It is said that the assumptions of kinetic theory are good for gases having low densities. Suppose a container is evacuated so that only one molecule is left in it. Which of the assumptions of kinetic theory will not be valid for such a situation? Can we assign a temperature to this gas?

Which one of the following is not an assumption of kinetic theory of gases ?

In defining the ideal gas temperature scale, It is assumed thet the pressure of the gas at constant volume is proportional to the temperature T. How can we verify wheter this is true of not? Are we using the kinetic theory of gases? Are we using the experimental result that the pressure is proportional to temperature?