### Excluded Volume

Real gases occupy volume because the atoms/molecules have an
effective radius:

The volume occupied per mole is given by:

$v_{molecules} = \frac{4}{3}\pi R^3 x N_{Avo}$

##### Test Yourself:

If our $CO_2$ from the previous example has effective radii
given as Carbon : 0.07 nm ; Oxygen : 0.062 nm; molecule : approx
0.19 nm, determine what the fractional volume occupied is.

How to account for this effect?

##### DEFINITION

The **excluded volume**, is the volume that is
occupied by atoms/molecules and is therefore "unavailable" for
molecular motion. Many EoS simply directly correct for this effect
by subtracting the excluded volume, $b$.

This is one of the most common (and simplest) modifications of
the ideal gas law.