# TBR Gen Chem chapter V number 13

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#### deleted647690

This question is part of a passage about reactions in a dry box. The question asks how temperature and pressure inside a gas chamber with a fixed volume would change as the gas is removed.

The answer was that both the temperature and pressure decrease as the gas exits. The explanation is that pressure is directly proportional to the decrease in moles of the gas as it leaves the chamber. Then, using thermodynamics, we can say that the temperature also drops because the remaining gas in the chamber will expand as some leaves, and expansion of a gas is endothermic.

However, I don't understand how you would come to this conclusion. You could see how pressure and temperature relate to moles using the ideal gas law, and based on that, I could see how pressure is directly proportional as they found, but I would also say that temperature is inversely proportional to the number of moles, meaning I would say that temperature increases.

Unless the change in temperature is a response to a change in pressure rather than a change in the number of moles (in that case, you would say that the temperature varies directly with the pressure, so it would also decrease.)

But how would you know that the initial compensatory response to the change given in the question (decrease in moles) is a change in pressure, followed by a change in temperature? If I just use the ideal gas law to answer this, I would get the wrong answer, unless I knew that the change in pressure would be in response to the change in moles, followed by the change in temperature which would vary with the change in pressure.

#### GreenDuck12

7+ Year Member
Can you post either a picture of the passage and the question or retype the question with the answer choices?

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#### deleted647690

Can you post either a picture of the passage and the question or retype the question with the answer choices?
Can you post either a picture of the passage and the question or retype the question with the answer choices?

Yes, thank you.

If the volume of the shuttle port is 10.0 liters, then what is true about the temperature and pressure inside the gas chamber as the gas is removed?

A. Both the temperature and pressure increase as the gas exits
B. The temperature increases while the pressure decreases as the gas exits
C. The temperature decreases while the pressure increases as the gas exits.
D. Both the temperature and pressure decrease as the gas exits.

The answer was D.

I would have thought B based on PV = nRT. When the moles of gas is decreasing, you'd expect the temperature to increase, while the pressure also decreases. This is because temperature is inversely proportional to n, and P is directly proportional to n.

What is the error in this line of thinking?

#### GreenDuck12

7+ Year Member
One thing I like about TBR is you sometimes really have to narrow down the answer choices.

A and C are definitely wrong because:
A. Is wrong because pressure would not increase as gas exits. Only if gas did not leak and temperature increased would the pressure increase.
C. Is wrong because temperature decreasing would cause pressure to decrease more as gas exits.

Also, A and C can be diagramed as follows
A. Increase, Increase
C Decrease, Increase

Without seeing the passage, you have two answer choices that boils down to

B. Increase, Decrease
D. Decrease, Decrease

Which one of these two would be true in all cases when gas is leaking? that the temperature decreases and the pressure decreases. If the temperature increases, the pressure may not decrease as moles of gas are removed. That may occur is some cases but isn't the best answer because it isn't true in all cases.

With this kind of question, doing a quick schematic diagram always helped me when I was practicing. Hope this helps and let me know if it doesn't.

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#### GreenDuck12

7+ Year Member
Also note that by may occur I mean it may be possible for both the moles of gas to decrease and the temperature to increase (from external source, of course) while still having the pressure drop. The gas leaking by itself would not cause the temperature to increase.

D

#### deleted647690

Also note that by may occur I mean it may be possible for both the moles of gas to decrease and the temperature to increase (from external source, of course) while still having the pressure drop. The gas leaking by itself would not cause the temperature to increase.

Thanks for the response.
Why would the gas leaking by itself not cause the temperature to increase? PV=nRT, so a change in moles could cause a change in temperature.

The reason I'm getting confused is because I'm not sure which variable is responding to which variable. I read it as simply, you decrease moles , so what would happen to these other two variables in the equation? Since T is inversely proportional to n, and P is directly proportional to n, I got B.

Are you saying that Temperature only varies as pressure varies, but not as moles varies?

What do you mean by "true in all cases"?

#### GreenDuck12

7+ Year Member
Why would the gas leaking by itself not cause the temperature to increase? PV=nRT, so a change in moles could cause a change in temperature.
If the decrease in moles was equal and opposite to the increase in temperature, that would cause the pressure to stay the same. That is not happening in this scenario. Because the moles of gas is decreasing, the pressure is also going to decrease.

PV = nRT
P = decreasing
V= same
n = decreasing
R= same
T = ?

What do you mean by "true in all cases"?
In answer B, if T is increasing through some mechanism (a heat source impacting the container of gas), we don't know necessarily that pressure will still be decreasing. Temperature could triple while the moles of gas could be halved. In this case the pressure would actually increase despite a decrease in the amount of gas. However, If moles of gas decreases and the temperature decreases, the pressure has to decrease in all cases.

