must be very, very cautious in trying to apply laboratory-valid gas laws to the free atmosphere.

Nonsense. The Earth's atmosphere is very accurately described by the ideal gas law.

 

[Chestermiller]

Nonsense. The Earth's atmosphere is very accurately described by the ideal gas law.

Well said!

 

[sophiecentaur]

Nonsense. The Earth's atmosphere is very accurately described by the ideal gas law.

The word "nonsense" is a bit overstated, I think a bit on the rude side, to be jumping in with that term, imo. The gas laws apply well within various regions of the atmosphere and describe how clouds and air masses function. Overall behaviour is a bit more complicated than can be dealt with by just using the gas laws, I think.
klimatos only said you need to be cautious and he is right.

 

[dauto]

The word "nonsense" is a bit overstated, I think a bit on the rude side, to be jumping in with that term, imo. The gas laws apply well within various regions of the atmosphere and describe how clouds and air masses function. Overall behaviour is a bit more complicated than can be dealt with by just using the gas laws, I think.
klimatos only said you need to be cautious and he is right.

The ideal gas law relates the density, pressure, and temperature very accurately everywhere in the atmosphere with the possible exception of the extremely thin layer of the exosphere where free path length becomes larger then the characteristic length of the temperature fluctuations.

PS. I don't find the word nonsense particularly rude but I've been known for dishing out terse responses before. I apologize if that word offended anybody.

 

[sophiecentaur]

If you use the word "nonsense' in your first salvo then you may have nowhere further to go without being offensive. Sometimes, a post contains 'nonsense' due to a misreading or mis-writing and it's normal to give someone a way out, at least the first time through, before that sort of response.
I think you mis-read the meaning of that post. It has to be true that air often follows the gas laws but it's only half the story if you are trying to predict what the weather is likely to do - or even how the temperature is going to vary with height in a real atmosphere. Factors such as the rate of absorption of various wavelengths of EM are very important - not to mention the Dynamics of a spinning globe. And there's the small matter of the way water behaves, too. As you were so ready to voice your objection, I am sure you are aware of all that.
I'm sure klimatos is more than capable of fighting his own battles but your response was a bit over-simplistic, I think (although not 'total nonsense' )

 

[dauto]

If you use the word "nonsense' in your first salvo then you may have nowhere further to go without being offensive. Sometimes, a post contains 'nonsense' due to a misreading or mis-writing and it's normal to give someone a way out, at least the first time through, before that sort of response.
I think you mis-read the meaning of that post. It has to be true that air often follows the gas laws but it's only half the story if you are trying to predict what the weather is likely to do - or even how the temperature is going to vary with height in a real atmosphere. Factors such as the rate of absorption of various wavelengths of EM are very important - not to mention the Dynamics of a spinning globe. And there's the small matter of the way water behaves, too. As you were so ready to voice your objection, I am sure you are aware of all that.
I'm sure klimatos is more than capable of fighting his own battles but your response was a bit over-simplistic, I think (although not 'total nonsense' )

The ideal gas law just states a relationship between temperature, density, and pressure of a gas which applies very accurately everywhere in the atmosphere (even when water changes states). That law by itself isn't enough to predict the weather off course, but it still applies.

 

[voko]

Ideal gas law applies when water changes states? Who mentioned "nonsense" in this thread?

 

[sophiecentaur]

I read that post again (the one you objected to). I, personally, took "applying" as meaning 'using the laws to predict or understand what's going on'. Merely confirming that a region of gas (up in the atmosphere) will follow those laws is pretty pointless. You need to do more than just verify the gas laws if you want to say anything useful about the atmosphere. You have said that they are not adequate for that purpose and that one should be careful in applying them and expecting a proper answer.
Like I said, you must have mis - read the meaning of that post because you took exception to something you have later agreed with. Much harder to step back whey you ave already used the N word.

 

[sophiecentaur]

Ideal gas law applies when water changes states? Who mentioned "nonsense" in this thread?

Far be it from me to mention that word.

 

[dauto]

Ideal gas law applies when water changes states? Who mentioned "nonsense" in this thread?

