Pressure, effect condensed phase

We consider a binary two-phase system al temperature T. One phase is a liquid and the other is a solid, Since the effect of pressure on condensed-phase proparties is notmally negligible at low or moderate pressures, we do not need to specify the pressure. Lei component 1 he the liquid solvent and component 2 the solid soluie. 

The standard-state fugacity of any component must be evaluated at the same temperature as that of the solution, regardless of whether the symmetric or unsymmetric convention is used for activity-coefficient normalization. But what about the pressure At low pressures, the effect of pressure on the thermodynamic properties of condensed phases is negligible and under such con-... 

Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely... 

Use the Third Law to calculate the standard entropy, S°nV of quinoline (g) p — 0.101325 MPa) at T= 298,15 K. (You may assume that the effects of pressure on all of the condensed phases are negligible, and that the vapor may be treated as an ideal gas at a pressure of 0.0112 kPa, the vapor pressure of quinoline at 298.15 K.) (c) Statistical mechanical calculations have been performed on this molecule and yield a value for 5 of quinoline gas at 298.15 K of 344 J K l mol 1. Assuming an uncertainty of about 1 j K 1-mol 1 for both your calculation in part (b) and the statistical calculation, discuss the agreement of the calorimetric value with the statistical... 

The value of this standard molar Gibbs energy, p°(T), found in data compilations, is obtained by integration from 0 K of the heat capacity determined by the translational, rotational, vibrational and electronic energy levels of the gas. These are determined experimentally by spectroscopic methods [14], However, contrary to what we shall see for condensed phases, the effect of pressure often exceeds the effect of temperature. Hence for gases most attention is given to the equations of state. 

For condensed phases (liquids and solids) the molar volume is much smaller than for gases and also varies much less with pressure. Consequently the effect of pressure on the chemical potential of a condensed phase is much smaller than for a gas and often negligible. This implies that while for gases more attention is given to the volumetric properties than to the variation of the standard chemical potential with temperature, the opposite is the case for condensed phases. 

The effect of curvature is much more pronounced for the thermodynamics of a gas bubble than for the liquid droplet. The curvature is a pressure effect, which is much larger for gases than for condensed phases, reflecting the much larger molar volume of the gas. 

Influence of subphase temperature, pH, and molecular structure of the lipids on their phase behavior can easily be studied by means of this method. The effect of chain length and structure of polymerizable and natural lecithins is illustrated in Figure 5. At 30°C distearoyllecithin is still fully in the condensed state (33), whereas butadiene lecithin (4), which carries the same numEer of C-atoms per alkyl chain, is already completely in the expanded state (34). Although diacetylene lecithin (6) bears 26 C-atoms per chain, it forms both an expanded and a condensed phase at 30°C. The reason for these marked differences is the disturbance of the packing of the hydrophobic side chains by the double and triple bonds of the polymerizable lipids. At 2°C, however, all three lecithins are in the condensed state. Chapman (27) reports about the surface pressure area isotherms of two homologs of (6) containing 23 and 25 C-atoms per chain. These compounds exhibit expanded phases even at subphase temperatures as low as 7°C. 

Although this book is devoted to molecular fluorescence in condensed phases, it is worth mentioning the relevance of fluorescence spectroscopy in supersonic jets (Ito et al., 1988). A gas expanded through an orifice from a high-pressure region into a vacuum is cooled by the well-known Joule-Thomson effect. During expansion, collisions between the gas molecules lead to a dramatic decrease in their translational velocities. Translational temperatures of 1 K or less can be attained in this way. The supersonic jet technique is an alternative low-temperature approach to the solid-phase methods described in Section 3.5.2 all of them have a common aim of improving the spectral resolution. 

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. 

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. 

For isotope effects on equilibrium constants in both gas and condensed phase the take-home lesson is there is no direct proportionality between measured isotope effects on logarithmic concentration or pressure ratios and isotopic differences in... 

Abstract Isotope effects on the PVT properties of non-ideal gases and isotope effects on condensed phase physical properties such as vapor pressure, molar volume, heats of vaporization or solution, solubility, etc., are treated in some thermodynamic detail. Both pure component and mixture properties are considered. Numerous examples of condensed phase isotope effects are employed to illustrate theoretical and practical points of interest. 

An important attribute of Equation 5.16 is that the pressure exerted on both phases, Ptot, is common to both isotopomers. The important difference between Equations 5.16 and 5.9 is that the isotopic vapor pressure difference (P/ — P) does not enter the last two terms of Equation 5.16 as it does in Equation 5.9. Also isotope effects on the second virial coefficient AB/B = (B — B)/B and the condensed phase molar volume AV/V are significantly smaller than those on AP/P ln(P7P). Consequently the corrections in Equation 5.16 are considerably smaller than those in Equations 5.9 and 5.10, and can sooner be neglected. Thus to good approximation ln(a") is a direct measure of the logarithmic partition function ratio ln(Qv Q7QvQcO> provided the pressure is not too high, and assuming ideality for the condensed phase isotopomer solution. For nonideal solutions a modification to Equation 5.16 is necessary. 

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

Table 13.1). In the solid P(CH4) > P(CD4) but the curves cross below the melting point and the vapor pressure IE for the liquids is inverse (Pd > Ph). For water and methane Tc > Tc, but for water Pc > Pc and for methane Pc < Pc- As always, the primes designate the lighter isotopomer. At LV coexistence pliq(D20) < Pliq(H20) at all temperatures (remember the p s are molar, not mass, densities). For methane pliq(CD4) < pLiq(CH4) only at high temperature. At lower temperatures Pliq(CH4) < pliq(CD4). The critical density of H20 is greater than D20, but for methane pc(CH4) < pc(CD4). Isotope effects are large in the hydrogen and helium systems and pLIQ/ < pLiQ and P > P across the liquid range. Pc < Pc and pc < pc for both pairs. Vapor pressure and molar volume IE s are discussed in the context of the statistical theory of isotope effects in condensed phases in Chapters 5 and 12, respectively. The CS treatment in this chapter offers an alternative description.

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