TBR Ideal Gas Question

[G1SG2]

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In the Gases chapter in TBR (I think this was an example problem), it was stated that when the pressure is halved in a real gas, the volume is 2v-a little bit. If the pressure were doubled, the volume would be ½+a little bit. WHY 2v-a little bit, and why 1/2+ a little bit? I believe the other answer choices were just 2v and 1/2 for the pressure and volume, respectively. Thanks.

 

[phEight]

In the Gases chapter in TBR (I think this was an example problem), it was stated that when the pressure is halved in a real gas, the volume is 2v-a little bit. If the pressure were doubled, the volume would be ½+a little bit. WHY 2v-a little bit, and why 1/2+ a little bit? I believe the other answer choices were just 2v and 1/2 for the pressure and volume, respectively. Thanks.

This is just off the top of my head, I could be wrong... but I think it has to do with the attractive / repulsion forces between the molecules that usually aren't accounted for. When pressure is doubled, the volume is halved, but now that the molecules are so much more closer to each other there is a repulsive force between them that causes the + a little bit. Now when pressure is halved and volume doubled, the molecules exert an attractive force between, so this causes volume to be - a little bit. When molecules are much closer to each other repulsive forces are dominant, when they are further apart attractive forces are dominant.

 

[DamienPro]

This is just off the top of my head, I could be wrong... but I think it has to do with the attractive / repulsion forces between the molecules that usually aren't accounted for. When pressure is doubled, the volume is halved, but now that the molecules are so much more closer to each other there is a repulsive force between them that causes the + a little bit. Now when pressure is halved and volume doubled, the molecules exert an attractive force between, so this causes volume to be - a little bit. When molecules are much closer to each other repulsive forces are dominant, when they are further apart attractive forces are dominant.

Your approach is right, but the reasoning is wrong. First off, gas pressure is defined by the collision of gas molecules with the walls of the container. In real situation, intermolecular forces among the gas molecules tend to reduce this effect. Whether or not the pressure is doubled, a tiny factor will always need to be added to P to make the situation ideal. Next, real gas molecules are incompressible and would always occupy a tiny bit of volume of the container. Again, to make the gases ideal, this intrinsic volume will need to be excluded from the calculation. This is an MCAT favorite on the van der Waals equation. Get the concept right once, and you're set to answer all questions related to it.

 

[Will Hunting]

In the Gases chapter in TBR (I think this was an example problem), it was stated that when the pressure is halved in a real gas, the volume is 2v-a little bit. If the pressure were doubled, the volume would be ½+a little bit. WHY 2v-a little bit, and why 1/2+ a little bit? I believe the other answer choices were just 2v and 1/2 for the pressure and volume, respectively. Thanks.

Here's why. If you look at the example they have 3 Liters. 2.9 liters of space and .1 liters of gas. If you compress, you only compress the space. So, you compress to 1.45 Liters plus the .1 liters of gas. The overall volume is bigger. The opposite is true for doubling volume. 2.9*2=5.8 Liters +.1=5.9 liters.

However, the ideal gas equation Volume is for FREE SPACE. So, a real gas has LESS volume than an IDEAL gas. This is why it is Vcontainer-nb=V of ideal. The actual volume of the gas is greater when you consider free space+volume of gas. So, to find an ideal we have to subtract the gas to get free space. Kaplan and EK say real gas=greater volume. However, they are talking about the volume of free space+gas. In our case, this is 1.55>1.5 that ideal gas would have had. Whereas, TBR and TPR say less because the actual free space 1.45<1.55.

 

[G1SG2]

Here's why. If you look at the example they have 3 Liters. 2.9 liters of space and .1 liters of gas. If you compress, you only compress the space. So, you compress to 1.45 Liters plus the .1 liters of gas. The overall volume is bigger. The opposite is true for doubling volume. 2.9*2=5.8 Liters +.1=5.9 liters.

However, the ideal gas equation Volume is for FREE SPACE. So, a real gas has LESS volume than an IDEAL gas. This is why it is Vcontainer-nb=V of ideal. The actual volume of the gas is greater when you consider free space+volume of gas. So, to find an ideal we have to subtract the gas to get free space. Kaplan and EK say real gas=greater volume. However, they are talking about the volume of free space+gas. In our case, this is 1.55>1.5 that ideal gas would have had. Whereas, TBR and TPR say less because the actual free space 1.45<1.55.

Awesome explanation, thanks a lot! 👍