# Mean distance between air molecules

1. Jan 18, 2017

### songoku

1. The problem statement, all variables and given/known data
Which of the following is closest to the mean distance between air molecules at room temperature and pressure (298 K and 101325 Pa)? Assume air is made of 79% N2 and 21% O2 by moles.
A 0.4 nm
B 4 nm
C 40 nm
D 400 nm
E 4 μm

2. Relevant equations
PV = nRT

3. The attempt at a solution
My idea is to find the volume and take the cube root of volume to get the mean distance between air molecules. However, I don't know how to find the n (number of moles)

2. Jan 18, 2017

### Staff: Mentor

What is the volume of 1 mole at room temperature/pressure?

You don't need V and n separately: The answer does not depend on the size of the room. Only their ratio is relevant.

3. Jan 18, 2017

### songoku

24 dm3?

I don't get this hint. I need to find the ratio of volume and number of moles? What is the relation of the ratio to the distance between molecules?

4. Jan 18, 2017

### Staff: Mentor

You know how many molecules are in one mole of gas, and you know the volume this mole occupies. How much volume is there per molecule?

The distances are not fixed, of course, but you can get something like a typical distance if you imagine all molecules arranged in a regular pattern, e.g. each molecule gets its own cube. That relates a volume to a distance.

5. Jan 19, 2017

### songoku

Volume per molecule = 24 x 10-3 / (6.02 x 1023)

I can image a molecule (sphere) located inside a cube with the sphere touches the inner of the cube but I still don't know how it relates to the mean distance between molecule.

What should I find actually to get the mean distance?

Thanks

6. Jan 19, 2017

### Staff: Mentor

Imagine a room filled with 1m x 1m x 1m cubes. Put an atom in the center of each cube. You now have 1 atom per cubic meter. The shortest distance between adjacent atoms is 1 meter.
1 cubic meter per atom leads to a distance of 1 meter between atoms.

How can you apply the same approach to your (smaller) volume per atom?

7. Jan 19, 2017

### songoku

Ah I see. I just need to take the cube root of 24 x 10-3 / 6.02 x 1023 and it is the answer.

So the information about percentage of nitrogen and oxygen doesn't matter at all?

Thanks

8. Jan 19, 2017

### haruspex

9. Jan 20, 2017

### Staff: Mentor

It matters if you start with the mean density of air, then you need the average mass per molecule.

@haruspex: Atoms are not arranged in a cubic lattice of course, but the question asks for a rough estimate, where we don't care about prefactors close to 1.

10. Jan 20, 2017

### haruspex

Yes, I appreciate that only a rough estimate is needed to answer the question. Just clarifying to the OP that the real answer is a bit different.

11. Feb 12, 2017