Gas Deviations

[EZR]

---

Members don't see this ad.

For an intert real gas, if you were to reduce the pressure to half of its original value, then what is the final volume relative to the initial volume?

The answer is 2V minus a little bit.

--Makes sense, since the molecules still occupy a bit of space (although I'm not altogether certain why that wouldn't have been accounted for in the initial volume)

The part that confuses me is that if the pressure were doubled, the new volume would be 1/2V plus a little bit. Why the "plus a little bit"?

 

[MedPR]

For an intert real gas, if you were to reduce the pressure to half of its original value, then what is the final volume relative to the initial volume?

The answer is 2V minus a little bit.

--Makes sense, since the molecules still occupy a bit of space (although I'm not altogether certain why that wouldn't have been accounted for in the initial volume)

The part that confuses me is that if the pressure were doubled, the new volume would be 1/2V plus a little bit. Why the "plus a little bit"?

Real volume is greater than ideal volume. You use the ideal gas law (pv=nrt) to know that doubling the pressure while keeping all other things constant means decreasing the volume by two (halving the volume). That's what happens with ideal gas. If it's a real gas, the volume will be a bit more (it always is), so it's .5V + a little.

 

[MT Headed]

For an intert real gas, if you were to reduce the pressure to half of its original value, then what is the final volume relative to the initial volume?

The answer is 2V minus a little bit.

--Makes sense, since the molecules still occupy a bit of space (although I'm not altogether certain why that wouldn't have been accounted for in the initial volume)

The part that confuses me is that if the pressure were doubled, the new volume would be 1/2V plus a little bit. Why the "plus a little bit"?

A lot of science problems can be solved by considering the absurd. Let's say that the molecules took up HALF of the volume, and the empty space that obeys the ideal gas law occupies the other half.

If you reduce the pressure by half, the volume of empty space doubles but the volume of the molecules won't change. Your new volume is 3/2 the original volume. The molecules still take up 1/2 the original volume, and the empty space doubles to the size of the original container. The new volume is 2V minus a fair amount.

Likewise, if you reduce the pressure to half of the original value, you are squeezing that empty space to half of its original value but you are never going to squeeze the molecules. The final volume is going to be 3/4 of the original volume... 1/2 is uncompressible molecules, and the other 1/4 is the new empty space. The new volume is V/2, plus a fair amount.

 

[Temperature101]

A lot of science problems can be solved by considering the absurd. Let's say that the molecules took up HALF of the volume, and the empty space that obeys the ideal gas law occupies the other half.

If you reduce the pressure by half, the volume of empty space doubles but the volume of the molecules won't change. Your new volume is 3/2 the original volume. The molecules still take up 1/2 the original volume, and the empty space doubles to the size of the original container. The new volume is 2V minus a fair amount.

Likewise, if you reduce the pressure to half of the original value, you are squeezing that empty space to half of its original value but you are never going to squeeze the molecules. The final volume is going to be 3/4 of the original volume... 1/2 is uncompressible molecules, and the other 1/4 is the new empty space. The new volume is V/2, plus a fair amount.

I am having a hard time visualizing this concept as well. I think I am gonna have to memorize it or figuring it out in some weird way. The way I see it is that: If you decrease the pressure by half, the volume will increase by 2 (ideal gas) since they are inversely proportional. However, when the volume of the gas increases, the molecules will collide less frequently. There will be less Kinetic Energy among the particle ie less heat (lower temperature). Refering back to the ideal gas law formula PV= nRT, if the temperature decreases a little bit, therefore, the vollume will decrease a little bit. Dont know if it makes sense or if I articulate it well enough...Correct me please if I am wrong.

 

[milski]

I am having a hard time visualizing this concept as well. I think I am gonna have to memorize it or figuring it out in some weird way. The way I see it is that: If you decrease the pressure by half, the volume will increase by 2 (ideal gas) since they are inversely proportional. However, when the volume of the gas increases, the molecules will collide less frequently. There will be less Kinetic Energy among the particle ie less heat (lower temperature). Refering back to the ideal gas law formula PV= nRT, if the temperature decreases a little bit, therefore, the vollume will decrease a little bit. Dont know if it makes sense or if I articulate it well enough...Correct me please if I am wrong.

There are problems with this way of thinking. First, if you double the volume and half the pressure, the left side of PV=nRT stays the same, which means that the temperature will stay the same. That makes sense in at least both ways - first you did not remove any energy from the system, so the KE (aka temperature) should stay the same. Second, you cannot use the ideal gas law to explain the discrepancies between the ideal and real behavior.

Something else to keep in mind - just because the molecules are hitting each other less often does not mean that they have less kinetic energy. It just means that they'll hit the walls less often, which can be measured as a lower pressure.

The difference between ideal and real behavior comes from the fact that the ideal gas law does not take into account the fact that the molecules/atoms of gas have a fixed, non-compressible volume.

MT Headed already tried to explain it, so I don't know if I'll be able to do any better. When you double the volume of some gas, you are increasing the empty space between the molecules but they still retain their size.

M--M - let's say that this is your gas in the beginning, and M and M are two molecules. You can see that while the distance between them is two dashes, they occupy a bit more space than that.

Now let's lower the pressure by half - that would make them be twice as far from each other:
M----M. The distance doubled, but all the space taken is slightly less than double. It used to be 2*M+2*-, now it's 2*M+4*-.

Because the space between the molecules doubled but the molecules themselves did not double in size, the new volume is not exactly twice but slightly less than twice the original.

 

[Temperature101]

There are problems with this way of thinking. First, if you double the volume and half the pressure, the left side of PV=nRT stays the same, which means that the temperature will stay the same. That makes sense in at least both ways - first you did not remove any energy from the system, so the KE (aka temperature) should stay the same. Second, you cannot use the ideal gas law to explain the discrepancies between the ideal and real behavior.

Something else to keep in mind - just because the molecules are hitting each other less often does not mean that they have less kinetic energy. It just means that they'll hit the walls less often, which can be measured as a lower pressure.

The difference between ideal and real behavior comes from the fact that the ideal gas law does not take into account the fact that the molecules/atoms of gas have a fixed, non-compressible volume.

MT Headed already tried to explain it, so I don't know if I'll be able to do any better. When you double the volume of some gas, you are increasing the empty space between the molecules but they still retain their size.

M--M - let's say that this is your gas in the beginning, and M and M are two molecules. You can see that while the distance between them is two dashes, they occupy a bit more space than that.

Now let's lower the pressure by half - that would make them be twice as far from each other:
M----M. The distance doubled, but all the space taken is slightly less than double. It used to be 2*M+2*-, now it's 2*M+4*-.

Because the space between the molecules doubled but the molecules themselves did not double in size, the new volume is not exactly twice but slightly less than twice the original.

Got it now...I knew the logic behind mine was not good but it was a way for me to remember it...Though, it make perfect sense the way you explain it.

 

[chiddler]

nevermind answered my own question.