Condensed phases entropy

For a condensed phase entropy is given by the relation S = NKb, In q+ E/T, where q is the partition function. Using this relation an expression for the entropy of an ideal gas, derived ... 

The theorem of Nernst applies only to chemically homogeneous condensed phases the entropy of a condensed solution phase has at absolute zero a finite value, owing to the mutual presence of the different components. 

It may reasonably be assumed that the terms in the expression for the entropy which depend on the temperature diminish, like the entropy of a chemically homogeneous condensed phase, to zero when T approaches zero, and the entropy of a condensed solution phase at absolute zero is equal to that part of the expression for the entropy which is independent of temperature, and depends on the composition (Planck, Thennodynamik, 3 Aufi., 279). 

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... 

Equilibrium vapor pressures were measured in this study by means of a mass spectrometer/target collection apparatus. Analysis of the temperature dependence of the pressure of each intermetallic yielded heats and entropies of sublimation. Combination of these measured values with corresponding parameters for sublimation of elemental Pu enabled calculation of thermodynamic properties of formation of each condensed phase. Previ ly reported results on the subornation of the PuRu phase and the Pu-Pt and Pu-Ru systems are correlated with current research on the PuOs and Pulr compounds. Thermodynamic properties determined for these Pu-intermetallics are compared to analogous parameters of other actinide compounds in order to establish bonding trends and to test theoretical predictions. 

Theoretically, the problem has been attacked by various approaches and on different levels. Simple derivations are connected with the theory of extrathermodynamic relationships and consider a single and simple mechanism of interaction to be a sufficient condition (2, 120). Alternative simple derivations depend on a plurality of mechanisms (4, 121, 122) or a complex mechanism of so called cooperative processes (113), or a particular form of temperature dependence (123). Fundamental studies in the framework of statistical mechanics have been done by Riietschi (96), Ritchie and Sager (124), and Thorn (125). Theories of more limited range of application have been advanced for heterogeneous catalysis (4, 5, 46-48, 122) and for solution enthalpies and entropies (126). However, most theories are concerned with reactions in the condensed phase (6, 127) and assume the controlling factors to be solvent effects (13, 21, 56, 109, 116, 128-130), hydrogen bonding (131), steric (13, 116, 132) and electrostatic (37, 133) effects, and the tunnel effect (4,... 

Many workers have offered the opinion that the isokinetic relationship is confined to reactions in condensed phase (6, 122) or, more specially, may be attributed to solvation effects (13, 21, 37, 43, 56, 112, 116, 124, 126-130) which affect both enthalpy and entropy in the same direction. The most developed theories are based on a model of the half-specific quasi-crystalline solvation (129, 130), or of the nonideal conformal solutions (126). Other explanations have been given in terms of vibrational frequencies involving solute and solvent (13, 124), temperature dependence of solvent fluidity in the quasi-crystalline model (40), or changes of enthalpy and entropy to produce a hole in the solvent (87). 

The metallothermic reduction of oxides is essentially a reaction involving only condensed phases. It follows therefore, that the entropy changes in these reactions are small and that the differences in the heats of formation of the pertinent compounds determine the feasibility of a given reaction. Among the metallic reductants, calcium forms the oxide whose heat of formation is the most negative. As a first approximation, calcium may be considered to be the most effective reducing agent for metal oxides. 

Unless otherwise said, our preferred sources for enthalpies of formation of hydrocarbons are Reference 8 by Roth and his coworkers, and J. B. Pedley, R. D. Naylor and S. P. Kirby, Thermochemical Data of Organic Compounds (2nd ed.), Chapman Hall, New York, 1986. In this chapter these two sources will be referred to as Roth and Pedley , respectively, with due apologies to their coworkers. We will likewise also occasionally take enthalpies of fusion from either E. S. Domalski, W. H. Evans and E. D. Hearing, Heat Capacities and Entropies of Organic Compounds in the Condensed Phase , J. Phys. Chem Ref. Data, 13, 1984, Supplement 1, or E. S. Domalski and E. D. Hearing, J. Phys. Chem Ref. Data, 19, 881 (1990), and refer to either work as Domalski . 

Data for a large number of organic compounds can be found in E. S. Domalski, W. H. Evans, and E. D. Hearing, Heat capacities and entropies in the condensed phase, J. Phys. Chem. Ref. Data, Supplement No. 1, 13 (1984). It is impossible to predict values of heat capacities for solids by purely thermodynamic reasoning. However, the problem of the solid state has received much consideration in statistical thermodynamics, and several important expressions for the heat capacity have been derived. For our purposes, it will be sufficient to consider only the Debye equation and, in particular, its limiting form at very low temperamres ... 

Equation (11.4) provides a convenient value for that constant. Planck s statement asserts that 5qk is zero only for pure solids and pure liquids, whereas Nernst assumed that his theorem was applicable to all condensed phases, including solutions. According to Planck, solutions at 0 K have a positive entropy equal to the entropy of mixing. (The entropy of mixing is discussed in Chapters 10 and 14). 

E. S. Domalski, W. H. Evans, and E. D. Hearing, Heat capacities and entropies of organic compounds in the condensed phase, J. Phys. Chem. Ref. Data 13, Supplement No. 1 (1984). 

Solutions of nonpolar solutes in nonpolar solvents represent the simplest type. The forces involved in solute-solvent and solvent-solvent interactions are all London dispersion forces and relatively weak. The presence of these forces resulting in a condensed phase is the only difference from the mixing of ideal gases. As in the latter case, the only driving force is the entropy (randomness) of mixing. In an ideal solution (AW, = 0) at constant temperature the free energy change will be composed solely of the entropy term ... 

Here, k(is the rate constant vk the stoichiometric coefficients of the kth component in the ith reaction of reagents and products, correspondingly A, the equilibrium constants the number of sites occupied by surface substance j of condensed phase n F," the surface site density in the th phase standard state and hk and sk the enthalpy and the entropy of the Arth substance. 

Where the k s designate the gaseous components at the nozzle exhaust and k s the condensed phases. From the product temperature and composition one can calculate the total entropy in the chamber. The unknowns in equation II. C. 4. are Te and n. Recall ... 

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