kinetic energies per molecule

[p8p3rkut]

How does the average kinetic energies per molecule compare in a mixture of hydrogen and nitrogen gases at the same temperature?

 

Really, I have read this stupid textbook 6 times. No explanation of this question no where. Please help!!!!

[DJBruce]

Look at the equation for the kinetic energy of a gas; what variables are there? When you look at it the answer should be obvious because there is only one variable and one constant.

[p8p3rkut]

Still no help, i just read about the kinetic energy section agian and I am still lost??

[CaptainPanic]

Maybe you can post an equation that you think might be useful?

 

Or tell us which parameters are involved?

 

Or explain something about kinetic energy in general?

 

What determines the velocity of a molecule?

 

In short: show us that you tried to understand some of it, and we'll gladly help you... I'm sorry, but saying that you read something 6x is not much help, although it's always nice to blow off some steam and complain. I know how frustrating it can be to really make an effort and still fail. It's not uncommon that the book is to blame, because of an unnecessarily complicated explanation.

[p8p3rkut]

Well the thing is I don't know. Because I cant find it no where in my book about the gaes and what they contain. This is a ezam study quiz and I am lost. have no idea what it is even talking about.

[swansont]

What is the definition of temperature?

[CaptainPanic]

Well the thing is I don't know. Because I cant find it no where in my book about the gaes and what they contain. This is a ezam study quiz and I am lost. have no idea what it is even talking about.

 

A gas is made up of molecules.

So, a mixture of hydrogen gas and nitrogen gas will contain: hydrogen (H2) and nitrogen (N2) molecules.

 

Can you say anything about any possible difference in speed between the hydrogen and nitrogen molecules in the gas? The temperature of both molecules is the same (because they're mixed).

[swansont]

A gas is made up of molecules.

So, a mixture of hydrogen gas and nitrogen gas will contain: hydrogen (H2) and nitrogen (N2) molecules.

 

Can you say anything about any possible difference in speed between the hydrogen and nitrogen molecules in the gas? The temperature of both molecules is the same (because they're mixed).

 

Looking at the speeds is probably not as helpful, since that adds more variables to the discussion. The question is about kinetic energy, and the answer should become apparent once the meaning of temperature is given.

[CaptainPanic]

Looking at the speeds is probably not as helpful, since that adds more variables to the discussion. The question is about kinetic energy, and the answer should become apparent once the meaning of temperature is given.

 

But the speed is very relevant, because kinetic energy equals:

 

[math]E=0.5\cdot{m\cdot{v^2}}[/math]

 

And hydrogen has a much higher speed than nitrogen, at the same temperature. I explained this once in another thread (post #8).

 

Since we're now confusing the novice people, I fear that I cannot leave out formulas. I have to go straight for the answer.

 

What's the velocity of a molecule? It depends on temperature and molar mass.

 

Nitrogen (N2):

[math]\overline{v}=\sqrt{\frac{8\cdot{R\cdot{T}}}{\pi\cdot{M}}}=\sqrt{\frac{8\cdot{8.3145\cdot{298}}}{3.14159\cdot{0.02802}}}=474.5 m/s [/math]

Hydrogen (H2):

[math]\overline{v}=\sqrt{\frac{8\cdot{R\cdot{T}}}{\pi\cdot{M}}}=\sqrt{\frac{8\cdot{8.3145\cdot{298}}}{3.14159\cdot{0.002016}}}= 1769 m/s [/math]

 

Kinetic energy is equal to:

 

[math]E=0.5\cdot{m\cdot{v^2}}[/math]

 

Nitrogen:

 

[math]E=0.5\cdot{0.02802\cdot{474.5^2}}=3154 J/mol[/math]

 

Hydrogen:

 

[math]E=0.5\cdot{0.002016\cdot{1769^2}}=3154 J/mol[/math]

 

Tadah.

Edited June 29, 2009 by CaptainPanic

[swansont]

But you took the long way around. Their kinetic energies are equal because they are at the same temperature, which is how temperature is defined — you used this information to show the answer, when you noted that speed depends on temperature and mass.

 

Temperature is proportional to the average KE of the molecules, and they are at the same temperature. Therefore, they have the same KE.

 

KE = 3/2 kT

 

Done. No mass, no speed. Not necessary.

[CaptainPanic]

I was assuming that p8p3rkut (who started this thread) was working on a homework assignment and might not even know Mr. Boltzmann.

 

Then again, the formula that I posted was also something I didn't learn at high school... so I'm not sure who gave the best homework-reply.

 

Anyway, together we probably gave the most complete answer possible.

[swansont]

I was assuming that p8p3rkut (who started this thread) was working on a homework assignment and might not even know Mr. Boltzmann.

 

Then again, the formula that I posted was also something I didn't learn at high school... so I'm not sure who gave the best homework-reply.

 

Anyway, together we probably gave the most complete answer possible.

 

But my answer works without the equation. So Mr. Boltzmann need not attend the party — the very definition of temperature tells you that any collection of molecules at a temperature will have the same average KE. It's a question one should be able to answer after 15 minutes of thermo class, before any of the equations are derived/given.

 

Going through the equations is a nice exercise, though.