Ideal Gas behavior?

[RubberToe]

I read the post by QofQuimica about Deviations from Ideal Gas Law Behavior, but I still have confusion about how "intermolecular interactions cause the gas's volume to be smaller than what is predicted by the ideal gas law". I thought Ideal gases have the No Volume, so how could intermolecular interactions cause the gas's volume to be smaller than zero? Maybe I'm confused about what is predicted by the ideal gas law. Any help or clarification would be greatly appreciated. Thanks in advance.

---

Members don't see this ad.

 

[Dr Durden]

Under either high pressure or low temperature, a gas starts to behave more like a liquid. This leads to intermolecular interactions causing molecules to coalesce and form a more compact state than that predicted by a gas law. Thus the true volume is smaller than that predicted by PV=nRT.

 

[RubberToe]

Wow... it makes sense now! Thanx Dr Durden. So the volume between the gas molecules gets smaller as the gas cools down into a liquid or even a solid.

So now I have another question... it seems the more I learn the more questions I have. Ideal Gas molecules have No Volume and No Intermolecular Attractions/Forces, correct? This is where I get confused. What does it mean for Ideal Gas Molecules to occupy No Volume? I thought No Volume is almost the same thing as a small volume (i.e. liquids or solids). Please clarify... Thanks again

 

[Dr Durden]

I'm sure you've seen pictures of atoms or molecules depicted as spheres in gen chem or physics textbooks. The ideal gas assumption just assumes these spherical volumes of nuclei and electrons are negligible when compared to the volume of the overall gas itself. This doesn't create a problem (read error) in any calculations until you get to the near liquid conditions of high pressure and low temperature.

Don't worry though, exact corrections for these conditions and more accurate equations of states than the ideal gas law are advanced chemical engineering or physical chemistry concepts not explicitly tested on the MCAT.

 

[RubberToe]

I'm sure you've seen pictures of atoms or molecules depicted as spheres in gen chem or physics textbooks. The ideal gas assumption just assumes these spherical volumes of nuclei and electrons are negligible when compared to the volume of the overall gas itself. This doesn't create a problem (read error) in any calculations until you get to the near liquid conditions of high pressure and low temperature.

Don't worry though, exact corrections for these conditions and more accurate equations of states than the ideal gas law are advanced chemical engineering or physical chemistry concepts not explicitly tested on the MCAT.

Thanks for the help Dr Durden... so I think I got it now. How is this analogy? I like analogies... The atoms of the gas molecules are like the stars that we see as we look up at the night sky. They take up very little volume (zero according to the Ideal Gas Law) when compared to the entire sky. Thats how I understand it. I hope that's what you meant. Thanks again and good luck to you.

 

[ssh18]

I'm confused about this as well...
so it says that at high pressures and low temperature, the gas deviates from ideal behavior...

I thought in the real gases the pressure is lower than the ideal pressure due to intermolecular forces (thereby, the particles don't hit the walls as much or with as much force due to intermolecular forces) so
so P real=P ideal-X


But for volume, I'm confused because I'm pretty sure I remember reading in a text book that the V real= V ideal + Y
because under ideal behavior we assume there is no volume but in reality there is so the actual volume is greater...so why does the TPR say otherwise?..I'm not convinced

 

[ssh18]

so it was my impression that the actual gas behavior is something like:

(P-x)(V+y)=nRT?

 

[estairella]

You guys are making it much more complicated than necessary. Memorize:

Vreal > Videal
Preal < Pideal

Saying that at medium temperatures the intermolecular forces cause a decrease in volume is totally misleading...

The intermolecular forces causes real pressure to decrease (so that it is lower than ideal pressure). Compared to the volume as predicted by ideal gas law AT IDEAL PRESSURE, the real volume is also lower (think of a balloon, it will contract if pressure lowers)...

BUT compared to the volume as predicted by ideal gas law AT REAL PRESSURE, the volume is still greater than it should be.

I hope that makes sense. If it doesn't make sense, ignore it, and just follow the two rules posted above.

