Question on Kinetic Molecular theory and gases.

[Slaughter421]

I am confused.

The following is true: The average kinetic energy of the molecules is proportional to absolute temperature (A result of Thermodynamics). At a given temperature the molecules of all species of gas, no matter what size shape or weight, have the same average kinetic energy.

Then how is it that Ar moves faster then Xe? Wouldnt they move at the same speed?

This gas stuff is really contradictory. Someone please explain.

ps I used this website for the fact: http://www.chem.ufl.edu/~itl/2045/lectures/lec_d.html

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[mightyrat]

I am confused.

The following is true: The average kinetic energy of the molecules is proportional to absolute temperature (A result of Thermodynamics). At a given temperature the molecules of all species of gas, no matter what size shape or weight, have the same average kinetic energy.

Then how is it that Ar moves faster then Xe? Wouldnt they move at the same speed?

This gas stuff is really contradictory. Someone please explain.

ps I used this website for the fact: http://www.chem.ufl.edu/~itl/2045/lectures/lec_d.html

Temperature is defined as the average kinetic energy!! So if a couple of gases exist together in a container, theoretically they should have the same temperature.

This, however, isnt correlated to the speed of the gas. They are two separate laws, so two things can have the same temperature but that doesnt neccessarily make them travel at the same speed.

Think of it this way, a 1000 g of feathers vs a 1000 g of iron...they weigh the same, but they arent the same density. Thats just one example to illustrate the concept.

So here, yes the Ar travels faster than Xe (~1.81 times to be exact lol) but that doesnt mean they should have different temperatures.

Hope this helps!

 

[Slaughter421]

Thanks man. Yeah it makes more sense now. I alwasys thought averge kinectic energy and speed were related in this theory.

 

[wantVCUdental]

I am confused.

The following is true: The average kinetic energy of the molecules is proportional to absolute temperature (A result of Thermodynamics). At a given temperature the molecules of all species of gas, no matter what size shape or weight, have the same average kinetic energy.

Then how is it that Ar moves faster then Xe? Wouldnt they move at the same speed?

This gas stuff is really contradictory. Someone please explain.

ps I used this website for the fact: http://www.chem.ufl.edu/~itl/2045/lectures/lec_d.html

Think of transfer of energy, all the energy can be thought of as potential and kinetic energies, which are transferable/exchangeable. You can think of heat as potential energy, which can be transfered to kinetic energy. At the same temperature, the potential energy for all molecules should be the same, and so when that energy transfers to kinetic energy, that should be the same also.
Kinetic energy is defined as 1/2 mv^2
if K (Ar) = K (Xe)
but masses of Ar and Xe differ, that means their speeds must also differ right?
hope this helps

 

[mightyrat]

Really?!? so are you saying that in a way if kinetic energy (KE) was altered, that means the masses should also change? Based on the formula that you gave, which i believe has more of a physics foundation than a chemical one, that is what your saying.

But i was always under the impression that average kinetic energy isnt really what KE is about here, because if thats the case, then temperature is dependent on mass and vice versa...which is incorrect...think of molality, its not dependent on temperature, but it is on the mass of the solvent.

I do agree with you on that the energies are transferrable, but i dont think that average KE and KE are correlated...at least in this respect.

Please correct me if i am wrong!! Im taking this beast soon and dont want to mess up this concept lol

 

[wantVCUdental]

Really?!? so are you saying that in a way if kinetic energy (KE) was altered, that means the masses should also change? Based on the formula that you gave, which i believe has more of a physics foundation than a chemical one, that is what your saying.

But i was always under the impression that average kinetic energy isnt really what KE is about here, because if thats the case, then temperature is dependent on mass and vice versa...which is incorrect...think of molality, its not dependent on temperature, but it is on the mass of the solvent.

I do agree with you on that the energies are transferrable, but i dont think that average KE and KE are correlated...at least in this respect.

Please correct me if i am wrong!! Im taking this beast soon and dont want to mess up this concept lol

Yes you are wrong, all the sciences are inter-related, you can't study one field thoroughly without a strong foundation in another, principles in chemistry are derived with help from those in physics and vice versa. You can't change the masses, masses are a given, what's more plausible to change? Mass or Speed? (also, in the question that is posed, masses are GIVEN, Ar and Xe have set masses)

It's like saying, if a car can only travel at 30mph. If the distance is 60 miles, how much time is required to travel that distance? you can't change the speed of the car. just like you can't change the masses of the given elements. I hope that clears things up...

