# EoS: Excluded Volume

### 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, $b$.

$P = \frac{RT}{v-b}$

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