Vapor pressure isotope effects

Chapter 5, vapor pressure isotope effects are discussed. There, a very simple model for the condensed phase frequencies is used, the Einstein model, in which all the frequencies of a condensed phase are assumed to be the same. From this model, one can derive the same result for the relationship between vapor pressure isotope effect and zero-point energy of the oscillator as that derived by Lindemann. 

We begin with a discussion of the vapor pressure isotope effect (VPIE). To do so we compare the equilibria between condensed and vapor phase for samples of two isotopomers. At equilibrium, condensed(c) = vapor(v), the partial molar free energies, a(v), and p,(c), of the two phases are equal this, in fact, is the thermodynamic... 

The Vapor Pressure Isotope Effect, Separated Isotopes... 

Equation 5.11 is important. It relates the experimentally observed vapor pressure ratio to the theoretically important isotope effects on the free energy differences and/or partition function ratios. This equation encapsulates the essential physics of the vapor pressure isotope effect and, as we shall see, provides a path for its theoretical interpretation in terms of molecular structure and dynamics via the partition function ratios. 

Fig. 5.2 H/D vapor pressure isotope effects (per atom D) for some representative compounds...

Jancso, G. and Van Hook, W. A. Condensed phase isotope effects (especially vapor pressure isotope effects). Chem. Rev. 74, 689 (1974). 

The vapor pressure ratio measurements of separated isotopes are particularly useful because they directly measure the isotopic free energy ratios of the solvent. The solvent vapor pressure isotope effect between H2O and D2O is determined... 

Equation 1 relates the force fields describing the motions of the molecule in the condensed and in the gaseous phase with the activity ratio. These fields are different owing to the effect of the intermolecular forces which are operative in the condensed phase. The intermolecular forces are exclusively solute-solute forces in the pure state (where the ratio P /P reduces to the vapor pressure isotope effect, VPIE),... 

In Figure 2 the vapor pressure isotope effect is plotted as the solid line, and it is to be noted that the deviations from ideality are in the expected direction—i.e., as the polarity of the solvent increases, the magnitude of the inverse isotope effect falls off. Clearly, on this basis the wet glass column must be considered as quite polar, a conclusion which is consistent with the results for other systems found on this column. 

Van Eldick R (1987) High pressure studies of inorganic reactions. In Van Eldick R, Jonas J (eds) High Pressure Chemistry and Biochemistry. Reidel, Dordrecht, The Netherlands, p 333-356 Van Eldiek R, Palmer DA (1982) Effects of pressure on the kinetics of the dehydration of carbonic acid and the hydrolysis of CO2 in aqueous solution. J Solution Chem 11 339-346 Van Hook WA (1972) Vapor pressure isotope effect in aqueous systems. III. The vapor pressure of HOD (-60 to 200°C). J Phys Chem 76 3040-3043... 

It is important to look into the implications of Eq. (1) since the development of the quantum-statistical mechanical theory of Isotope chemistry from 1915 until 1973 centers about the generalization of this equation and the physical interpretation of the various terms in the generalized equations. According to Eq. (1) the difference in vapor pressures of Isotopes is a purely quantum mechanical phenomenon. The vapor pressure ratio approaches the classical limit, high temperature, as t . The mass dependence of the Isotope effect is 6M/M where 6M = M - M. Thus for a unit mass difference in atomic weights of Isotopes of an element, the vapor pressure isotope effect at the same reduced temperature (0/T) falls off as M 2. Interestingly the temperature dependence of In P /P is T 2 not 6X0/T where 6X.0 is the heat of vaporization of the heavy Isotope minus that of the light Isotope at absolute zero. In fact, it is the difference between 6, the difference in heats of vaporization at the temperature T from (> that leads to the T law. 

Herzfeld and Teller (15) showed that a more general form of Eq. (1) could be derived through the use of the Wlgner distribution function. For the vapor pressure isotope effect between a condensed phase and a monatomic vapor they obtained... 

Condensed Phase Isotope Effects, Especially Vapor Pressure Isotope Effects Aqueous Solutions... 

The theory of Isotope effects In condensed phase systems, especially vapor pressure Isotope effects (VPIE) Is briefly reviewed. It Is pointed out that the VFIE can be enqtloyed as one measure of the effect of Intermolecular forces on the motions of molecules In condensed phases. This Is Illustrated with a number of examples from the recent literature and from our own laboratory. A more detailed description of our recent work on thermodynamic solvent Isotope effects In aqueous systems Is presented. Experiments on vapor pressures, freezing points, and heats of solution and dilution of solutions of electrolytes In HOH and DOD are described. Implications are discussed with respect to the aqueous solvent structure problem. 

Figure 3. Hydrogen-deuterium vapor pressure isotope effects for some compounds (5)...

Figure 4. Vapor pressure isotope effects for organic acids deuterated at the carboxyl position (5, 40). X = CH3COOH, O = CH3CH3CH3-COOH, = (CHshCHCOOH, A = (CH hCHCH COOH.

Experimental. The vapor pressure Isotope effects were measured on either of two systems. Each was based on the same principle and we briefly describe the later and improved apparatus. The earlier equipment has been previously described (5A) ... 

Figure 6. Vapor pressure isotope effects of some electrolyte solutions. AZnR = lnR ...

The simplest possible model for the partition-function ratio for isotopic species in a common solvent involves the assumption that the solute-phase species can be treated as gas-phase species. As noted earlier, as far as isotope-exchange reeictions are concerned, this assumption is equivalent to the assumption that there is no vapor pressure isotope effect. For the reeiction... 

One can see from the above examples that the lighter isotopic molecule is usually more volatile than the heavier one ( normal vapor pressure isotope effect ). Sometimes, however, the heavier molecule has a higher vapor pressure ( inverse vapor pressure isotope effect ) and in some cases the direction of the isotope enrichment between the liquid and gaseous phases changes its direction with temperature at the cross-over temperature. There are very small, but still measurable differences between different dideuterobenzenes. 

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