 

[mightyrat]

Yes you are wrong, all the sciences are inter-related, you can't study one field thoroughly without a strong foundation in another, principles in chemistry are derived with help from those in physics and vice versa. You can't change the masses, masses are a given, what's more plausible to change? Mass or Speed? (also, in the question that is posed, masses are GIVEN, Ar and Xe have set masses)

It's like saying, if a car can only travel at 30mph. If the distance is 60 miles, how much time is required to travel that distance? you can't change the speed of the car. just like you can't change the masses of the given elements. I hope that clears things up...

True that KE = 1/2mv^2, and also true that physics and chemistry are related...i didnt deny that part lol, however, average KE (temperature) doesnt equal 1/2mv^2! Thats how you can deduce that temperature isnt affected by the masses and vice versa. Will higher temperature increase the speed? yes, but to the same extent to both gases so its a constant, thats why you can overlook it.

Sorry if i didnt make that clear the first time around

 

[wantVCUdental]

True that KE = 1/2mv^2, and also true that physics and chemistry are related...i didnt deny that part lol, however, average KE (temperature) doesnt equal 1/2mv^2! Thats how you can deduce that temperature isnt affected by the masses and vice versa. Will higher temperature increase the speed? yes, but to the same extent to both gases so its a constant, thats why you can overlook it.

Sorry if i didnt make that clear the first time around

OP's question is asking
At a given temperature the molecules of all species of gas, how is it that Ar moves faster then Xe? Wouldnt they move at the same speed?

Temperature is a given, you can't overlook what is given. Given this condition, and given the masses of respective elements Ar and Xe, you are looking for their speeds, and E=1/2 mv^2 is how you derive their respective speeds.

Had the OP asked how the INCREASE in temperature affect the changes between Ar and Xe's speeds, i would have agreed that since the increase in temperature is the same for both elements, you can overlook it.

 

[wizi]

OP's question is asking
At a given temperature the molecules of all species of gas, how is it that Ar moves faster then Xe? Wouldnt they move at the same speed?

Temperature is a given, you can't overlook what is given. Given this condition, and given the masses of respective elements Ar and Xe, you are looking for their speeds, and E=1/2 mv^2 is how you derive their respective speeds.

Had the OP asked how the INCREASE in temperature affect the changes between Ar and Xe's speeds, i would have agreed that since the increase in temperature is the same for both elements, you can overlook it.

wantVCUDental,

you are right about KE is transferred between the molecules BUT the overall KE of the gas molecules remains constant. If you use KE formula, you only calculate the speed of 2 single atoms, not the whole thing. Therefore, KE is not related to gas velocity in this situation.

Use this formula:

C (average speed of molecules) = [ 8*R*T^(1/2) ] / (pi* M) ( I dont think we need to know this formula for DAT).

R, T are the same. After simplification, we have this.

C(ar) / C(Xe) = M(xe) / M (ar) = 131/40 = 3.25

--> C (ar) > C(xe)

 

[chromosome21]

I am confused.

The following is true: The average kinetic energy of the molecules is proportional to absolute temperature (A result of Thermodynamics). At a given temperature the molecules of all species of gas, no matter what size shape or weight, have the same average kinetic energy.

Then how is it that Ar moves faster then Xe? Wouldnt they move at the same speed?

This gas stuff is really contradictory. Someone please explain.

ps I used this website for the fact: http://www.chem.ufl.edu/~itl/2045/lectures/lec_d.html

Nice question. I spent much time understanding this concept myself. I'm trying to simplify as much as I could. You need to know two laws for this:

1. KE is proportional to T (kelvin), it means, KE = c T(kelvin); and KE=1/2*m*v2 [don't worry about 'c', it's just a constant]
2. Vrms1/Vrms2 = square root of (MW2/MW1)

[Review the topic: graham's law of effusion]

Now you see, when T increases, KE increases, but KE does NOT equal to v. KE is equal to 1/2 mv2. So we can't clearly say that the "speed" (means v) also increases b/c of the temp! It depends on the "m" (weight") of the molecule as well.

Therefore, we kjnow that at the same temperature, all molecules would have the same "KE", but they may not have the same speed. In order to know the difference in speed of the molecules containing same KE, we need to know the second law. Law of effusion. That way, we could able to calculate which molecule would be "faster" (which molecule would have a higher speed), and by how much faster. Simply plug in the Molecular Weights of both molecules and do the simple math here. Remember: if you call Ar = molecule # 1, then Xe would be molecule #2. And place them properly on the equation. Don't make a mistake on numerator and denominator .
So, Vrms of Ar/Vrms of Xe = square root of (MW of Xe / MW of Ar).