Yes it does. Not to the water off course since it won't be a gas any more. But the remaining atmospheric gasses pressure, temperature, and density will indeed be related by the ideal gas law. The water vapor itself near the phase transition deviates from the ideal gas law but it is a small component by volume of the total atmosphere. Small enough that there isn't much to be gained by including the water vapor anomalous behavior near the phase transition into the calculations. In other words, the ideal law is an accurate description of the gases in the atmosphere everywhere on earth.

 

[cjl]

I read that post again (the one you objected to). I, personally, took "applying" as meaning 'using the laws to predict or understand what's going on'. Merely confirming that a region of gas (up in the atmosphere) will follow those laws is pretty pointless. You need to do more than just verify the gas laws if you want to say anything useful about the atmosphere. You have said that they are not adequate for that purpose and that one should be careful in applying them and expecting a proper answer.

I disagree with this sentiment. To me, this is like stating that one must be careful when applying Ohm's law to a flashlight, since it doesn't predict when the battery will die. While true, it's largely irrelevant to the accuracy or applicability of the law. The ideal gas law applies very nearly everywhere in the Earth's atmosphere to a very high accuracy, and whether or not it predicts atmospheric behavior or not is irrelevant. The law neither claims to nor is it intended to do such a thing. All the law does is relate a gas's temperature, pressure, and density. At any point in the atmosphere, given two of those three things, one can apply the ideal gas law to find the third (and it will be correct, to a high degree of accuracy).

 

[voko]

The ideal gas law is pretty accurate for all the gases except water vapor in the atmosphere. Mentioning water, and especially stressing its "changing states" to support its accuracy was very, very strange.

 

[Chestermiller]

The ideal gas law is pretty accurate for all the gases except water vapor in the atmosphere. Mentioning water, and especially stressing its "changing states" to support its accuracy was very, very strange.

I guess I disagree. What is the reason you say that the ideal gas law does not apply to air with water vapor in it under atmosphereic conditions? At what locations in the atmosphere is this not accurate enough? Even at ground level, water vapor mole fraction is only about 1% of the air. In the stratosphere, it is typically less than 6 ppm mole fraction.

 

[sophiecentaur]

It would be interesting to know of any serious model of the atmosphere that's based solely on the gas laws.
Would it predict the temperature lapse rate, I wonder?

 

[dauto]

It would be interesting to know of any serious model of the atmosphere that's based solely on the gas laws.
Would it predict the temperature lapse rate, I wonder?

Why solely on the gas law? Try predicting the atmosphere solely on the universal law of gravity. Not possible is it? does that mean that the law of gravity does not apply?

So it turns out that even in places where water vapor is changing phases such as inside clouds, serious models of the atmosphere use the ideal gas law. Guess why...

 

[voko]

So it turns out that even in places where water vapor is changing phases such as inside clouds, serious models of the atmosphere use the ideal gas law.

Do they specifically use the ideal gas law to deal with the water vapor?

 

[Chestermiller]

Do they specifically use the ideal gas law to deal with the water vapor?

Are you referring to liquid water droplets and ice crystals, or are you really referring to the tiny fraction of actual water vapor molecules in the gas (air) phase?

I might add that, even for pure water vapor at pressures up to 10 atmospheres, the ideal gas law accurately describes the behavior (to within about 5%). If you don't believe this, just compare the specific volume of saturated water vapor up to pressures of 10 atm. (temperatures up to about 175C) with the predictions of the ideal gas law. I made this calculation yesterday, just to see.

Chet

 

[voko]

Are you referring to liquid water droplets and ice crystals, or are you really referring to the tiny fraction of actual water vapor molecules in the gas (air) phase?

All of the above, since dauto said "changing states".

I might add that, even for pure water vapor at pressures up to 10 atmospheres, the ideal gas law accurately describes the behavior (to within about 5%).

Does it accurately describe the state changes that are observable right now at ground level at many a place in the Northern hemisphere?

 

[sophiecentaur]

Why solely on the gas law? Try predicting the atmosphere solely on the universal law of gravity. Not possible is it? does that mean that the law of gravity does not apply?

So it turns out that even in places where water vapor is changing phases such as inside clouds, serious models of the atmosphere use the ideal gas law. Guess why...

