How long does it take for air molecules to collide at STP?

[flower76]

My text doesn't seem to talk about average separation of molecules, so I can only get so far with this problem. Help would be appreciated.

The problem reads:
From the average separation between air molecules at STP, and their mean speed, estimate how long it would take one molecule to move into the region occupied by another. Assume that air consists mainly of nitrogen molecules.

so far I have figured our the mean speed

v=sqrt(3kT/m) = 490m/s

then if I can figure out the avg separation which should be in meters, I figure I would just divide the avg separation by the speed which would give me the time.

Am I on the right track? And how do I find average separation?

Thanks

 

[SpaceTiger]

Am I on the right track? And how do I find average separation?

What is the density of air? How might this related to the average separation?

 

[flower76]

Density of air is 1.29 kg/m^3, and the mass of N2 is 0.028 kg. If I divide the mass by the air density I have 0.022m^3. I'm not sure if this is what I am supposed to be doing?

 

[SpaceTiger]

Density of air is 1.29 kg/m^3, and the mass of N2 is 0.028 kg. If I divide the mass by the air density I have 0.022m^3. I'm not sure if this is what I am supposed to be doing?

That's a good start. Now, let's say I have a particle in the air. How large a sphere do I have to draw around it before I expect to find another particle?

 

[flower76]

Well the vol of a sphere is 4/3(pi(r^3)) therefore r by my calculations would be 0.174 m. so to find another particle it would be 2r which is 0.348 m?

 

[SpaceTiger]

I'm not paying enough attention here. Your number density estimate is way off. Would you please show how you converted to number density from mass density.

 

[flower76]

I'm not sure which calculation you're referring to. If its distance between atoms, I just took the the mass of N2 0.028kg and divided by the density of air 1.29kg/m^3 to get 0.022m^3

 

[flower76]

Oops I see where I may have gone wrong my mass for N2 should be 4.7x10-26kg.

So with this number I know have a volume of 3.64x10-26 m^3 for each N2 molecule.

Do I continue using this for volume of a sphere?

 

[SpaceTiger]

So with this number I know have a volume of 3.64x10-26 m^3 for each N2 molecule.

Do I continue using this for volume of a sphere?

Yes, that will be fine.

 

[flower76]

Ok so I found that r=2x10-9 m

I took this distance of molecules and divided it by my previously found velocity (490m/s) and found that it would take 4.1x10-12 sec for one molecule to move into the region occupied by another.

Can anyone verify if this is correct? Or do I have to consider the radius of the molecule who's space I'm moving into? I'm confused.

 

[flower76]

I'm still not sure about this question, I came across a similar question and in it they took the cubic root of the N2 volume to find the average separation. Therefore the separation would be 3.3 a 10-3 m.

I don't know which is the right one to use.

 

[SpaceTiger]

Well, I'm not sure what the problem means by "how long it would take one molecule to move into the region occupied by another", but I'll assume they're asking how long a molecule goes before colliding with another. the average separation only tells you the approximate distance to the nearest molecule. Most of the time the particle won't be moving in the direction of that nearest molecule, so you need to take a different approach.

Suppose your particle, with a radius, R, is moving along through the gas. How much volume does it sweep out in a time, t? How large does this volume need to be before it encloses one other molecule, on average?

 

[flower76]

so I've been playing around with this questionand I think that I need to figure out average distance between molecules. So far I have only determined the volume/molecule and the radius of them based on this.
So if I use the mean free path equation I think I should have all the variables to find the distance between each molecule.

I'm thinking it looks like: l= m/(sqrt of 2)(pi*density*diameter^2)
based on my prev finding l = 5.2x10-10m

Does this sound right?

 

[flower76]

I have to hand my assignment in tomorrow and would really like to get this question, can anyone tell me if it is the mean free path that I'm supposed to be finding and if it looks right?

I then took the number for mean free path and divided by the velocity I previously found and got 1.06 x 10-12 sec?

I don't have a clue if this is right!?