A recently introduced mapping approach to the equation of state of classical fluids is used to study the dilute gas phase. The approach introduces mean collision diameters sigma(T) and R(T), which reflect the contributions to the pressure from the repulsive and attractive forces, respectively. The mean diameters are analyzed for a variety of molecules in the gas phase. The temperature dependence of sigma(T) and R(T) is shown to be essentially dominated by two shape factors, S-R and S-A, characterizing the form of the repulsive and attractive parts of a the Interaction, respectively. The method gives insight into the collision diameters and second virial coefficients, B(T), of model molecules, both spherical and nonspherical, including three-parameter potential functions and diatomic Lennard-Jones molecules. As a practical bonus, the theory provides a compact and highly accurate model for B(T) of model and real molecules. The theory also provides a route to reliable information on the effective intermolecular potential from a knowledge of B(T). The theory is applied to gaseous neon, argon, krypton, dinitrogen, dioxygen, difluorine, methane, and tetrafluoromethane, and their mean collision diameters and potential parameters are determined and analyzed.