Entropy of the liquid

From a thermodynamic perspective, Stillinger and Weber demonstrated that the total entropy of the liquid can similarly be divided into two additive terms, a configurational and a vibrational contribution.5,6 The configurational part Sc measures the number of structurally distinct basins of attraction on the PEL that the configuration point accesses at a given temperature, whereas the vibrational contribution Svib characterizes the number of states associated with intra-basin fluctuations. Thus, the AG relationship, when viewed from the PEL perspective, suggests that it is the thermodynamic availability of basins on the landscape that dominates the rate of liquid-state diffusive processes. 

To p. 11. According to N. H. Fletcher, J. Crystal Growth 28, 375 (1975), the free energy of solid - melt interfaces in many systems (e.g., water - ice) is determined above all by the low entropy of the liquid layers adjacent to the solid surface. This loss of entropy occurs because the above layers are more ordered than the melt far from the solid. 

Ordering. This is the deficit of entropy of the liquid solvent relative to the solvent vapor or the dipole orientation correlation. 

Adsorbed Phase Entropy. Since Equations 7 and 8 can accurately describe the relationship between q, T, and p, we may use them to calculate the integral molar entropy of the adsorbed phase. At temperatures significantly lower than critical for the adsorbate, the entropy of the adsorbed phase is usually compared with the entropy of the liquid at same temperature in order to compare the freedom of each phase. Because our experimental domain was higher, we shall make this comparison with the gaseous phase compressed to the same density p as determined by Equation 8. 

Even in an ideal solution, a solute increases the entropy of the liquid phase we can no longer be sure that a molecule picked at random from the solution will be a solvent molecule. Because the entropy of the liquid phase is raised by a solute but the enthalpy is left unchanged, overall there is a decrease in the molar free energy of the solvent. 

This measure, however, pertains to the normal boiling point rather than to ambient conditions. The deficit of the entropy of the liquid solvent relative to the solvent vapour and to a similar non-structured solvent at any temperature, such as 25 °C, has also been derived (Marcus 1996). An alkane with the same skeleton as the solvent, i.e., with atoms such as halogen, O, N, etc. being exchanged for CH3, CH2, and CH, etc., respectively, can be taken as the non-structured solvent. Since the vapour may also be associated, the temperature dependence of the second virial coefficient, B, of the vapour of both the solvent and the corresponding alkane, must also be taken into account. The entropy of vaporization at the temperature T, wherep P°, is given by ... 

It is important to emphasize the role of the solid state in providing a medium for the formation of the molecular assembly 2(resorcinol) 2(4,4 -bpe). Indeed, that 2(resorcinol) 2(4,4 -bpe) is stabilized by weak forces (i.e. hydrogen bonds) comparable in strength to structure effects of solvent and entropy of the liquid phase [13] means that the components of 2(resorcinol)-2(4,4 -bpe) may assemble in solution to produce multiple equilibria involving individual molecules and undesirable (photostable) complexes. In effect, the solid state was used to sequester [23] 2(resorcinol) 2(4,4 -bpe) from the liquid phase, facilitating the formation of the desired photoactive complex and construction of the cyclobutane product. 

If water or some other compound with a simple molecular structure has been studied, it is possible to combine the entropy of vaporization, A5 = AHyl T, with the third-law calorimetric entropy of the liquid to obtain a thermodynamic value for the entropy of the vapor. The statistical mechanical value of Sg can be calculated using the known molar mass and the spectroscopic parameters for the rotation and vibration of the gas-phase molecule. A comparison of Sg (thermodynamic) with Sg (spectroscopic) provides a test of the validity of the third law of thermodynamics. The case of H2O is particularly interesting, since ice has a nonzero residual entropy at 0 K due to frozen-in disorder in the proton positions. ... 

The pertinent thermodynamic data needed to carry out the calculation of 5g(thermo-dynamic) for water vapor are as follows 5 (1 bar, 298.15 K) = 66.69 J mol which is the calorimetric value obtained by assuming (erroneously) that the third law is valid for ice Cp(l), which is essentially independent of temperature over the range 298-355 K, has the average value 75.36 J mol You may neglect the effect of pressure on the value of the molar entropy of the liquid, an approximation that has very little effect on the calculated thermodynamic value of Sg(p , T ,) for H20(g) at the vapor pressure... 

The constant heat capacity, 17.59 cal k mol extrapolated above and below the experimental range. A lower value of 16.7 cal K mol was derived by Dworkin (2) from enthalpy data (1050-1110 K) obtained in an enthalpy of melting study. The entropy of the liquid is calculated in a manner analogous to that used for enthalpy of formation. 

Alternatively A and Vf may be calculated on the basis of the cage-model from equations (12.64) and (12.54), but no better agreement is achieved. It appears that the actual entropy of the liquid is greater than that given by the cage-model, but less than that corresponding to the van der Waals model. 

Justify the statement that the solidification of a supercooled liquid is accompanied by a decrease in the entropy of the liquid but a greater increase in the entropy of the surroundings. Suggest how the change from supercooled water at... 

He is a liquid at 0 K and 1 bar (liquid Hell) its equilibrium freezing pressure at 0 K is 26 bar. At this point, the entropies of the liquid and the crystal are equal, and this is therefore a Kauzmann point. The melting eurves of both He and He exhibit pressure minima these occur at ca. 0.32 K ( He) and 0.8 K C He). These are also equal-entropy (Kauzmann) points. 

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