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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

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  • $\begingroup$ 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. $\endgroup$
    – velut luna
    Aug 23, 2016 at 8:31

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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.

Similarly, elastic collisions and neglecting of intermolecular forces are considered as otherwise the pressure would need to be corrected. Intermolecular force interactions will accelerate or decelerate the molecules thus changing force (and pressure) applied to the edge of our box.

Van der Waals equation attempts to take these corrections into account:

$$ \ (P + a(n/V)^2)((V/n) - b ) = RT $$

Where $a$ and $b$ are the Van der Waals (correction) coefficients. Hope this helps :)

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