# The attached plot shows the ratio of PV to RT for 1.0 mole of nitrogen gas as a function of pressure at T=1000K. Explain why the ratio should be 1.0 for an ideal gas, and why nitrogen does not behave ideally at high pressures?

May 26, 2016

The ideal gas law holds that $P V = n R T$

#### Explanation:

The ideal gas law is an idealization. What does this mean? It means that we idealize the behaviour of real gases. We assume that gases are mostly empty space, that the volume of the gaseous particles are negligible compared to the volume occupied by the gas, and that pressure is the result of the gaseous particles hitting the sides of the container elastically.

Under conditions of moderate pressure (and moderate to high temperature), all gases behave ideally. And in fact the graph shows that $\frac{P V}{R T}$ $\cong 1$ under a low to moderate pressure regime. At high pressures the volume of the gaseous particles themselves become significant, and the gas is not so compressible at higher pressures. Gas law variations propose a correction factor to account for this excluded volume at high pressures.