Why are you trying to defend that "nonsense" word?
Of course one would need to be 'cautious' in applying the laws of Gravity to the Atmosphere because they would be inadequate. You said it yourself. Likewise for the Gas Laws. This would appear to be a majority view.
Can we drop it now?

 

[Chestermiller]

All of the above, since dauto said "changing states".
Does it accurately describe the state changes that are observable right now at ground level at many a place in the Northern hemisphere?

No, of course not. I just describes the P-V-T state of the gas phase. That's all it is expected to do. For example, when you have gas containing water vapor and liquid water in a closed container, the ideal gas law is only expected to describe the behavior of the gas phase.

 

[voko]

No, of course not. I just describes the P-V-T state of the gas phase. That's all it is expected to do. For example, when you have gas containing water vapor and liquid water in a closed container, the ideal gas law is only expected to describe the behavior of the gas phase.

I am not sure what you mean by that. If we had some gas, say nitrogen, in a closed box, then lowering or raising its temperature within the range occurring in the atmosphere would only be changing its pressure, just like the ideal gas law has it.

But, if we had water vapor in that box, that would not only change the pressure of the gas. That would also change the amount of gas. Surely that is a major deviation from the law.

 

[Chestermiller]

I am not sure what you mean by that. If we had some gas, say nitrogen, in a closed box, then lowering or raising its temperature within the range occurring in the atmosphere would only be changing its pressure, just like the ideal gas law has it.

But, if we had water vapor in that box, that would not only change the pressure of the gas. That would also change the amount of gas. Surely that is a major deviation from the law.

Excuse me, but what does the "n" stand for in PV=nRT?

 

[voko]

It stands for the amount of gas, obviously.

 

[Chestermiller]

It stands for the amount of gas, obviously.

So I guess we are in agreement now.

Chet

 

[voko]

In agreement about what?

 

[dauto]

In agreement about what?

On agreement that the ideal gas law does not preclude a change in the amount of matter. that's why n shows up in there so that the amount of matter (and its possible change) is taken into account.

 

[dauto]

Why are you trying to defend that "nonsense" word?
Of course one would need to be 'cautious' in applying the laws of Gravity to the Atmosphere because they would be inadequate. You said it yourself. Likewise for the Gas Laws. This would appear to be a majority view.
Can we drop it now?

I don't think the idea that the laws of gravity might be inadequate constitute a majority view. Not even close. I already apologized for using the word "nonsense" because I think politeness is important. That doesn't mean that the post I was responding to was correct. It was most definitely not correct because it turns out that the ideal gas law is actually very accurate everywhere on Earth's atmosphere. even at places where water is changing states. That's just the truth. The ideal gas law will give you at least 3 correct significant digits. If you just plug in the correct temperature, pressure, and volume, the law gives you the correct number of moles of gas inside of that volume to high accuracy and that's all that law is meant to do.

 

[sophiecentaur]

I don't think the idea that the laws of gravity might be inadequate constitute a majority view. Not even close. I already apologized for using the word "nonsense" because I think politeness is important. That doesn't mean that the post I was responding to was correct. It was most definitely not correct because it turns out that the ideal gas law is actually very accurate everywhere on Earth's atmosphere. even at places where water is changing states. That's just the truth. The ideal gas law will give you at least 3 correct significant digits. If you just plug in the correct temperature, pressure, and volume, the law gives you the correct number of moles of gas inside of that volume to high accuracy and that's all that law is meant to do.

And how does that, alone, help you in predicting what will happen in the atmosphere? I think you are having a problem with comprehension here. It was perfectly clear to most of us what was meant by 'that post'. You clearly mis-interpreted it and can't bring yourself to say so.

 

[dauto]

And how does that, alone, help you in predicting what will happen in the atmosphere? I think you are having a problem with comprehension here. It was perfectly clear to most of us what was meant by 'that post'. You clearly mis-interpreted it and can't bring yourself to say so.

Nah... I think you're the only one talking about using equations alone. The statement I was responding to clearly said you must be careful applying the ideal gas law to Earth's atmosphere. Turns out that you can always apply the ideal gas law to Earth's atmosphere with good accuracy so the statement was misleading. I pointed that out.

