Final answer:
The greatest deviation of a real gas from the ideal gas law occurs at low temperature and high pressure, where reduced kinetic energy emphasizes intermolecular forces and the volume of individual particles cannot be ignored.
Step-by-step explanation:
The greatest deviation of a real gas from the ideal gas law is expected at conditions of low temperature and high pressure. At high pressures, the gas molecules are pushed close together, reducing the space between them, and making the assumption that the volume of the individual gas particles is negligible less valid. At low temperatures, the kinetic energy of the gas particles decreases, which makes the intermolecular forces more prominent. This is contrary to an ideal gas, where these forces are considered negligible. Therefore, real gases deviate the most from ideal gas behavior under these conditions.