Temperature and molecular kinetic energy. [PLEASE help me]

[gabloammar]

Homework Statement

Okay I've been stuck with this problem for two whole freaking days now, and it's really gotten on my nerves and I've given up completely on it because I'm positive I didn't pick up the concept for this even though I studied it from about 4 different books! It's just a simple calculation but I don't know how to think while solving it, so PLEASE help me. Here it is.Q. Calculate the average speed of helium molecules at room temperature and pressure.

That's it. Not a word more.

Homework Equations

I've only got temperature [it's supposed to be 293 K in my case] and 10⁵ Pa is the pressure. So the single equation that comes to my mind is,

E = $\frac{3kT}{2}$

with 'k' being the Boltzmann constant 1.38 x 10^-23 J K^-1

The Attempt at a Solution

I find the value for E, which is a retardedly low value but I use it nonetheless because I've got nothing else going for me.

E = 6.0651x10^-21

Now, I use $\frac{1}{2}$m<c²>.
m equals the mass for one mole of helium, which is 4g. [going on a whim here]
and c² is the mean square speed. So now it's,

$\frac{1}{2}$ x 4 x <c²> = 6.0651x10^-2

I get <c²> = 3.03x10^-21

and then I take the square root to get the value of c and over here c equals 5.505x10^-11 ms^-1.

The actual answer is supposed to be 1350 ms^-1.

I see I haven't used the pressure anywhere in this. That's because I don't see where I CAN use it. -____-
Someone PLEEASEE help! I've been stuck with this for HOURS and my brain's turning into mush now! Plus if someone could clear up what my misconceptions about this specific equation are, then that'd be welcome so I don't make this mistake again. [I've got another question asking about finding the speed of molecules as well and I can't find it again because of the ridiculously low values I'm getting, but I'm not putting that up here because I know if I'm able to solve this single question then the rest should be cake. Thanks! [and sorry I've made it so long, just wanted to make sure I didn't miss anything]]

 

[Spinnor]

You could work backwards using the velocity to find the mass. It's the mass of a single helium atom.

 

[gabloammar]

Okay wait let me do that, and I'll get back to you.

 

[gabloammar]

Okay I took the answer and put it in the energy formula and I got the mass as 6.65x10^-27 kg. The problem with this is that, the only things I can use in this question are the temperature, the pressure I suppose, the mass of one mole of Helium atoms [in kg, I'd been doing it in grams uptil now, but that's not helped me in the slightest], the Boltzmann constant, and that's it I think.

Finding the mass of one atom of Helium through this way [which I'm not even sure if I've done the right way or not] would require me to know the value for speed beforehand, but I don't. So NOW help me.

 

[gabloammar]

Btw, I googled 'the mass of a helium atom,' and though it didn't give the value for that, I did find a yahoo answers page with a question mostly similar to mine. But the equation that guy uses, I haven't ever seen it. He even gets the speed for the Helium, but I don't really understand how he gets it. Any help?

http://answers.yahoo.com/question/index?qid=20110106221858AA9QS1T

 

[gabloammar]

Omg I feel like crying! Done! I completely got the idea that I COULD find the mass of one atom of helium from the molar mass of helium out of my head! It came back and I did it and the now my answer's correct! :D

1351.82 metres per second!

Thank youu!