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Offline jennielynn_1980

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Kinetic Molecular Theory (I think)
« on: May 28, 2006, 02:09:21 PM »
I have to answer this question and I am wondering if I am understand what is being asked:

A cylinder contains a mixture of hydrogen and chlorine molecules.  Compare without doing any calculations:

a) the relative mass of the molecules (check periodic table)
My answer: Hydrogen has an atomic mass of 1.00794 and chlorine has an atomic mass of 35.453.  Therefore each chlorine moleclue has approx. 35 times the mass of each hydrogen molecule.

b) the temperature of each gas
My answer: the temperature of the each gas must be the same if they are occupying the same space.  As both are gases, the temperature must be around 273K for them both to maintain this state.

c) the average kinetic energy of the molecules
My answer: Although each molecule in the mixture may have different kinetic energy, the average kinetic energy of the mixutre would be proportional to the temperature.

d) the average speed of the molecules
My answer: The molecules would be in constant, rapid motion in a straight line.  The speed and degree of motion would be dependant upon the exact temperature of the gases.

Offline Yggdrasil

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Re: Kinetic Molecular Theory (I think)
« Reply #1 on: May 28, 2006, 02:40:04 PM »
Quote from: jennielynn_1980
d) the average speed of the molecules
My answer: The molecules would be in constant, rapid motion in a straight line.  The speed and degree of motion would be dependant upon the exact temperature of the gases.

If the K = (1/2)mv2 and the molecules have different masses and the same kinetic energies, how can their speeds be the same?

Offline jennielynn_1980

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Re: Kinetic Molecular Theory (I think)
« Reply #2 on: May 28, 2006, 03:51:42 PM »
You raise a good point....hmmm, does that qualify as a calculation though?  We aren't allowed to do any calculations.  Or is it just saying that the kinetic energy of something with more mass will be more than the kinetic energy of something with less mass?

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Re: Kinetic Molecular Theory (I think)
« Reply #3 on: May 28, 2006, 04:25:43 PM »
You raise a good point....hmmm, does that qualify as a calculation though?  We aren't allowed to do any calculations.  Or is it just saying that the kinetic energy of something with more mass will be more than the kinetic energy of something with less mass?

I don't see a need for any "calculations" here. If two molecules with different masses have the same kinetic energy they MUST have dfferent speeds. Lighter one must be faster to have the same kinetic energy as the heavier one. That's qualitative reasoning, without any calculations - you will need calculations to say what is the ratio of the speeds, but that will be quantitative question.

each chlorine moleclue has approx. 35 times the mass of each hydrogen molecule.

Right. You remember these are diatomics?

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As both are gases, the temperature must be around 273K for them both to maintain this state

That's completely wrong. At 500K they will change to solids, or what?

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average kinetic energy of the mixutre would be proportional to the temperature.

Of the mixture, or the molecule?
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Offline jennielynn_1980

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Re: Kinetic Molecular Theory (I think)
« Reply #4 on: May 28, 2006, 10:44:41 PM »
-they are Cl2 and H2 Does this change my answer?  No, right, because I said the molecules have 35 times more mass.  Were you just pointing out that it is correct to say molecule not atom because they are diatomic?


-Okay, so how do I know the temperature?  I mean, they are both gases and 273K right?  So they have to be at a temperature where this state is maintained.  Or is it right to say that I can't know the temperature to any degree of accuracy because they would maintain their state over a wide range of temperatures?


-The average kinetic energy of the mixture becasue the Kinetic MOlecular Theory says that the average kinetic energy of a whole system is proportional to the temperature.

Offline Donaldson Tan

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Re: Kinetic Molecular Theory (I think)
« Reply #5 on: May 28, 2006, 11:06:45 PM »
I believe the term relatve mass refers to the relative molecular mass (RMM), and not the ratio of the molecular mass of Cl2 to that of H2. Both masses are compared to the mass of 1/12 of the C-12 atom, so the RMM is 2 for H2 and 71 for Cl2

If both hydrogen and chlorine are in the same container, they must be at thermal equilibrium, so both gases share the same temperature, and thus exhibits the same average kinetic energy. There is no way you can quantify the temperature of the mixture, unless more information/data is provided in the question.
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Offline jennielynn_1980

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Re: Kinetic Molecular Theory (I think)
« Reply #6 on: May 29, 2006, 12:32:25 PM »
So my revised answers would be:

a) Hydrogen has an atomic mass of 1.00794 and chlorine has an atomic mass of 35.453.  (here I am not sure I should include the RMM because I am not supposed to be doing any calculations).

b) Because both gases are in the same container, they must share the same temperature.  However, it is impossible to know the exact temperature to an degree of accuracy because there are a wide range of temperatures in which the molecules would remain in a gaseous state.

c) If both gases share the same temperature, then the average kinetic energy would be the same for both types of molecules.  Kinetic Molecular Theory postulates that although each molecule may not have the same kinetic energy, the average kinetic energy of a system is proportional to the temperature.

d) The molecules would be in constant, rapid motion in a straight line.  The degree of motion would be related directly to the temperature.  If the molecules were at a high temperature they would move more quickly than at a low temperature.  However their speeds of the two types of molecules would be different.  The hydrogen molecules would be moving faster than the chlorine molecules because they are lighter and it follows that to maintain the same kinetic energy of the heavier chlorine molecules, they would have to be moving more rapidly.

