# Finding velocity of gas molecule

1. Sep 10, 2013

### Miike012

Equations:
1. vrms = √(3RT/M)
2. PV = nRT
3.M = mNA

I want to answer part a.
I am given T,P, and the density of gas molecules (d).

From equation 3. I want to solve for m.
m = dV = d(nRT/P)
m[NA] = M = d(nRT/P)[NA] = dNRT/P; N = nNA.

From equation 1.
vrms = √(3RTP/(dNRT)) = √(3P/dN).
I get stuck at this part because I dont know the value of N.

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2. Sep 10, 2013

### Staff: Mentor

What is that equation?

3. Sep 10, 2013

### Miike012

Is M molar mass or mass?
I thought it was molar mass...

4. Sep 10, 2013

### Staff: Mentor

I'm asking you! The equation doesn't make sense to me. I think it is wrong and that this is where your problem lies.

Please detail what are M, m and NA.

5. Sep 10, 2013

### Miike012

I added the equations in the attachment from the book

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6. Sep 10, 2013

### Miike012

I think I figured it out. M=mNa and m = M/Na = d*v, so M = d*v*Na

7. Sep 10, 2013

### Staff: Mentor

If $m$ is the mass of one molecule, then how can $m = d \times V$?

8. Sep 10, 2013

### Miike012

Well it could be the integral of a single mass through volume V. But I am not sure. Do you have a suggestion?

9. Sep 10, 2013

### Miike012

And it didn't work because the variable V from equation 2 contains the value n which is unkown

10. Sep 10, 2013

### Staff: Mentor

What about $M_\mathrm{sam}$?

11. Sep 10, 2013

### Miike012

Msam = M*n

12. Sep 10, 2013

### Miike012

And M = dRT/P

13. Sep 10, 2013

### Miike012

Thank you!

14. Sep 10, 2013

### Miike012

I am now solving for M for part b.

M = 3RT/(Vrms)2

The units of this RHS is Joul/(mol*Kelvin)*Kelvin/(meter/second)2 = Joul*Second2/(mol*meter2)

The LHS has units of

kilograms/mole.

How does the RHS turn into kilograms/mole?

15. Sep 10, 2013

### Staff: Mentor

I didn't understand $M = m N_\mathrm{A}$ because you had written $m = d \times V$, so I had taken $m$ to be the total mass of the gas. Using the notation of the book, $m$ is the mass of one molecule and $M_\mathrm{sam}$ the total mass of the gas, therefore the correct relation is $M_\mathrm{sam} = d \times V$, which I guess is what you now have figured out, which you used along with $n = M_\mathrm{sam} / M$.

Go back to the definition of the joule in terms of base units:

J = kg m2 s-2

16. Sep 10, 2013

### Miike012

Thank you for all your help.

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