# Kinetic Diameter: How to calculate it? Pressure influence?

Wikipedia states:

Kinetic diameter is a measure applied to atoms and molecules that expresses the likelihood that a molecule in a gas will collide with another molecule. It is an indication of the size of the molecule as a target.

And the following equation is given:

$$d^2 = \frac{1}{πln}$$

where,
$$d$$ is the kinetic diameter,
$$r$$ is the kinetic radius, $$r = d/2$$,
$$l$$ is the mean free path, and
$$n$$ is the number density of particles.

To me, this implies that the kinetic diameter can be altered by changing the number density of particles. Therefore, a change in pressure, volume, or concentration should would effect the kinetic diameter.

However, kinetic diameters are often discussed as if they were constants. Indeed, Wikipedia even gives a table of kinetic diameters for some common molecules.

1. Another definition of the kinetic diameter would be useful.

2. How is the kinetic diameter related to molecular structure? Can it be quantified as the distance between a pair of atoms?

3. If someone could also suggest a computational program to calculate the kinetic diameter of a molecule, that would also be of use.

• Keep in mind that while altering the pressure, volume etc. changes the number density, it also changes the mean free path of the particles, and these effects are compensated. As for calculating the kinetic diameter by computational programs, well, it is a tricky business... Depending on your proficiency with theoretical chemistry, you might look up the pair potential expression for the second virial coefficient, and start from there... – Ezze Oct 29 '19 at 13:10
• Further to Ezze's comment, the reason that $d$ is expressed in that way is because it is in terms of measurable quantities, $l$ and $n$. Most molecules are not spherical however, benzene, anthracene etc so $d$ would then be some odd sort of average. You can get good ideas of size from van der Waals radii, see the JSMOL image on the molecule's Wikipedia page. – porphyrin Oct 30 '19 at 8:43