Thanks for all you help everyone!  I swear I would be getting nowhere fast without all of you help :)

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Re: Kinetic Molecular Theory (I think)
« Reply #7 on: May 29, 2006, 12:47:25 PM »
Much better now, although you are still partially wrong, or at least your answers are ambiguous.

b) Because both gases are in the same container, they must share the same temperature.  However, it is impossible to know the exact temperature to an degree of accuracy because there are a wide range of temperatures in which the molecules would remain in a gaseous state.

Why do you still try to say ANYTHING about the temperature, if you are NOT ASKED ABOUT? They have the same temperature. Period.

Quote
c) If both gases share the same temperature, then the average kinetic energy would be the same for both types of molecules.  Kinetic Molecular Theory postulates that although each molecule may not have the same kinetic energy, the average kinetic energy of a system is proportional to the temperature.

Perhaps my English fails me, but for me "average kinetic energy of a system" is something completely different from "avareage kinetic energy of the molecule in a system". Your "system" will have some kinetic energy once you will throw the cylinder. As long as it stands still on the desk it have no kinetic energy by itself.

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d) The molecules would be in constant, rapid motion in a straight line.

No. They are in a zig-zag motion, as they collide billions times per second.

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The degree of motion would be related directly to the temperature. 

Average speed will be related to temperature - no idea what is "degree of motion".
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Offline jennielynn_1980

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Re: Kinetic Molecular Theory (I think)
« Reply #8 on: May 29, 2006, 01:43:59 PM »
Much better now, although you are still partially wrong, or at least your answers are ambiguous.

b) Because both gases are in the same container, they must share the same temperature.  However, it is impossible to know the exact temperature to an degree of accuracy because there are a wide range of temperatures in which the molecules would remain in a gaseous state.

Why do you still try to say ANYTHING about the temperature, if you are NOT ASKED ABOUT? They have the same temperature. Period.

Quote
c) If both gases share the same temperature, then the average kinetic energy would be the same for both types of molecules.  Kinetic Molecular Theory postulates that although each molecule may not have the same kinetic energy, the average kinetic energy of a system is proportional to the temperature.

Perhaps my English fails me, but for me "average kinetic energy of a system" is something completely different from "avareage kinetic energy of the molecule in a system". Your "system" will have some kinetic energy once you will throw the cylinder. As long as it stands still on the desk it have no kinetic energy by itself.



Quote
d) The molecules would be in constant, rapid motion in a straight line.

No. They are in a zig-zag motion, as they collide billions times per second.

Quote
The degree of motion would be related directly to the temperature. 

Average speed will be related to temperature - no idea what is "degree of motion".


In the information I was given to read on Kinetic Molecular Theory it states that "although each molecule does not necessarily have the same kinetic energy, the average kinetic energy of the whole system is proportional to the temperature.  The theory assumes that particles are in constant motion and that the degree of motion is governed by heat."  It also says that "all collisions are perfectly elastic and the whole system has constant kinetic energy."

Also it says as one of the theory postulates that: "these molecules are in constant rapid motion in a straight line."

Again the text I have uses that phrase "degree of motion" and I thought it was referring to the general motion of gas particles.

I completely understand your points and I agree with you.  So either I am reading the info I have wrong or the info itself is incorrect.  Unfortunately I dont' know which.  :-\

Offline xiankai

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Re: Kinetic Molecular Theory (I think)
« Reply #9 on: May 29, 2006, 10:52:44 PM »
Quote
a) Hydrogen has an atomic mass of 1.00794 and chlorine has an atomic mass of 35.453.  (here I am not sure I should include the RMM because I am not supposed to be doing any calculations).

find the mass of 2 hydrogen atoms, because thats what a molecule of hydrogen (H2). Same goes for chlorine, Cl2

i dont think they were asking for the ratio of the masses. geo just pointed out that the "relative" is to mean their mass as defined by 1/12 of a C atom , not that Cl is relative to H.

Quote
b) Because both gases are in the same container, they must share the same temperature.  However, it is impossible to know the exact temperature to an degree of accuracy because there are a wide range of temperatures in which the molecules would remain in a gaseous state.

Borek mentioned that you need not explained so much, because a mixture has the same properties as its constituents, after all.

