How close are the atoms that make up the air we breathe ?

At room temperature and pressure one mole (6 x 10^23 particles/atoms/molecules) of a gas fills 24 dm^3 (Litres).

This means that in every cubic centimeter (one millilitre) of air there are 2.5 x 10^19 molecules.

If we forget about the rapid movement and think how many static molecules this means in each dimension we find that each 1-dimensional 1-cm long line contains 2,924,017 molecules (let's say 3 million to keep things simpler).

Over 70% of air is Nitrogen and the length of an N2 molecule is about (keeping things simple) 100 pm (picometers; 10^-12 m) so 3 million molecules take up 300 million picometers or 300 micrometers (following conversion)

There are 10,000 micrometers in a centimeter so the molecules only 3% of the available distance.

If all 3 million molecules were equally spaced they would be approximately 3.3 nm (nanometers; 10^-9 m) apart.

A division of the molecular length (100 pm) by the separation (3.3 nm) shows that they are about 33 molecules length apart.

Now I've made plenty of assumptions here. I'm more than happy for people to point out where I've gone wrong (if I have). Please PM me.

Just divide Loschmidt's number into one cubic centimeter (use a calculator?) to obtain the space occupied by one air molecule which will just touch the space occupied by the next nearest air molecule. Of course that is a snapshot because the molecules are traveling at tremendous speed at normal temperature. The gas nuclei occupy very little space (like our sun compared to the planets of the solar system) and the electrons orbiting the gas atoms or molecules keep them apart because electrons repel each other. The space between nuclei and electrons and atoms is devoid of matter (having mass) but may be traversed by photons (like sunlight passing through the near-perfect vacuum of outer space. Check the link for the correct exponents in the constant (1019 should be 10 to the 19th power, etc.).

<<The first person to have calculated the number of molecules in any mass of substance was Josef Loschmidt, (1821-1895), an Austrian high school teacher, who in 1865, using the new Kinetic Molecular Theory (KMT) calculated the number of molecules in one cubic centimeter of gaseous substance under ordinary conditions of temperature of pressure, to be somewhere around 2.6 x 1019 molecules. This is usually known as "Loschmidt's Constant." (This value, no, is now listed at the NIST web site as 2.686 7775 x 1025 m-3)>>

To answer your question simply. A gas occupies approximately 1000 times the volume as the same mass of liquid so the molecules are quite widely spaced. (Avogadro was the first scientist to work out this)

Kes knows her stuff, did she learn all that from star ship voyager?