# deviation from PV=nRT

#### Smooth Operater

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q: for any given substance at pressure 50 atm and a temperature of 30K, which of the following statments is most likely accurate?

a: the volume of substance is slightly greater than that predicted by PV=nRT

can anyone explain why? THANKS!

#### djeffreyt

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all I can explain for this is that the gas state is common for a substance when the pressure is low and the temperature is high. Therefore, the low temperature and high atm given in this problem means that a gas under these circumstances will vary somewhat from the ideal gas law because it isn't in ideal gas conditions.

Why the volume would be slightly greater rather than slightly lower...I cannot explain

#### DrWanahbe

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I'm just learning about gas laws in class right now, so I may not be much of help, but here's what I'm thinking....

The gas used in the example is at a fairly high pressure (higher than anything I've worked with in a problem so far) and a very low temperature (30 K is the equivalent of -243 degrees C).

It is my understanding that a gas cannot withstand that kind of cold without becoming at least a liquid, as the cooling causes the gas molecules to slow down.

So, could the volume be slightly greater because the gas has achieved liquid status? We haven't started liquids yet, so I haven't studied this to know for absolute certainity.

#### thehipster

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I think your answer is wrong, the volume would be much lower. This is question 29 from Kaplan Chem Subject Test #29 right?

If you setup the PV=nRT eqn to solve for volume and by removing the constant values, you get: V= T/P

Under normal conditions, the Press=1 atm, and Temp is around 273K (0 C), so under the conditions given, you can see that the press is much higher and the temp is much lower. If you put these into the eqn you can see that the volume decreases when temperature decreases and pressure increases

V1 = T/P = (273)/(1) = 273

V2 = T/P = (30)/(50) = 3/5

#### crazy_sherm

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In order for the Ideal Gas Law to work, you have to make several assumptions:
1. Gases consist of small particles (molecules) which are in continuous random motion
2. The volume of the molecules present is negligible compared to the total volume occupied by the gas
3. Intermolecular forces are negligible
4. Pressure is due to the gas molecules colliding with the walls of the container

Although not real, at "normal" conditions close to STP, real gasses will behave close enough to an ideal gas.

However, real gasses actually have these properties:
1. at low temperatures the gas molecules have less kinetic energy (move around less) so they do attract each other
2. at high pressures the gas molecules are forced closer together so that the volume of the gas molecules becomes significant compared to the volume the gas occupies

Therefore, you have several limitation to the Ideal Gas Law:
1. Works well at low pressures and high temperatures
2. Most gases do not behave ideally above 1 atm pressure (high pressure)
3. Does not work well near the condensation conditions of a gas (low temp)

So to answer your question, the volume is higher because at such high pressure, the volume is being partially made up by the size of the molecule as well as the kinetic energy of the gas. If it were an ideal gas, the volume of the molecules are non-existent.

#### allstardentist

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I think the volume should be lower because real gases particles have finite volume and thus the effective volume, Veff, will decrease according to van der Waals equations. I know i saw the same question myself recently (I think we are on similiar pace for studying DAT) but yeah the kaplan answer might be wrong... and hopefully nothing like that quesiton will show up on the real test.

#### thehipster

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Yeah, Kaplan might have a wrong answer and explanation, but I this setup seems to make sense to me, which would agree with Kaplan's answer of the volume being lower. They have an explanation relating to the deviations that crazy_sherm mentions, but still say that the volume decreases.

V1 = T/P = (273)/(1) = 273

V2 = T/P = (30)/(50) = 3/5

#### djeffreyt

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Crazy Sherm has it right.

One of the assumptions of the ideal gas law is that since gas particles occupy so little volume relative to the volume of space between these gas particles, the volume of the gas particles themselves is insignificant. Thus, the ideal gas law does not account in it's volume the volume of the gas molecules themselves. At STP, this makes sense because it would probably be the difference between saying a gas takes up 22.414L of space of a gas takes up 22.4140001 L of space.

When you drop the temperature and raise the pressure significantly, you greatly decrease the volume, so the size of the gas particles becomes more and more significant. As the pressure increases, the ratio of "open" volume between moecules (space between molecules accounted for in the ideal gas law) to volume occupied by gas molecules gets smaller. So the ideal gas law would predict a volume that was smaller than the real volume.

A lot of you have been saying that the answer should be that the volume is smaller than predicted by the ideal gas law...and to some extent, that makes sense. As you decrease volume (by increasing pressure or decreasing temperature), intermolecular forces begin coming into play, and if a molecule is polar, the molecules may attract each other. Of course, most polar molecules would begin to liquify or solidify at high pressure and low temperatures. However, if the molecule is nonpolar, like H2, or just a single atom, Xe, the electron shells at the exterior of the molecules would actually be repulsive of each other. Either way, I don't think you need to consider these possibilities since it's not asking about a particular type of gas moecule...just a general gas moelcule.

OP
S

#### Smooth Operater

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hey, thanx, that makes sense now

So, at STP, would ideal gas law predict a volume that is smaller than the real volume since ideal gas law assume each molecule do not occupy volume?

#### DMDorDDS

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Sherm is right...

but on a happier note... DAT chem isnt gonna ask that kinda detailed info

atleast I dont think so