real gas example

[Oh_Gee]

can someone please explain to me why when you increase pressure on a gas, the volume will decrease to some value PLUS a little more to that value and vice versa for reducing pressure?

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[Cawolf]

An ideal gas is assumed to have no volume occupied by the molecules and to lack interaction between the molecules.

Real gasses take up some volume and have interactions so their compressibility is not exactly modeled the ideal gas equation.

Van der Waal's equation accounts for these differences in real gasses.

 

[Oh_Gee]

An ideal gas is assumed to have no volume occupied by the molecules and to lack interaction between the molecules.

Real gasses take up some volume and have interactions so their compressibility is not exactly modeled the ideal gas equation.

Van der Waal's equation accounts for these differences in real gasses.

but for increased pressure, why is the volume change some value PLUS a little more instead of a little less. Doesn't the volume of the gas molecules take away from the volume of the container?

 

[Cawolf]

The volume of the molecules is not accounted for in ideal calculations - so real calculations will account for them and show an increased volume.

The collisions between the molecules will also cause an increase in energy of the gas - increasing the volume.

 

[The Brown Knight]

If a real gas is really tightly compressed, the volumes of individual molecules become significant so it has to be ADDED to the volume you would calculate using ideal gas law.

Here's a modified Van der Waals equation (I took out the modification component for the pressure since pressure is independent variable here) :
Vreal = (nRT/Papplied) + nb
Videal = nRT/Papplied
The b coefficient accounts for the volume of individual real gas molecules and would be expected to be 0 for ideal gas. This is, mathematically, the "PLUS a little more" you are referring to. The real molecular volume accounts for the additional volume.

 

[Oh_Gee]

If a real gas is really tightly compressed, the volumes of individual molecules become significant so it has to be ADDED to the volume you would calculate using ideal gas law.

Here's a modified Van der Waals equation (I took out the modification component for the pressure since pressure is independent variable here) :
Vreal = (nRT/Papplied) + nb
Videal = nRT/Papplied
The b coefficient accounts for the volume of individual real gas molecules and would be expected to be 0 for ideal gas. This is, mathematically, the "PLUS a little more" you are referring to. The real molecular volume accounts for the additional volume.

what about deviations when pressure is low and volume is high?

 

[The Brown Knight]

I might have made a mistake in using the equation previously since Vreal is actually the volume of the container (can someone verify?).

Here's a better qualitative picture:
1. High pressure, Low volume: the particles are forced together so closely that they cause repulsion since bringing two densely charged nuclei VERY close together causes a very strong repulsion; if repulsive forces dominate, the individual molecules want to get away as far as possible from each other, making the real gas have greater volume than the ideal one.

2. Low to moderate pressure, High volume: especially a MODERATE amount of pressure will force molecules just close enough to promote intermolecular attractions (just like a parent promoting the social life of a shy child by forcing the latter just enough in making friends rather than forcing too much or not trying at all); increased intermolecular attractions will cause the real gas to have a lower volume than what an ideal gas would occupy

The ideal gas pretty much gives extrema in how much volume they it occupies: lowest possible volume for case 1 and highest possible volume for case 2.
That said, the b term in the Van der Waals equation still accounts for molecular volume and the repulsions encountered at high pressure in case 1; the a term in the equation accounts for the attractions encountered at moderate to low pressures in case 2.
The following diagram summarizes very well what I said above (Z is the compressibility factor defined as Vreal/Videal):
http://wikis.lawrence.edu/download/attachments/298444/IMG00081.GIF

I apologize for any confusion.

 

[Oh_Gee]

I might have made a mistake in using the equation previously since Vreal is actually the volume of the container (can someone verify?).

Here's a better qualitative picture:
1. High pressure, Low volume: the particles are forced together so closely that they cause repulsion since bringing two densely charged nuclei VERY close together causes a very strong repulsion; if repulsive forces dominate, the individual molecules want to get away as far as possible from each other, making the real gas have greater volume than the ideal one.

2. Low to moderate pressure, High volume: especially a MODERATE amount of pressure will force molecules just close enough to promote intermolecular attractions (just like a parent promoting the social life of a shy child by forcing the latter just enough in making friends rather than forcing too much or not trying at all); increased intermolecular attractions will cause the real gas to have a lower volume than what an ideal gas would occupy

The ideal gas pretty much gives extrema in how much volume they it occupies: lowest possible volume for case 1 and highest possible volume for case 2.
That said, the b term in the Van der Waals equation still accounts for molecular volume and the repulsions encountered at high pressure in case 1; the a term in the equation accounts for the attractions encountered at moderate to low pressures in case 2.
The following diagram summarizes very well what I said above (Z is the compressibility factor defined as Vreal/Videal):
http://wikis.lawrence.edu/download/attachments/298444/IMG00081.GIF

I apologize for any confusion.

sorry for the late reply. for a very low pressure/high volume, would there be any deviation from a calculation of volume?

