An extension of the theory of van der Waals and Platteeuw was recently proposed by Tanaka and co-workers, In this work, we extend these studies to apolar spherical models of ethylene, ethane, and carbon dioxide at different temperatures in the region of experimental equilibrium between ice and hydrate. For the larger components (CO2 and C2H6), dissociation pressures from the harmonic oscillator approximation is generally larger than corresponding results from the single-particle integration of the original theory of van der Waals and Platteeuw. Differences increase with increasing the ratio of guest size to the free cavity space, For the specific sets of model parameters applied here, the agreement between experiment and calculations is qualitative in the region of ice in equilibrium with hydrate. In the liquid water region estimated dissociation pressures for ethylene and carbon dioxide are in better agreement with experiments for the harmonic oscillator approach and underpredicted from the single-particle integration. Extension to mixtures are discussed, and some examples are presented. The results for mixtures generally reflect the same type of behavior as that observed for pure components.