Gas effusion problem

[Fila Delphia]

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Hey everyone, here's a question from exam kracker's 1001 gen chem. Question 195

What is the ratio of the average speed of an atom of neon to another atom of neon at the same temperature but twice the pressure?

I thought that using the gas law, PV = nRT, that P and T are directly related.

T is proportional to KE.

V = sqrt KE = sqrt of T

So if P goes up by 2 than T goes up by 2 and since V = sqrt KE = sqrt of T then the average speed of neon at twice the pressure is sqrt of 2 = 1.4, making the ratio 1:1.4

But this is not the case because KE only depends on temperature and apparently not Pressure. So why isn't pressure directly proportional to temperature? Wouldn't an increase in pressure increase the speed of the molecules which would thereby have more momentum and collide the walls of the container with more force?

Thanks for your help

 

[mehc012]

Hey everyone, here's a question from exam kracker's 1001 gen chem. Question 195

What is the ratio of the average speed of an atom of neon to another atom of neon at the same temperature but twice the pressure?

I thought that using the gas law, PV = nRT, that P and T are directly related.

T is proportional to KE.

V = sqrt KE = sqrt of T

So if P goes up by 2 than T goes up by 2 and since V = sqrt KE = sqrt of T then the average speed of neon at twice the pressure is sqrt of 2 = 1.4, making the ratio 1:1.4

But this is not the case because KE only depends on temperature and apparently not Pressure. So why isn't pressure directly proportional to temperature? Wouldn't an increase in pressure increase the speed of the molecules which would thereby have more momentum and collide the walls of the container with more force?

Thanks for your help

You are WAAAAY overthinking this. Yes, PV=nRT is a thing, but that doesn't mean that a gas at a higher pressure is always hotter. They specified that the pressure of the other sample was 2x higher, and did not even mention the other variables. That implies that they are ONLY asking about the effect of pressure.

They could have decreased the volume by half, or added more Neon, or some combo of both in order to obtain that pressure. And yes, depending on how they did it, perhaps the T was transiently higher...but if you set the container in a room for a few minutes, it would return to equilibrium T.

TL;DR the question asks about pressure, and you answered about temperature.

 

[mehc012]

Hey everyone, here's a question from exam kracker's 1001 gen chem. Question 195

What is the ratio of the average speed of an atom of neon to another atom of neon at the same temperature but twice the pressure?

I thought that using the gas law, PV = nRT, that P and T are directly related.

T is proportional to KE.

V = sqrt KE = sqrt of T

So if P goes up by 2 than T goes up by 2 and since V = sqrt KE = sqrt of T then the average speed of neon at twice the pressure is sqrt of 2 = 1.4, making the ratio 1:1.4

But this is not the case because KE only depends on temperature and apparently not Pressure. So why isn't pressure directly proportional to temperature? Wouldn't an increase in pressure increase the speed of the molecules which would thereby have more momentum and collide the walls of the container with more force?

Thanks for your help

You are WAAAAY overthinking this. Yes, PV=nRT is a thing, but that doesn't mean that a gas at a higher pressure is always hotter. They specified that the pressure of the other sample was 2x higher, and did not even mention the other variables. That implies that they are ONLY asking about the effect of pressure.

They could have decreased the volume by half, or added more Neon, or some combo of both in order to obtain that pressure. And yes, depending on how they did it, perhaps the T was transiently higher...but if you set the container in a room for a few minutes, it would return to equilibrium T.

TL;DR the question asks about pressure, and you answered about temperature.

 

[sps27]

You are WAAAAY overthinking this. Yes, PV=nRT is a thing, but that doesn't mean that a gas at a higher pressure is always hotter. They specified that the pressure of the other sample was 2x higher, and did not even mention the other variables. That implies that they are ONLY asking about the effect of pressure.

They could have decreased the volume by half, or added more Neon, or some combo of both in order to obtain that pressure. And yes, depending on how they did it, perhaps the T was transiently higher...but if you set the container in a room for a few minutes, it would return to equilibrium T.

TL;DR the question asks about pressure, and you answered about temperature.

Yes I agree. This is a simple KE v/s Temp question. Think Boltzman's equation E = 3/2(kt) where k = boltzman constant, E is the average KE of a gas molecule and T is the temp. There is no pressure term here at all.