 

[The Brown Knight]

sorry for the late reply. for a very low pressure/high volume, would there be any deviation from a calculation of volume?

Yeah you'll see deviation for real gases for both cases: very low pressure/high volume and very high pressure/low volume

 

[Czarcasm]

My interpretation: When the line is straight, that is: n=PV/RT equals 1, it's an ideal gas. We make two big assumptiosn with ideal gases: 1. no attractive forces 2. gases are volume-less

The graph above presents deviations of real gas from ideal behavior. Real gases deviate from ideal gases in the following ways:

Gases really do have attractive forces as a consequence, the real pressure is higher than what we used in the ideal gas equation. Why? Well because atoms are attracted to one another, they spend less time hitting the container and so, the predicted pressure is actual higher than anticipated. So the negative curve indicates how using a lower pressure (according to ideal gas assumption) would reflect on the graph above (a negative slope).

As pressure increases, molecules become even closer confined together. Above a certain threshold, their volume does become significant and so the real volume of the container is actual lower than what it is in reality. So based on the values we use for the ideal gas assumption, a real gas would curve upwards due to the effects of volume. So there is a shift higher from pressure to low volume considerations in the graph above. Initially, there is a large amount of volume but as pressure increases, the volume of the atoms within the container becomes increasingly significant.

At higher temperatures, molecules move on average more frequently and can avoid the attractive nature that pulls them together, spending less time together, and hitting the container more frequently; in this case, the predicted ideal gas pressure is very close to the real gas behavior. Likewise, by moving on average more frequently, there is less interactions between the molecules and their volume considerations individually are insignificant as to when they are close together.

 

[Lighthill-FFT]

For the sake of nuance (don't memorize this or you'll get confused), the kinetic theory of ideal gases (from which PV=nRT is derived) does treat things as point masses. However, we can justify such treatment because relative to the size of the container the atoms are close enough that it makes no difference.

As you compress is, Brown Knights point gets emphasized more: the ratio of the volumes of the actual molecules to the size of the container increases. However, the increase in volume doesn't matter so much because the container is still supposed to be so big that the size of the molecules doesn't really matter (unless we are talking huge 10,000 Dalton molecules or something). The idea is that unlike ideal gases, real gases always interact someway.

An Ideal gas is something like a bunch of metal balls. They bump into each other and they bounce and fly off. A real gas is much more complex: even the noble gases are subject to Van der Waals forces (or London Dispersion forces). The more complex the molecule, the more likely they will not interact ideally. In fact, the probability of them interacting ideally goes down exponentially fast. For Noble Gases, the deviation as indicated in Czarcasm's graph from the ideal gas is very small. For anything else, it gets really large really fast.

This is corrected in several ways, the two most common of which are Van der Walls equation and the Virial equation. If you want, I can type out a detailed explanation of either but I think Brown Knight does a sufficient job of getting the point across (although generally attraction forces are greater then the volume for most molecules given to students).

 

[Oh_Gee]

For the sake of nuance (don't memorize this or you'll get confused), the kinetic theory of ideal gases (from which PV=nRT is derived) does treat things as point masses. However, we can justify such treatment because relative to the size of the container the atoms are close enough that it makes no difference.

As you compress is, Brown Knights point gets emphasized more: the ratio of the volumes of the actual molecules to the size of the container increases. However, the increase in volume doesn't matter so much because the container is still supposed to be so big that the size of the molecules doesn't really matter (unless we are talking huge 10,000 Dalton molecules or something). The idea is that unlike ideal gases, real gases always interact someway.

An Ideal gas is something like a bunch of metal balls. They bump into each other and they bounce and fly off. A real gas is much more complex: even the noble gases are subject to Van der Waals forces (or London Dispersion forces). The more complex the molecule, the more likely they will not interact ideally. In fact, the probability of them interacting ideally goes down exponentially fast. For Noble Gases, the deviation as indicated in Czarcasm's graph from the ideal gas is very small. For anything else, it gets really large really fast.

This is corrected in several ways, the two most common of which are Van der Walls equation and the Virial equation. If you want, I can type out a detailed explanation of either but I think Brown Knight does a sufficient job of getting the point across (although generally attraction forces are greater then the volume for most molecules given to students).

i understand that if particles have overall attractive intermolecular forces, the a value will be postive and negative for overall repulsive intermolecular forces. so say you have a pure gas that has overall attractive intermolecular forces. wouldn't the pressure that gas exerts on the container be less than ideal? if so, why is it P + (square of density) instead of P - (square of density)

and for V - nb
is it minus because at high pressures the molecules' volume take away from the volume of the container?

i think i am confused because of the distinction between V being the volume the gas takes up or V being the volume of the container not being taken up by the gas

correct me if i am wrong

at high pressures:
the volume of gas will be a little more than an ideal gas because of the space that the molecules take up
the volume of the container will be a little less than ideal because of the space the molecules take up