With a new development of corresponding states principle involving quasi-second virial coefficients of alkali metals, the free parameter of the ISM analytical equation of state, Gamma, is shown to incorporate quantum effects. This observation is justified by the assumption that Gamma adjusts itself with the value of a second virial coefficient so much that both describe the compressibility behavior of the system. Calculations along with the present data show that Li, and to some extent Na, deviates from the corresponding states behavior, succeeded by K, Rb, and Cs. By developing a corresponding states principle involving Delta H-v, which the scaling factor used in the calculation of the quasi-second virial coefficients of alkali metals, the quantum effect in Gamma is well justified. The same behaviors are observed among noble gases, where only He deviates. The statistical mechanical view of the open-shell electronic structure of alkalis must be considered as a special difference in physical behavior with noble gases.