Methane and Xenon Complexation

The ratio between the cavity and guest size in terms of their molecular volumes may be expressed in terms of the cavity occupancy factor (p). A p value of 1 represents a completely filled cavity. Occupancy factors for various cryptophanes and guests are shown in Table 6.9. 

Clearly, methane is a much poorer fit to the cavity than the haloalkanes. However, it is interesting to compare the p value obtained (0.35) with various other states of matter of methane. Gaseous methane, for example, has a p of 0.77 X 10 at 1 atm pressure and 298 K. At its critical point (45.6 atm, 

the temperature and pressure at which there is no longer any distinction between liquid and gas), p rises to 0.17, while solid methane at 0 K exhibits a p value of 0.67. In occupancy terms, then, the intracavity environment is akin to a supercritical fluid. Translated to the macroscopic scale, one molecule of methane in the cavity of cryptophane-A is equivalent to one mole of methane in 49 mL, exerting a pressure of 610 atm at 298 K. In contrast, for CHCI3 the occupancy factor of 0.89 is akin to a very densely packed crystal, and indeed the entropic and enthalpic changes on binding are similar to those that occur in the formation of crystalline organic compounds. 

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