# Homework Help: V_RMS problem . Need help with it!

1. Dec 7, 2012

### NasuSama

V_RMS problem..... Need help with it!

1. The problem statement, all variables and given/known data

Find T, the temperature at which O2 gas molecules have an rms speed of v = 699 m/s.

2. Relevant equations

It's the rms form I have used.

$v_{rms} = √(3RT/M)$

3. The attempt at a solution

Let

M = 32 g/mol ≈ 32 * 10^(-3) kg/mol
v_rms = 699 m/s
R = 8.314 J/(mol * K)

Attempted to solve for T. Here is what I have:

$v_{rms}^{2} = 3RT/M$
$T = v_{rms}^{2}M/(3R)$

Plug and chug in the values, and I got 627 K, which is not correct.

2. Dec 7, 2012

### TSny

Re: V_RMS problem..... Need help with it!

Your work looks good to me. Are you sure the answer is incorrect?

3. Dec 7, 2012

### Staff: Mentor

Re: V_RMS problem..... Need help with it!

I seem to recall that the available energy modes for a diatomic gas are different than for a monatomic gas. 5/2 vs 3/2 as I recall. Some googling may be in order. Try "kinetic energy diatomic" or something along those lines.

4. Dec 7, 2012

5. Dec 7, 2012

### Staff: Mentor

Re: V_RMS problem..... Need help with it!

Well, so much for my memory then. Carry on, nothing to see here...

6. Dec 8, 2012

### NasuSama

Re: V_RMS problem..... Need help with it!

Check your calculation. What do you get? I have the answer 627 K, but the system marks it incorrect.

7. Dec 8, 2012

### TSny

Re: V_RMS problem..... Need help with it!

I also get 627 K. I assume the answer in to be in Kelvins.

8. Dec 8, 2012

### NasuSama

Re: V_RMS problem..... Need help with it!

Increasingly strange.

My professor told me to use this form which is right. v_rms = √(5RT/M).

I entered in the value of T for the HW assignment, and I got the right answer. How strange... :\

9. Dec 8, 2012

### TSny

Re: V_RMS problem..... Need help with it!

Yes, strange. Don't think he/she is correct. The 5 should be a 3. Just web-search "rms speed gas" for many examples.

10. Dec 8, 2012

### NasuSama

Re: V_RMS problem..... Need help with it!

Actually, he said that because the velocity is diatomic, but as you said; no matter if the particles are atomic or not, v_rms = √(3RT/M). I believe he is thinking of the kinetic energy of the diatomic particles.