 

[voko]

On agreement that the ideal gas law does not preclude a change in the amount of matter. that's why n shows up in there so that the amount of matter (and its possible change) is taken into account.

So how can I apply the ideal gas law to 1 kg of water at T = 200 K and P = 1 atm? What volume does that occupy?

 

[sophiecentaur]

Nah... I think you're the only one talking about using equations alone. The statement I was responding to clearly said you must be careful applying the ideal gas law to Earth's atmosphere. Turns out that you can always apply the ideal gas law to Earth's atmosphere with good accuracy so the statement was misleading. I pointed that out.

Perhaps if that original post had said "there's more to it than just the gas laws", (which is how I took it) we wouldn't be arguing. I think we agree that there gas laws aren't enough.

 

[Chestermiller]

So how can I apply the ideal gas law to 1 kg of water at T = 200 K and P = 1 atm? What volume does that occupy?

Dear Voko,

This is kind of an ambiguous question, so maybe you can help us out and provide some clarification. Thanks.
1. Are you referring here to water ice crystals in the atmosphere at 200K? If so, the ideal gas law doesn't apply to them.
2. When you say P = 1 atm, are you talking about the total pressure of the air, or are you referring to the partial pressure of the water vapor in the air? Of course, the partial pressure of the water vapor in the air at 200K can't be much higher than the equilibrium vapor pressure of water vapor over ice at 200K, but, if you know the partial pressure, you can use the ideal gas law to accurately calculate the concentration of water vapor in the gas phase in m³/kg.

Please help us by stating your question just a little more precisely. Thanks.

 

[dauto]

Perhaps if that original post had said "there's more to it than just the gas laws", (which is how I took it) we wouldn't be arguing. I think we agree that there gas laws aren't enough.

Yes, I agree with that.

 

[voko]

Dear Voko,

This is kind of an ambiguous question, so maybe you can help us out and provide some clarification. Thanks.
1. Are you referring here to water ice crystals in the atmosphere at 200K? If so, the ideal gas law doesn't apply to them.
2. When you say P = 1 atm, are you talking about the total pressure of the air, or are you referring to the partial pressure of the water vapor in the air? Of course, the partial pressure of the water vapor in the air at 200K can't be much higher than the equilibrium vapor pressure of water vapor over ice at 200K, but, if you know the partial pressure, you can use the ideal gas law to accurately calculate the concentration of water vapor in the gas phase in m³/kg.

Please help us by stating your question just a little more precisely. Thanks.

Those are interesting questions, given your previous statement: "I might add that, even for pure water vapor at pressures up to 10 atmospheres, the ideal gas law accurately describes the behavior (to within about 5%)."

1 atmosphere is certainly less than 10 atmosphere, yet now you say that "the ideal gas law doesn't apply".

 

[Chestermiller]

Those are interesting questions, given your previous statement: "I might add that, even for pure water vapor at pressures up to 10 atmospheres, the ideal gas law accurately describes the behavior (to within about 5%)."

1 atmosphere is certainly less than 10 atmosphere, yet now you say that "the ideal gas law doesn't apply".

Here's how it works. For a single component H2O system (pure water), if the pressure is 1 atm., water vapor (i.e., a gas phase) can be present only at temperatures greater than 100 C. Below this temperature, all the water will condense to liquid water or ice (depending on the temperature). So, if you have liquid water or ice only, you don't expect them to be able to be described by the ideal gas law. Otherwise it would be called the ideal liquid law or the ideal solid law. At temperatures above 100C, if the pressure of the system is ≤ the equilibrium vapor pressure of water at that temperature and also less than 10 atm., the water will be purely in the gas phase and will satisfy the ideal gas law to a good approximation.