Are you saying that Temperature only varies as pressure varies, but not as moles varies?
Yes, temperature is a measure of kinetic energy. Simply decreasing the moles of gas in a system would not increase the amount of kinetic energy but rather decrease the amount of kinetic energy

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#### deleted936470

PV = nRT is wrong here, that equation denotes an ideal, somewhat static situation. Large fluctuations of any variable render a system 'non-ideal' i.e. large leakage of 'n' for this problem.

So, what is temperature? It increases as a result of molecule collision due to their KE - when kinetic temperature is applied, two objects with the same average translational KE will have the same temperature. Less 'n' = less collisions = less KE => temperature decreases in this system.

It follows that the answer is D.

I recommend a brush up on kinetic theory and the limitations of the ideal gas law.

D

#### deleted647690

Why would the gas leaking by itself not cause the temperature to increase? PV=nRT, so a change in moles could cause a change in temperature.
If the decrease in moles was equal and opposite to the increase in temperature, that would cause the pressure to stay the same. That is not happening in this scenario. Because the moles of gas is decreasing, the pressure is also going to decrease.

PV = nRT
P = decreasing
V= same
n = decreasing
R= same
T = ?

What do you mean by "true in all cases"?
In answer B, if T is increasing through some mechanism (a heat source impacting the container of gas), we don't know necessarily that pressure will still be decreasing. Temperature could triple while the moles of gas could be halved. In this case the pressure would actually increase despite a decrease in the amount of gas. However, If moles of gas decreases and the temperature decreases, the pressure has to decrease in all cases.

Are you saying that Temperature only varies as pressure varies, but not as moles varies?
Yes, temperature is a measure of kinetic energy. Simply decreasing the moles of gas in a system would not increase the amount of kinetic energy but rather decrease the amount of kinetic energy
PV = nRT is wrong here, that equation denotes an ideal, somewhat static situation. Large fluctuations of any variable render a system 'non-ideal' i.e. large leakage of 'n' for this problem.

So, what is temperature? It increases as a result of molecule collision due to their KE - when kinetic temperature is applied, two objects with the same average translational KE will have the same temperature. Less 'n' = less collisions = less KE => temperature decreases in this system.

It follows that the answer is D.

I recommend a brush up on kinetic theory and the limitations of the ideal gas law.

Thank you both for your help, it is much appreciated.

D

#### deleted647690

PV = nRT is wrong here, that equation denotes an ideal, somewhat static situation. Large fluctuations of any variable render a system 'non-ideal' i.e. large leakage of 'n' for this problem.

So, what is temperature? It increases as a result of molecule collision due to their KE - when kinetic temperature is applied, two objects with the same average translational KE will have the same temperature. Less 'n' = less collisions = less KE => temperature decreases in this system.

It follows that the answer is D.

I recommend a brush up on kinetic theory and the limitations of the ideal gas law.

So PV=nRT does not apply in this situation. I see a contradiction there between the theories. Would there ever be a situation where an ideal gas has a change in moles that influences a change in temperature? Based on their relationship in PV=nRT, they have an inverse effect. If you decreased number of moles of gas, while holding pressure and volume constant, you would increase temperature. However, with a thermochemical explanation, with less molecules moving around the container, you have less kinetic energy and therefore lower temperature. So PV = nRT would predict an increase in termperature, and a kinetic explanation would predict a decrease in temperature.

#### BerkReviewTeach

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So PV=nRT does not apply in this situation. I see a contradiction there between the theories. Would there ever be a situation where an ideal gas has a change in moles that influences a change in temperature? Based on their relationship in PV=nRT, they have an inverse effect. If you decreased number of moles of gas, while holding pressure and volume constant, you would increase temperature. However, with a thermochemical explanation, with less molecules moving around the container, you have less kinetic energy and therefore lower temperature. So PV = nRT would predict an increase in termperature, and a kinetic explanation would predict a decrease in temperature.

Greenduck has done a wonderful job laying out why PV=nRT is not applicable here. It's not so much that it breaks down or that there is some nonideality wreaking havoc on it, it's that you have too many variables changing. You have only been looking at moles and temperature, but as GreenDuck points out, you have moles decreasing and pressure decreasing, so the third variable (temperature) cannot be predicted using that equation. You'd have to know exactly how much the moles and pressure decrease in order to determine how temperature is affected. We don't have exact numbers, so we have nothing to go by in PV=nRT to decide about T.

To determine the impact on temperature, you need to look at thermodynamics. If you have ever let air out of a compressed container (aerosol can, keyboard cleaner, gas cylinder, etc...) you will notice the container gets cold. This is caused by the gas that remains behind breaking intermolecular forces as the particles spread apart (or in the case of a liquid/gas mixture, the liquid endothermically evaporating into gas). The example in the text where you blow on a hot beverage with pursed lips to cool it is a practical example where you know this intuitively. The gas leaving your lips expands and in doing so cools. This cooler gas sucks heat from the surface of the hot beverage.

