Mean Free Path: Definition, Impact of Size & Density

[lando45]

My teacher has set me this question:

Which of the following statements about the mean free path is correct?

1. The mean free path decreases as the size of the molecules increases.
2. The mean free path increases with the size of the molecules.
3. The mean free path decreases as the density of molecules increases.
4. The mean free path increases with the density of molecules.
5. The mean free path depends on the temperature of the gas.
6. The mean free path is the average distance traveled by a molecule between collisions.
7. The mean free path is the longest distance a particle can travel without colliding.

It doesn't specify how many of the statements are correct, so I tried selecting 1, 5 and 6, but that's incorrect.

I believe the definition of "mean free path" to the be the average distance a particle travels in a container before it collides with another particle.

So I chose 1 because increasing the size of the particles would make collisions more frequent, due to less free space in the container, and therefore a lower mean free path.

I chose 5 because if the temperature of the gas increases, the particles will have more energy, and will therefore move more eratically, causing more collisions, and therefore a low mean free path.

And finally, I chose 6 because this is basically a definition of the term.

Now why didn't I get this question right? Are the 3 options I've chosen correct? Should I be selecting any additional options? Or are the ones I've selected incorrect?

 

[daveb]

Have you seen the formula for mean free path? From this can you tell what cause it to increase and decrease.

 

[kyle8921]

I would like to clarify that the correct statements about the mean free path are:

1. The mean free path decreases as the density of molecules increases.
2. The mean free path depends on the temperature of the gas.
3. The mean free path is the average distance traveled by a molecule between collisions.

Option 1 is correct because as the density of molecules increases, there are more collisions happening in a given space, resulting in a shorter mean free path.

Option 2 is also correct because the temperature of a gas affects the speed and energy of its molecules, which in turn affects their movement and likelihood of collisions. A higher temperature can lead to a longer mean free path.

Option 3 is the correct definition of the mean free path. It is the average distance a molecule travels before colliding with another molecule.

Option 4 is incorrect because as the density increases, the mean free path decreases, as explained in option 1.

Option 5 is incorrect because the temperature affects the speed and energy of the molecules, which affects their movement and likelihood of collisions, as explained in option 2.

Option 6 is correct and is the definition of the mean free path.

Option 7 is incorrect because the mean free path is an average and there is no specific limit or maximum distance a particle can travel without colliding. It depends on various factors such as temperature, density, and size of the molecules.