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?

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