Mean free path

there is a formula that describes mean free path for gases http://en.wikipedia.org/wiki/Mean_free_path

But perhaps we can reason out the problem without that formula. We have to assume that we have the same molar quantities of each gas otherwise the problem can not be solved.

Because we have the same number of molecules in each case we have the same average distance between molecules.

Now, let's focus on a single molecule. It seems that we can assume that the other molecules are stationary because they are as likely to be moving towards our molecule as away from it. Therefore, a given molecule has to travel the same distance before it bumps into another one whether it is He or CO2. In other words, speed does not matter, because we are dealing with distances here. He will get there faster but it still will travel the same distance.

If the gases were ideal (zero volume), then we would not expect any difference in mean travel path. But the volume of the molecule will contribute to collision frequency if gases are ideal with smaller molecules missing each other more often.

Notice that the formula above has the diameter in denominator. So, C is the correct answer.

Entadus said:

The mean free path of a gas molecule is the average distance that it will travel before it collides with another gas molecule. The molecules of a pure sample of which of the following gases (at 25°C and 1 atm) would be expected to have the shortest mean free path?

A.
Helium, because its molecules have the greatest velocity

B.
Oxygen, because its molecules are diatomic

C.
Carbon dioxide, because its molecules are the largest

D.
Nitrogen, because it is uncharged

I chose A (mean free path depends on velocity!!) and PR says the answer is C. I see how increasing the size of the molecules would decrease mean free path, but how do I eliminate answer A? The faster the molecules are going, the more often they collide, and therefore the shorter the mean free path. It seems like there are 2 correct answers! Thoughts?

Click to expand...

As you wrote, mean free path is the average distance. It does not matter how long it takes, it just matters how far it has to go. And the bigger the molecules are, the less the molecules need to travel.

Entadus said:

The mean free path of a gas molecule is the average distance that it will travel before it collides with another gas molecule. The molecules of a pure sample of which of the following gases (at 25°C and 1 atm) would be expected to have the shortest mean free path?

A.
Helium, because its molecules have the greatest velocity

B.
Oxygen, because its molecules are diatomic

C.
Carbon dioxide, because its molecules are the largest

D.
Nitrogen, because it is uncharged

I chose A (mean free path depends on velocity!!) and PR says the answer is C. I see how increasing the size of the molecules would decrease mean free path, but how do I eliminate answer A? The faster the molecules are going, the more often they collide, and therefore the shorter the mean free path. It seems like there are 2 correct answers! Thoughts?

Click to expand...

Answer is C, think of grahams law....molecules that are the largest travel slower, which means they have a shorter mean free path.