Now let's consider a multicomponent gaseous system like air (where H2O is not the only chemical species present). In atmospheric air, water vapor is only one component of the gas phase, and its mole fraction is everywhere less than 0.03. So its partial pressure at sea level in the gas phase is less than 0.03 atm. At locations in the atmosphere where the temperature is 200K (i.e., close to the tropopause), the equilibrium vapor pressure of water is only about 0.000002 atm, while the total air pressure at these locations is on the order of 0.1 atm. At these locations, if ice crystals are present, we expect the partial pressure of the water vapor in the air to be about 0.000002 atm, but, if ice crystals are not present in the air, the partial pressure of the water vapor can be somewhat less than 0.000002 atm. In either case, the gas phase at these locations will behave as an ideal gas, both with respect to the overall gas mixture as well as to the water vapor. In applying the ideal gas law to the water vapor in a gas mixture, however, one uses the partial pressure of the water vapor, not the total pressure.

 

[voko]

Here's how it works. For a single component H2O system (pure water), if the pressure is 1 atm., water vapor (i.e., a gas phase) can be present only at temperatures greater than 100 C. Below this temperature, all the water will condense to liquid water or ice (depending on the temperature). So, if you have liquid water or ice only, you don't expect them to be able to be described by the ideal gas law. Otherwise it would be called the ideal liquid law or the ideal solid law.

I think you are too restrictive by saying "only" there. A mixture of phases at some particular temperatures and pressures would also give the ideal gas law a hard time.

Yet some people claim that the ideal gas law works even when water changes states. It is about time you guys made up your minds.

 

[Chestermiller]

I think you are too restrictive by saying "only" there. A mixture of phases at some particular temperatures and pressures would also give the ideal gas law a hard time.

Yet some people claim that the ideal gas law works even when water changes states. It is about time you guys made up your minds.

I never made such a claim, so please don't lump me in.

In terms of a mixture of phases, what I'm saying is that the ideal gas law describes the gas phase (i.e., excluding the volume of the solid or liquid) if you use the partial pressure of each species when you apply the ideal gas law to that species in the gas phase. It also describes the gas phase as a whole at the total pressure of the system.

 

[russ_watters]

I think you are too restrictive by saying "only" there. A mixture of phases at some particular temperatures and pressures would also give the ideal gas law a hard time.

Yet some people claim that the ideal gas law works even when water changes states. It is about time you guys made up your minds.

Depends what you mean by "a hard time". A great deal of thermodynamics involves analyzing multiphase mixtures and the ideal gas law is a very important part of the analysis.

For example, at a given temperature there is a certain vapor pressure of water - let's say saturated for simplicity. If you reduce the temperature, you get a new vapor pressure. Comparing the states with the ideal gas law tells you how much was converted to liquid water.

The ideal gas law rarely the only tool used in a thermo problem, but it is very often an important one. Not being the only tool, however, doesn't to me constitute "a hard time".

 

[voko]

I never made such a claim, so please don't lump me in.

Then I don't understand what you are debating here. If you agree that the ideal gas law does not apply "even when water changes states", just say so and let's be done with that.

You keep re-iterating trivia of the behavior of water vapor that does not change states, but that is beside my point.

 

[Chestermiller]

Then I don't understand what you are debating here. If you agree that the ideal gas law does not apply "even when water changes states", just say so and let's be done with that.

You keep re-iterating trivia of the behavior of water vapor that does not change states, but that is beside my point.

I'm sorry my comments have been so frustrating and trivial to you. You and I seem to be on different wavelengths in this discussion. The discussion has become too contentious for me, so I am withdrawing from further postings in this thread. I hope that other readers of the thread have been able to relate more to what I have been saying. No hard feelings.

Chet

 

[voko]

The ideal gas law rarely the only tool used in a thermo problem, but it is very often an important one. Not being the only tool, however, doesn't to me constitute "a hard time".

My point is that the ideal gas law cannot describe phase transitions at all. Those are described by more accurate equations of state, which then can be used for the gas part just as well, making the ideal gas law fully redundant.

My stronger point is that if we treat the system as a black box (say a vessel at constant pressure and varying temperature), then the ideal gas law fails completely.

In the broader context of this entire thread, there was a statement that the ideal gas law should be applied with caution to the atmosphere. That was denounced as nonsense, the ideal gas law was said to describe the atmosphere very accurately and it was proclaimed correct "even when water changes states". While it is precisely here that caution must be exercised, because liquid and solid phases have to be dealt with differently, so the ideal gas law does not in fact describe all the atmosphere.