# Mean distance between air molecules

• songoku
In summary, at room temperature and pressure, the mean distance between air molecules is around 0.4 nm.
songoku

## Homework Statement

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

PV = nRT

## 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)

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.

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

24 dm3?

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

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.

mfb said:
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?
Volume per molecule = 24 x 10-3 / (6.02 x 1023)

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.
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

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?

mfb said:
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?

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

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

songoku
mfb said:
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
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.

songoku

Thank you very much

mfb

## What is the mean distance between air molecules?

The mean distance between air molecules, also known as intermolecular spacing, is the average distance between neighboring molecules in a gas. It is typically measured in nanometers or angstroms.

## How is the mean distance between air molecules calculated?

The mean distance between air molecules can be calculated using the ideal gas law, which relates the pressure, volume, and temperature of a gas to its number of molecules and their average kinetic energy. It can also be estimated using the Van der Waals equation, which takes into account the size and attractive forces between the molecules.

## Does the mean distance between air molecules vary?

Yes, the mean distance between air molecules can vary depending on factors such as temperature, pressure, and the type of gas. In general, as temperature increases, the molecules move faster and the mean distance between them increases. As pressure increases, the molecules are forced closer together and the mean distance decreases.

## Why is the mean distance between air molecules important?

The mean distance between air molecules is important for understanding the behavior and properties of gases. It affects the density, compressibility, and diffusion rate of a gas, and can also impact chemical reactions and gas interactions with surfaces.

## Is the mean distance between air molecules constant?

No, the mean distance between air molecules is not constant. It can change depending on external conditions such as temperature and pressure, as well as internal factors such as molecular size and intermolecular forces. However, for a given gas at a specific temperature and pressure, the mean distance between molecules will remain relatively constant.

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