Final answer:
Among helium, neon, krypton, and xenon, xenon (Xe) will show the greatest deviation from ideal gas behavior at high pressures due to its larger molecular size and stronger London dispersion forces.
Step-by-step explanation:
The gas that will show the greatest deviation from ideal gas behavior at high pressure among helium (He), neon (Ne), xenon (Xe), and krypton (Kr) is xenon (Xe). This is attributed to xenon having a larger molecular size and stronger intermolecular forces, particularly London dispersion forces, compared to the smaller noble gases. At high pressures, the volume of these gases becomes small enough that the interactions between the molecules can't be ignored, thus causing greater deviation from ideal behavior for xenon.
Significant deviations from ideal gas behavior commonly occur at low temperatures and very high pressures. Since xenon is much heavier than helium, neon, or krypton, it has more electrons that can contribute to temporary dipoles leading to stronger dispersive forces. Hence, at high pressure, xenon deviates more from ideal gas behavior than He, Ne, or Kr, which have lesser electron counts and weaker dispersion forces.