So in simple language, we have the SAME KE for both Ar and Xe. But Ar has smaller MW, so it's faster than Xe.
KE = 1/2 m v2
For Ar: m is small, but v (speed) is faster = KE1
For Xe: m is large, but v (speed) is smaller = KE2
And, KE1 = KE2 at the same temperature!

Am I right or am I right? .. I am just bragging myself.. lol.. pardon me for that!

 

[wizi]

Nice question. I spent much time understanding this concept myself. I'm trying to simplify as much as I could. You need to know two laws for this:

1. KE is proportional to T (kelvin), it means, KE = c T(kelvin); and KE=1/2*m*v2 [don't worry about 'c', it's just a constant]
2. Vrms1/Vrms2 = square root of (MW2/MW1)

[Review the topic: graham's law of effusion]

Now you see, when T increases, KE increases, but KE does NOT equal to v. KE is equal to 1/2 mv2. So we can't clearly say that the "speed" (means v) also increases b/c of the temp! It depends on the "m" (weight") of the molecule as well.

Therefore, we kjnow that at the same temperature, all molecules would have the same "KE", but they may not have the same speed. In order to know the difference in speed of the molecules containing same KE, we need to know the second law. Law of effusion. That way, we could able to calculate which molecule would be "faster" (which molecule would have a higher speed), and by how much faster. Simply plug in the Molecular Weights of both molecules and do the simple math here. Remember: if you call Ar = molecule # 1, then Xe would be molecule #2. And place them properly on the equation. Don't make a mistake on numerator and denominator .
So, Vrms of Ar/Vrms of Xe = square root of (MW of Xe / MW of Ar).

So in simple language, we have the SAME KE for both Ar and Xe. But Ar has smaller MW, so it's faster than Xe.
KE = 1/2 m v2
For Ar: m is small, but v (speed) is faster = KE1
For Xe: m is large, but v (speed) is smaller = KE2
And, KE1 = KE2 at the same temperature!

Am I right or am I right? .. I am just bragging myself.. lol.. pardon me for that!

Chromosome21,

I am sorry but I doubt it. Don't get me wrong, I did use Law of Effusion to answer this question at first but then I thought about the definition of the Effusion (and watch Chad G3.2 again lol).

Law of Effusion basically compare the rate of speed of 2 gases to see which one ESCAPE faster and how much (lets say you put 2 gases in a container, and there is a hole somewhere on your container, Law of Effusion will be right in this situation). It doesn't apply to this situation where the question doesn't talk about any HOLE or diffusion.

From wiki: "....Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other"


Therefore, we can't use the law of effusion here. Although, it will give you the right answer for this question but if the question tells you to find the rate, Effusion won't be right.

Am I right? Are I right?

 

[chromosome21]

Chromosome21,

I am sorry but I doubt it. Don't get me wrong, I did use Law of Effusion to answer this question at first but then I thought about the definition of the Effusion (and watch Chad G3.2 again lol).

Law of Effusion basically compare the rate of speed of 2 gases to see which one ESCAPE faster and how much (lets say you put 2 gases in a container, and there is a hole somewhere on your container, Law of Effusion will be right in this situation). It doesn't apply to this situation where the question doesn't talk about any HOLE or diffusion.

From wiki: "....Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other"


Therefore, we can't use the law of effusion here. Although, it will give you the right answer for this question but if the question tells you to find the rate, Effusion won't be right.

Am I right? Are I right?

hahaha.. I love sdn for this reason! There are always ppl trying to prove you wrong!

First of all, I wasn't talking about the "definition" of effusion, and this question was not asking for diffusion. The op had trouble understanding why KE is the same at the same temp but the speeds are different! The two laws will make a person understand this concept very well.

Secondly, what are you pin pointing at? are you saying that we cant find the "speed" of Ar or Xe molecules? I never said Ar or Xe molecules are "this" fast! I only used the word "faster" or "bigger" etc. I was "comparing" two speeds, not giving speed of Ar or Xe.

are you trying to prove that v cannot be measured so we can't measure KE, and therefore, we can't really say if KE of both types of molecules are the same? What can't you find? and where I am wrong? I never wrote "the speed of Ar is this".. I wrote v of Ar is "faster"..

what is your question?

 

[wantVCUdental]

Chromosome21,

From wiki: "....Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other"


Therefore, we can't use the law of effusion here. Although, it will give you the right answer for this question but if the question tells you to find the rate, Effusion won't be right.

Am I right? Are I right?

