External condensed phase modes

ACS Symposium Series American Chemical Society Washington, DC, 1975. 

Equations (1) and (2) refer to measurements on separated Isotopes. It is also Important to develop a relation between the reduced partition function ratio (RPFR) and measured separation factors, a, referring to single stage Isotopic enrichments (on distillation) for dilute nonideal solutions. In the case of infinite dilution the molar volumes of the two Isomers are Identical (they are determined by environment) and one obtains (19) 

Here 3 is the Isothermal compressibility and V the molar volume of the condensed phase. The last term is usually very small and is often neglected. This accounts for the common and mistaken idea that RPFRs are directly measured in distillation experiments. 

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In the condensed phase the sum is over all 3n frequencies, but in the ideal vapor phase the six external (zero) frequencies do not contribute to the IE s, the sum is over the remaining 3n — 6 internals. For condensed rare gases the harmonic assumption is highly approximate, and this is also true for the lattice modes of polyatomics. However as molecular size increases the relative contribution of the external modes becomes less and less important relative to internals. 

Compared to fixed bed multiphase reactors additional modes of operation are available with slurry reactors as also the solid phase can be feeded continuously and eventually recirculated temperature control can be assured by internal cooling coils or/ and external circulation through heat exchangers (for the gas as well as for the liquid phase). Furthermore also partial evaporation and external condensation with recirculation of the liquid phase can support the cooling. 

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