To address your question about a scenario where n would cause a change in T, can you think of a scenario where P and V remain constant for a system? Let me propose the opposite of your question. If I heat a closed system containing gas in a rigid container, would you expect the moles go down? or would you expect the pressure to increase? This is a case where you need to combine PV=nRT with your real life intuition to answer the question.

I hope this helps.

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D

#### deleted647690

Greenduck has done a wonderful job laying out why PV=nRT is not applicable here. It's not so much that it breaks down or that there is some nonideality wreaking havoc on it, it's that you have too many variables changing. You have only been looking at moles and temperature, but as GreenDuck points out, you have moles decreasing and pressure decreasing, so the third variable (temperature) cannot be predicted using that equation. You'd have to know exactly how much the moles and pressure decrease in order to determine how temperature is affected. We don't have exact numbers, so we have nothing to go by in PV=nRT to decide about T.

To determine the impact on temperature, you need to look at thermodynamics. If you have ever let air out of a compressed container (aerosol can, keyboard cleaner, gas cylinder, etc...) you will notice the container gets cold. This is caused by the gas that remains behind breaking intermolecular forces as the particles spread apart (or in the case of a liquid/gas mixture, the liquid endothermically evaporating into gas). The example in the text where you blow on a hot beverage with pursed lips to cool it is a practical example where you know this intuitively. The gas leaving your lips expands and in doing so cools. This cooler gas sucks heat from the surface of the hot beverage.

To address your question about a scenario where n would cause a change in T, can you think of a scenario where P and V remain constant for a system? Let me propose the opposite of your question. If I heat a closed system containing gas in a rigid container, would you expect the moles go down? or would you expect the pressure to increase? This is a case where you need to combine PV=nRT with your real life intuition to answer the question.

I hope this helps.

Thanks. I don't always think so much about if it actually makes sense; I just see the question, think of the applicable equation, and plug-n-chug. That is a difficult habit to break, especially on a timed exam

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#### deleted936470

Thanks. I don't always think so much about if it actually makes sense; I just see the question, think of the applicable equation, and plug-n-chug. That is a difficult habit to break, especially on a timed exam
This problem doesn't need a tome of justification or advanced understanding of thermodynamics. Simply put, if there's a large change in variable(s), don't use PV=nRT. You wouldn't spend 10 minutes thinking like this during the real test. This is a critical flaw of the TBR series, especially their B/B section.

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#### deleted647690

This problem doesn't need a tome of justification or advanced understanding of thermodynamics. Simply put, if there's a large change in variable(s), don't use PV=nRT. You wouldn't spend 10 minutes thinking like this during the real test. This is a critical flaw of the TBR series, especially their B/B section.

How could you ever know the "quick answer" though if you don't truly understand the reasoning? That isn't a good way for the information to stick

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#### deleted936470

How could you ever know the "quick answer" though if you don't truly understand the reasoning? That isn't a good way for the information to stick
You are right in knowing that understanding the theory precedes practice problems. It follows then that plug and chug is not a good way to answer conceptual problems and the test writers have this in mind.
Kinetic theory as it relates to temperature is a high yield topic. Try to think about these problems as it relates to a major theory you’ve learned in general chemistry and brush up accordingly.
Plug and chug works for dimensional analysis, but truly learning when to use and when NOT to use a certain formula will increase your score.

The question can be answered with knowing kinetic theory is based on the dependence of temperature on the kinetic energy of the rapidly moving particles of a substance. Gas leaks --> less rapid movement of particles within the container --> less collisions --> less KE --> less T.

Thinking of endothermic rxns, intermolecular forces, the 4th law of thermodynamics is a good way to psych yourself out during test day.

You know more than you think. Good luck!

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#### deleted936470

And using PV = nRT should've led you to:

P ∝ T

↓ P ⇒ ↓ T

Anyone can look up the answer at the back of the book and transcribe the convoluted, although correct, approach to a simple question, but on a very time-limited exam, you should find your own strategy that suits you.

#### GreenDuck12

7+ Year Member
Thanks. I don't always think so much about if it actually makes sense; I just see the question, think of the applicable equation, and plug-n-chug. That is a difficult habit to break, especially on a timed exam
Be careful with this when approaching the mcat. Most questions are not going to rely on your ability to calculate an answer but rather reason through relationships. knowing when something does or doesn’t make sense is incredibly useful unless the passage gives you reason to believe something shouldn’t follow a trend.

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#### deleted647690

Thank you all for your contributions

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