Standard absolute entropy

The Third Law of Thermodynamics postulates that the entropy of a perfect crystal is zero at 0 K. Given the heat capacity and the enthalpies of phase changes, Eq. (12-3) allows the calculation of the standard absolute entropy of a substance, S° = AS for the increase in temperature from 0 K to 298 K. Some absolute entropies for substances in thermodynamic standard states are listed in Table 12-1. 

Given standard absolute entropies and standard enthalpies of formation, one can compute standard Gibbs free energies offormation, A Gf. Just as for standard enthalpies of formation, A Gf for elements... 

In the case of reactions, as opposed to processes, in order to calculate AS we can use standard absolute entropies or standard entropies of formation derived from thermochemical tables. 

Mu, L. and Peng, C. (2007) Quantitative structure-property relations (QSPRs) for predicting standard absolute entropy, S 298, of inorganic compounds. MATCH Commun. Math. Comput. Chem., 57, 111-134. 

Standard absolute entropy. The entropy of a substance compared to its entropy when crystalline and at 0 K. 

Based on their measurements of the low temperature heat capacities, the standard absolute entropy of ThN is reported as SJae=13.38 0.24 cal-mor K" by Danan etal. [23] and Danan [22] and as 13.7 0.2 cal-mor -K by Dell, Martin [24]. Following the precedent set by Rand [8], the latter value is adopted for consistency with data on Th3N4. 

Jenkins, H.D.B. and Glasser, L., Standard absolute entropy, S°29s values from volume or density. 1. Inorganic materials, Inorg. Chem. 42 (26), 8702-8708 (2003). 

Standard (absolute) entropy (S°) the entropy value for the standard state of a species. (19.3)... 

Think About It Remember that standard enthalpies of formation have units of kJ/mol, whereas standard absolute entropies have units of J/K mol. Make sure that you convert kilojoules to joules, or vice versa, before combining the terms. 

Ideal gas absolute entropies of many compounds may be found in Daubert et al.,"" Daubert and Danner," JANAF Thermochemical Tables,TRC Thermodynamic Tables,and Stull et al. ° Otherwise, the estimation method of Benson et al. " is reasonably accurate, with average errors of 1-2 J/mol K. Elemental standard-state absolute entropies may be found in Cox et al." Values from this source for some common elements are listed in Table 2-389. ASjoqs may also be calculated from Eq. (2-52) if values for AHjoqs and AGJoqs are known. 

The third law of thermodynamics establishes a starting point for entropies. At 0 K, any pure perfect crystal is completely constrained and has S = 0 J / K. At any higher temperature, the substance has a positive entropy that depends on the conditions. The molar entropies of many pure substances have been measured at standard thermodynamic conditions, P ° = 1 bar. The same thermodynamic tables that list standard enthalpies of formation usually also list standard molar entropies, designated S °, fbr T — 298 K. Table 14-2 lists representative values of S to give you an idea of the magnitudes of absolute entropies. Appendix D contains a more extensive list. 

Entropy changes are important in every process, but chemists are particularly interested in the effects of entropy on chemical reactions. If a reaction occurs under standard conditions, its entropy change can be calculated from absolute entropies using the same reasoning used to calculate reaction enthalpies from standard enthalpies of formation. The products of the reaction have molar entropies, and so do the reactants. The total entropy of the products is the sum of the molar entropies of the products multiplied by their stoichiometric coefficients in the balanced chemical equation. The total entropy of the reactants is a similar sum for the reactants. Equation... 

The standard states of these materials are taken as the pure components at 298 °K and a pressure of 101.3 kPa. The following data on the absolute entropies of the hydrocarbons at 298 °K are available. 

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

Table 2.15 Absolute standard molar entropies for some aqueous ions (in J K" mol - )...

Work done with electrochemical cells, with particular reference to the temperature dependence of their potentials, has demonstrated that an accurate value for S (H h, aq) is — 20.9 J K mol-1. Table 2.15 gives the absolute molar entropies for the ions under consideration. The values of the absolute standard molar entropies of the ions in Table 2.15 are derived by using the data from Tables 2.13 and 2.14 in equations (2.51) and (2.57). 

Absolute Standard Molar Entropies of Hydration of Ions... 

The Absolute Standard Molar Entropy of Hydration of the Proton... 

Table 2.17 Absolute standard molar entropies of hydration for some ions (in J K-1 mol-1)...

Values of S° for some common substances at 25°C are listed in Table 17.1, and additional values are given in Appendix B. Note that the units of S°are joules (not kilojoules) per kelvin mole [J/(K mol)] Standard molar entropies are often called absolute entropies because they are measured with respect to an absolute reference point—the entropy of the perfectly ordered crystalline substance at 0 K [S° = 0 J/(K mol) atT = OK]. 

The standard molar entropy, S°, of a substance is the absolute entropy of 1 mol of the pure substance at 1 atm pressure and a specified temperature, usually 25°C. The standard entropy of reaction, AS0, can be calculated from the relation AS° = S°(products) — S°( reactants). 

What are the units of (a)standard molar entropies and (b) standard entropies of reaction Why are standard molar entropies sometimes called absolute entropies ... 

H, F and G) can be defined only with reference to some standard state. Entropy, however, can be defined in absolute terms with the help of the third law... 

Over the years, many experiments have been carried out which confirm the third law. The experiments have generally been of two types. In one type the change of entropy for a change of phase of a pure substance or for a standard change of state for a chemical reaction has been determined from equilibrium measurements and compared with the value determined from the absolute entropies of the substances based on the third law. In the other type the absolute entropy of a substance in the state of an ideal gas at a given temperature and pressure has been calculated on the basis of statistical mechanics and compared with those based on the third law. Except for well-known, specific cases the agreement has been within the experimental error. The specific cases have been explained on the basis of statistical mechanics or further experiments. Such studies have led to a further understanding of the third law as it is applied to chemical systems. 

Figure 3.6 shows schematically the molar entropy of a pure substance as a function of temperature. If a structural transformation occurs in the solid state, an additional increase in the molar entropy comes from the heat of the transformations. As shown in the figure, the molar entropy of a pure substance increases with increasing temperature. In chemical handbooks we see the tabulated numerical values of the molar entropy calculated for a number of pure substances in the standard state at temperature 298 K and pressure 101.3 kPa. A few of them will be listed as the standard molar entropy, s , in Table 5.1. Note that the molar entropy thus calculated based on the third law of thermodynamics is occasionally called absolute entropy. 

Table 5.1. Standard chemical potentials pi , standard molar enthalpy h , and standard molar absolute entropy values s of substances in the standard state of 298 K and...

Using standard absolute molar entropy data, S° Equation (11.10) applies. 

Absolute standard molar entropy values, >9 (298 K) can be provided. They are tabulated at 25 °C and for P° = 1 bar pressure. It should be noted from equation (16.4) that the values are absolute entropy values (in contrast to values of AfH° and AfG° values which are quoted as differences (i.e. relative values) in thermochemical tables (Frame 11, section 11.2)). 

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