Quote
c) If both gases share the same temperature, then the average kinetic energy would be the same for both types of molecules.  Kinetic Molecular Theory postulates that although each molecule may not have the same kinetic energy, the average kinetic energy of a system is proportional to the temperature.

Borek has a point. be specific in your descriptions to avoid ambiguity. try not to copy your text word-by-word, but adapt it to what you understand. the text is correct, but it is quite vague. its your job to clear it up  :)

Quote
d) The molecules would be in constant, rapid motion in a straight line.  The degree of motion would be related directly to the temperature.  If the molecules were at a high temperature they would move more quickly than at a low temperature.  However their speeds of the two types of molecules would be different.  The hydrogen molecules would be moving faster than the chlorine molecules because they are lighter and it follows that to maintain the same kinetic energy of the heavier chlorine molecules, they would have to be moving more rapidly.

you need not say anything about the direction. they asked for "speed", not "velocity". so just explain the magnitude of speed.

degree of motion can be meant as the direction it moves, or the magnitude at which it moves. again this is ambiguous and should be rectified.
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Offline jennielynn_1980

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Re: Kinetic Molecular Theory (I think)
« Reply #10 on: May 31, 2006, 11:43:06 AM »
So are these revised answers more concise?

A cylinder contains a mixture of hydrogen and chlorine molecules.  Compare without doing any calculations:

a) the relative mass of the molecules (check periodic table)
 Hydrogen has an atomic mass of 1.00794 and chlorine has an atomic mass of 35.453.  

b) the temperature of each gas
Because both gases are in the same container, they must share the same temperature.

c) the average kinetic energy of the molecules
If both gases share the same temperature, then the container would have an average kinetic energy that would be relative to the temperature inside the container.

d) the average speed of the molecules
The molecules would be in constant, rapid motion.  The speed of motion would be related directly to the temperature.  However the speeds of the two types of molecules would be different.  The hydrogen molecules would be moving faster than the chlorine molecules because they are lighter and to maintain the same kinetic energy of the heavier chlorine molecules, they would have to be moving faster.

Offline Yggdrasil

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Re: Kinetic Molecular Theory (I think)
« Reply #11 on: May 31, 2006, 01:28:04 PM »
All good except for (a)

a) the relative mass of the molecules (check periodic table)
 Hydrogen has an atomic mass of 1.00794 and chlorine has an atomic mass of 35.453.  

The question is asking about hydrogen and chlorine molecules (H2 and Cl2), not hydrogen and chlorine atoms, so you should put the molecular weights of the molecules rather than the atomic weights of the atoms.

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Re: Kinetic Molecular Theory (I think)
« Reply #12 on: May 31, 2006, 01:59:34 PM »
c) the average kinetic energy of the molecules
If both gases share the same temperature, then the container would have an average kinetic energy that would be relative to the temperature inside the container.

We have been throug that already. Not "container have kinetic energy" but "molecules in the container have kinetic energy".
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Offline jennielynn_1980

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Re: Kinetic Molecular Theory (I think)
« Reply #13 on: May 31, 2006, 02:37:05 PM »
I suck.  You guys must think I am a total moron.  :(  Here are my revised and hopefully final answers.  If these aren't right, shoot me!

a)The hydrogen molecules would have a molar mass 2.0 g/mol and the chlorine molecules would have amolar mass of 70.9 g/mol.

b) Because both gases are in the same container, they share the same temperature. 

c) If both gases share the same temperature, then the molecules would have an average kinetic energy that would be relative to the temperature inside the container.

d) The molecules would be in constant, rapid motion.  The degree of motion would be related directly to the temperature.  The speeds of the two types of molecules would be different.  The hydrogen molecules would be moving faster than the chlorine molecules because they are lighter and to maintain the same kinetic energy of the heavier chlorine molecules, they would have to be moving faster

Offline Donaldson Tan

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Re: Kinetic Molecular Theory (I think)
« Reply #14 on: May 31, 2006, 04:44:28 PM »
I suck.  You guys must think I am a total moron.  :(

We wouldn't help you if we think this way. In fact, your revised answer reflets you are not a moron :D

c) If both gases share the same temperature, then the molecules would have an average kinetic energy that would be relative to the temperature inside the container.

Kinetic Gas Theory states that the average kinetic energy (KEaverage) is directly proportional to the thermodynamic temperature (T), ie. KEaverage = (3/2)kT where k is boltzman constant.

d) The molecules would be in constant, rapid motion.  The degree of motion would be related directly to the temperature.  The speeds of the two types of molecules would be different.

KEaverage = (3/2)kT (where k is boltzman constant)

3 reflects the fact that there is 3 degrees of freedom in the motion of the gas molecules (ie. the gas molecules can move in the x-, y- or z- direction (or a combination of x-y-z). The speeds are different because of the different mass of the molecules.

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