Isotopes, free energy scale

Equation A1.3 shows that isotope effects calculated from standard state free energy differences, and this includes theoretical calculations of isotope effects from the partition functions, are not directly proportional to the measured (or predicted) isotope effects on the logarithm of the isotopic pressure ratios. Rather they must be corrected by the isotopic ratio of activity coefficients. At elevated pressures the correction term can be significant, and in the critical region it may even predominate. Similar considerations apply in the condensed phase except the fugacity ratios which define Kf are replaced by activity ratios, a = Y X and a = y C , for the mole fraction or molar concentration scales respectively. In either case corrections for nonideality, II (Yi)Vi, arising from isotope effects on the activity coefficients can be considerable. Further details are found in standard thermodynamic texts and in Chapter 5. 

Concentrations of aqueous electrolyte solutions are conventionally expressed using the aquamolality scale (L = moles salt per 55.508 mol solvent (l,000g for H20)). Some typical solubilities (298.15K) are listed in Table 5.13. Almost all salts are less soluble in D20 than in H20. For those salts whose solubility increases with temperature, which is the ordinary behaviour, the isotope effects decrease with temperature. Writing the standard state partial molar free energy of pure solid salt as Pxsalt) and its standard state in solution as p, (HorD) we have on comparing the saturated solutions in H20 and D20,... 

A concentration scale for solutes in aqueous solutions, equal to moles of solute/55.51 mol water. It is frequently used in studies of solvent isotope effects. As pointed out by Schowen and Schowen the choice of standard states can change the sign for the free energy of transfer of a species from one solvent to another, even from HOH and DOD. The commonly used concentration scales are molarity, mole fraction, aquamolality, and molality. Free energies tend to be nearly the same on all but the molality scale, on which they are about 63 cal mol more positive at 298 K than on the first three scales. The interested reader should consult Table I of Schowen and Schowen ... 

H2O this is 1000 grams. Our choice of the aquamolal concentration scale Insures that all Isotope effects are conqiared at equivalent mole fractions.) The properties of the solution are known in a thermodynamlc sense when the standard and excess molal free energies, Pi and Ua, and and their appropriate tem erature and pressure derivatives, H and hS, H — — ... 

Figure 30. Schematic variation of the Ssns SoF = I and Ssns S F = I hyperfine components of Sr with principal quantum number . The energies are not drawn to scale. For each value of n the origin of the energy scale has been taken to lie halfway between the corresponding Sq and 5 states of the even isotopes (dashed lines). The states of the free ion appear on the right-hand side. State mixing (cf. Section 3.1.4) has not been taken into account. (Taken from Ref. 65.)...

The majority of experimental data has been measured for two blend systems PS/PVME, and isotopic blends of PS and poly(perdeutero-styrene). The surface compositions for PS/PVME blends were found to scale directly with the surface energy difference between the constituents (23), showing that the latter factor dominates the surface behavior, a result that might be expected for these nearly athermal blends with large surface energy differences. (The PS/PVME system has an interaction parameter estimated to be —0.0011 and can be considered as effectively athermal.) The square gradient theory with the Flory-Huggins free... 

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