Why is intermolecular potential energy given in 'per mole'? I was just wondering that if intermolecular potential is the interaction potential energy of two atoms/molecules, then why do we give its value in J/mole? I don't understand why 'per mole' specification is required?
This is the situation where I am confused. When using LJ potential in molecular dynamics simulation, the $\epsilon$ parameter has value of the order of 1 kJ/mole. If I am using only 1000 particles in my simulation, what value of $\epsilon$ should I use?
 A: I think about these things in microscopic units, like eV/atom.  However measurements are made with macroscopic amounts of material and tend to be tabulated in macroscopic units.  The two units aren't that different ($\rm 1\,eV/atom \approx 100\,kJ/mol$) but pointless uncertainty can be introduced in the conversion.
A: The mole essentially denotes "number of molecules". When you say "per mole", you are implying "per molecule", which is highly desirable since it directly converts a macroscopic property such as 'total heat released during reaction' to a microscopic property such as 'heat released per molecule'.
Since $\epsilon$ is an intensive function as it is per molecule, the number of molecules don't matter, whether 2 or 1000.
A: You should probably still use kJ/mole for consistency. It is clear what you mean, just like you might use "1 g/L" even when dealing with quantities less than a litre. In general, when working with multiples of units derived as ratios of other units, it is better to scale the denominator than the numerator. Compare "km/s" and "m/ms". Both have a thousand times the value of m/s but the first one makes thus much more apparent.
