Why do we have to neglect intermolecular forces and consider particles with a volume near $0$ when using ideal gas theory?

To use the ideal gas theory, there are two conditions. We suppose that:

• the particles must theoretically speaking have a volume equal to 0 and collisions must be completely elastic.

• the ideal gas molecules to be very far apart so we can neglect intermolecular forces.

I don't see why those conditions are so important. Could somebody please explain?

Thank you

• In kinetic theory, we assume that a particle bouncing between the walls and between two successive collisions with the walls there is no force acting on it and no collisions with other particles. Aug 23, 2016 at 8:31

The first condition is because if we did treat particles as having a volume then we would have to correct for the volume they take up. So the volume $V$ of a box would need to be corrected for the small volume taken up by the particles.
$$\ (P + a(n/V)^2)((V/n) - b ) = RT$$
Where $a$ and $b$ are the Van der Waals (correction) coefficients. Hope this helps :)