The distance traveled by a molecule at a specific temperature

[Hananism]

Homework Statement

In the homework, I am supposed to know the average distance traveled by the given molecule (see the attached image for the full exercice)

Relevant Equations

I've found one equation not sure if it is the one I should use. ( it's in the second image attached)

I found this equation:

and kB and T are Boltzmann constant and temperature, respectively.

 

[mjc123]

The mean free path is irrelevant, as that refers to the gas phase, and we are talking about the diffusion of CO molecules on a nickel surface. Presumably the CO molecules are loosely bound to Ni atoms, and the process involves jumping from one Ni atom to a neighbour, so you need to know the rate of jumping, and how far apart the Ni atoms are on a (100) surface. You also need to know the rate of desorption.

 

[Hananism]

The mean free path is irrelevant, as that refers to the gas phase, and we are talking about the diffusion of CO molecules on a nickel surface. Presumably the CO molecules are loosely bound to Ni atoms, and the process involves jumping from one Ni atom to a neighbour, so you need to know the rate of jumping, and how far apart the Ni atoms are on a (100) surface. You also need to know the rate of desorption.

Sorry I modefied everything! I found another equation, other than the free path one, what do you think?

 

[mjc123]

Do not modify your original post (except to correct obvious errors like typos). It makes responses to that post, like mine, look meaningless. If you've got something new to say, say it in a fresh post.

Yes, the Arrhenius equation is what you want. Actually, thinking about it, perhaps you don't need the Ni atom spacing after all, as D is a diffusion constant rather than a rate constant.

 

[Hananism]

Do not modify your original post (except to correct obvious errors like typos). It makes responses to that post, like mine, look meaningless. If you've got something new to say, say it in a fresh post.

Yes, the Arrhenius equation is what you want. Actually, thinking about it, perhaps you don't need the Ni atom spacing after all, as D is a diffusion constant rather than a rate constant.

I am truly sorry to have done so, I thought of modifying it as long as no one has answered it yet, byt I modified it with the time you answered. Sorry again and thank you very much.
But I don't know, how can I use this to calculate that average distance? I don't understand how it is related to the Arrhenius equation and the diffusion constant.
As this physics part is entirely new to me, I would appreciate it if I get an answer from you about that.

 

[mjc123]

If it is entirely new, why are you being given homework questions on it? What have you learned?

Hmm.. doesn't seem as obvious as I first thought. Bulk diffusion rate depends on the concentration gradient, which you have no information about. If the concentration is uniform, there is no net diffusion, but individual molecules are still moving around. The diffusion coefficient can be related to molecular properties e.g. in the kinetic theory of gases, but gas diffusion is not an Arrhenius process like this. I suppose the diffusion coefficient could be related to the rate of molecular jumping, as mentioned in my first post, but that seems a bit much for a homework question - unless it's something you're supposed to have studied.