I agree with chromosome21:
Vrms1/Vrms2 = square root of (MW2/MW1)

which is derived from 1/2mv^2 equation, as I previously stated.

no wizi, you are not right. What the wiki quotation state is basically what chromosome21's equation represent, if MW2=4, MW1=1, then V1/V2=2 which means the larger mass moves at half the speed as the smaller mass.

Also Law of Effusion can help you here, Law of effusion is derived from 1/2mv2 and the derivation assumes that the particles are floating around at random and they are bumping into the walls of the container. At the same average KE, smaller molecules move faster and has more chances of bumping against the walls and finding a hole whereas larger molecules move slower and have a lower chance.

 

[wizi]

hahaha.. I love sdn for this reason! There are always ppl trying to prove you wrong!

First of all, I wasn't talking about the "definition" of effusion, and this question was not asking for diffusion. The op had trouble understanding why KE is the same at the same temp but the speeds are different! The two laws will make a person understand this concept very well.

Secondly, what are you pin pointing at? are you saying that we cant find the "speed" of Ar or Xe molecules? I never said Ar or Xe molecules are "this" fast! I only used the word "faster" or "bigger" etc. I was "comparing" two speeds, not giving speed of Ar or Xe.

are you trying to prove that v cannot be measured so we can't measure KE, and therefore, we can't really say if KE of both types of molecules are the same? What can't you find? and where I am wrong? I never wrote "the speed of Ar is this".. I wrote v of Ar is "faster"..

what is your question?

lol... i love discussion. Its where you learn the concept.

I didn't say anything about K. I didn't say that you are wrong in term of explaining KE, forget about KE. I didn't ask any question. I also didn't state that we have to find the speed (or velocity) of Ar because base on the question, we can't find it. However, we can find the RATE between Ar and Xe.

My point here is that we can't use the Law of Effusion to explain this concept. Its different. Effusion is the rate where we have gas escape or diffusion.

....

 

[chromosome21]

lol... i love discussion. Its where you learn the concept.

I didn't say anything about K. I didn't say that you are wrong in term of explaining KE, forget about KE. I didn't ask any question. I also didn't state that we have to find the speed (or velocity) of Ar because base on the question, we can't find it. However, we can find the RATE between Ar and Xe.

My point here is that we can't use the Law of Effusion to explain this concept. Its different. Effusion is the rate where we have gas escape or diffusion.

....

what concept? you are asking to forget KE, but the question/the concept is about KE and speed and temp. umm.. i am confused.. see.. i didn't read other replies.. i only read the op's question and tried to explain what the op iddn't understand.. so.. please tell me what "concept" are you talking about?

 

[wizi]

no wizi, you are not right. What the wiki quotation state is basically what chromosome21's equation represent, if MW2=4, MW1=1, then V1/V2=2 which means the larger mass moves at half the speed as the smaller mass.

wantVCUdental,
I use that quote because I just want to make my point that if there is a " porous plug or escape" of gases then we can use Effusion to explain why "1" is faster "2" etc... but the question doesnt say anything about that.

So we can't apply rate of effusion here.

 

[chromosome21]

I agree with chromosome21:
Vrms1/Vrms2 = square root of (MW2/MW1)

which is derived from 1/2mv^2 equation, as I previously stated.

no wizi, you are not right. What the wiki quotation state is basically what chromosome21's equation represent, if MW2=4, MW1=1, then V1/V2=2 which means the larger mass moves at half the speed as the smaller mass.

Also Law of Effusion can help you here, Law of effusion is derived from 1/2mv2 and the derivation assumes that the particles are floating around at random and they are bumping into the walls of the container. At the same average KE, smaller molecules move faster and has more chances of bumping against the walls and finding a hole whereas larger molecules move slower and have a lower chance.

wantVCUdental,
I use that quote because I just want to make my point that if there is a " porous plug or escape" of gases then we can use Effusion to explain why "1" is faster "2" etc... but the question doesnt say anything about that.

So we can't apply rate of effusion here.

wantVCUdental is right.. The last paragraph of wantVCUdental should be the answer to your question.

 

[wizi]

what concept? you are asking to forget KE, but the question/the concept is about KE and speed and temp. umm.. i am confused.. see.. i didn't read other replies.. i only read the op's question and tried to explain what the op iddn't understand.. so.. please tell me what "concept" are you talking about?

When i say forget about KE, I really mean just forget it for our argument sake. i didnt mean to forget it for the question. I agree with you on that KE part.

All I want to say is that I am not sure using Effusion would be right

Anyway, the question should be giving more info...No point of arguing on this question anymore since both of us has the right answer. We just have different point of view on how to explain this question.

gotta study for Probability which is killing me