The question gave me the temperature and pressure of water vapor. I need to figure out the distance (in nanometers) between each molecule of gas assuming it is an ideal gas. It gives me the diameter of a water molecule (in nanometers).

 

I figured out the density of the water vapor in molecules/liter. Now I'm stuck. I think I could figure out how much space the total amount of molecules takes up in nm^3 in one liter, and also the total space of one liter in nm^3, but I'm not sure if that is relevant.

 

I just don't know how to proceed, this is a brain buster. I know the the number of molecules and volume, so I know it's possible to calculate, but I don't know what method I would use to do such a thing.

The volume occupied by a particle is the average distance between particles to the third power.

I'm not sure if atheist's method is more precise but I suspect that your question is expecting you to assume the water molecules occupy no volume in themselves (they are point masses). This is a common assumption in the kinetic theory of gases, although it's obviously not true it often gives a very respectable answer.

 

I'm not actually sure how to go about the math but i suspect that assumption is your first step.

Assuming it is an ideal gas means he should assume the molecules are point masses (and also don't have intermolecular forces). But I'm not sure if that matters.

 

Since you know the number of molecules per liter, you should be able to calculate the number of liters per molecule. But volume is distance cubed, so if you take the cube root you get a distance like Atheist said. I think this is what they are looking for but I'm not sure.