# Deviation from Ideal Gas Law: Nonzero volume of a gas (Don't understand how this explains compressibilities>1)

The ideal gase law (PV=nRT) assumes that the volume of a gas is negligible. We know this is not a valid assumption for real gases, and this is particularly pronounced when the container that the gas takes up has low volume.

Compressibility (PV/nRT) is constant for an ideal gas, which makes sense because we are assuming that the volume taken up by the gas is negligible and that there are no intermolecular interactions. However, for real gases, compressibility is not constant. I’ve been taught that for compressibility values > 1, the deviations is due to nonzero molecular volume, while compressibility values < 1 is due to intermolecular attractions. The latter (compressibility values < 1) makes sense to me, because intermolecular attractions should make the actual pressure less than what is expected from the ideal gas law.

I also understand that the volume of a real gas is greater than an ideal gas. But the value for volume in the ideal gas law pertains to the volume of the CONTAINER, not the gas particles themselves. So, if we are dealing with a real gas, the volume of the container should be less than what is predicted by the ideal gas law because some of that volume is being taken up by gas particles. So, why would the V value for compressibility of a real gas lead to a compressibility > 1, instead of < 1?

• Related: chemistry.stackexchange.com/a/60439/41556. The issue is that compressibility is defined a for a fixed temperature and pressure, not a fixed volume. Comparing a real gas and an ideal gas in the same size container, the real gas will have a smaller volume, but then the comparison isn't being made at the same pressure. Also, if the real gas takes up less volume, than its molar volume is increasing and that is what is being compared by compressibility.
– Tyberius
Jan 4 at 20:00