 

[ssh18]

I agree with you on:

Vreal > Videal
Preal < Pideal

that's what I was trying to say in my previous post. My confusion is that in TPR book, it actually says Vreal<Videal
I guess that's my concern...

 

[Noeljan]

ok
I think that it can go either way. When you think of real gases having intermolecular forces (ie VanDerWaals). Now, this would usually cause attraction between them thus making the volume less than expected.
Except, there is a certain ideal radius known as the Vanderwaal radius (dont know if I am spelling this correctly). If you exceed that (like moving way to close together) I think you could start getting some repulsion, thus expanding the volume a tad. Anyways, I learned that in my protein structure and function class so I'm not sure how applicable it is to the MCAT and my memory can be off right now bc I didn't sleep last night.
ps. yes I really did take an entire class called Protein structure and Function

 

[TheHunter]

I agree with you on:

Vreal > Videal
Preal < Pideal

that's what I was trying to say in my previous post. My confusion is that in TPR book, it actually says Vreal<Videal
I guess that's my concern...

let me break it down for you:
Vreal < Videal because of attactive forces
Vreal > Videal because molecules do actually take up space

overall, Vreal < Videal because attractive forces own (so I guess TPR is right)


if you want to get technical:

Pideal = Pobserved + (attraction coefficient) * n^2/v^2,
Videal = Vcontainer - n * (size coefficient)
combine these two equations into PV = nRT, and notice they can counter the effects of one another, or reverse what usually happens (for example negative attraction coefficient in ionized gas)

hope that helps you out

 

[ssh18]

thanks! i just wanted to make sure the book was right

 

[estairella]

http://www.chem.ufl.edu/~itl/2045/lectures/lec_e.html

That page provides a good explanation... especially look at the graphs...

But in any case, Vreal > Videal... ALWAYS, as far as the MCAT is concerned. That's unless they say something different in the passage. I'm really not getting why people keep saying the opposite ... in the equation

(P + A)(V - B) = nRT

Pideal = Preal + A
Videal = Vreal - B

A and B are always positive (see http://en.wikipedia.org/wiki/Van_der_Waals_constants_(data_page))

And yes, it's an approximation of a real gas, but you can't be expected to know that, for example, H2 always shows a positive deviaton from a real gas (volume always dominates), while N2 shows a negative deviation at low pressures (attractive forces dominate) and positive deviation at high pressures (volume dominates)

 

[ssh18]

here's why, because in TPR book it says otherwise
sorry to drag this conversation on but that's where my confusion was...
i always thought that Vreal>Videal as well
but in TPR it says the opposite

 

[Noeljan]

I repeat
I believe it can be either, depending on conditions and how close the two molecules are

 

[grapeflavorsoda]

http://www.chem.ufl.edu/~itl/2045/lectures/lec_e.html

That page provides a good explanation... especially look at the graphs...

But in any case, Vreal > Videal... ALWAYS, as far as the MCAT is concerned. That's unless they say something different in the passage. I'm really not getting why people keep saying the opposite ... in the equation

(P + A)(V - B) = nRT

Pideal = Preal + A
Videal = Vreal - B

A and B are always positive (see http://en.wikipedia.org/wiki/Van_der_Waals_constants_(data_page))

And yes, it's an approximation of a real gas, but you can't be expected to know that, for example, H2 always shows a positive deviaton from a real gas (volume always dominates), while N2 shows a negative deviation at low pressures (attractive forces dominate) and positive deviation at high pressures (volume dominates)

you can reasonably expect it. Redlich-kwong equation, etc are commonly used.

anyway,

have you heard about virial expansion equation?

although you need knowledge of statistical mechanic to derive it, you can get cloe approx. of it by applying taylor expansion to van der waal's equation of state for gases; first set the equation in the form of the compressibility, then do the polynomial approximation by performing taylor expansion, which becomes finite polynomial with obvious physical approx. b<<Vm.

or you get just get one from web. anyway, if you do stare that for a min or two, you will see that you can reasonably predict the deviation pattern of real gas from its expected ideal behavior.