Elements absolute entropies

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. 

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. 

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... 

Note that Gibbs free energy is listed as a single entry for each substance in Table 16-1, but entropy must be calculated by taking the difference of the tabulated absolute entropies of the substance and its elements from which it is made. 

Because absolute entropies, rather than entropies of formation, are tabulated, the entries for entropies of elements are not zero and must not be neglected in using Eq. (15). 

Necessary data for estimating the standard heat of formation and the absolute entropy by Equations 3 and 4 are the elemental analysis, structural parameters, fa and a, and the normal boiling point. For a practical purpose, it will be more convenient if we could calculate AHf° and S° only from elemental analysis data and normal boiling point. The aromaticity fa for coal liquids may be estimated by the correlation shown in Figure 1. On the other hand, the value of 0 may be taken as 0.3 for its average value based on the reported data (lf3, 20, 21). Substitution of these relations into Equations 3 and 4 gives... 

For entropy, one does assume S°=0 at T = 0K for pure elements, so "absolute entropies" are used (ignoring zero-point motion at 0 K). Therefore the standard enthalpies of formation of molecules can be positive or negative Sideline. There was a committee-encouraged effort to replace Aby AfC,0, but, luckily, that bad idea has lost favor. Remember Eisenhower s66 dictum that "a camel is a horse designed by a committee". 

While absolute entropy values can now be determined absolute values of Internal Energy and Enthalpy cannot be conceived. For ease of calculation, related especially to metallurgical reactions (constant pressure processes), a suitable reference point of enthalpy is conventionally chosen and that is - for pure elements, the enthalpy is zero when in Standard State . Standard... 

Tables for this defined reference state, including the heat capacity, the heat content relative to 298.15° K., the absolute entropy, and the free energy function at even 100° intervals from 298.15° to 3000° K. have b n assembled for the first 92 elements. These tables are arranged alphabetically beginning on page 36. The choice of 298.15° K. as the reference temperature is made because the low temperature heat capacities of many elements and compounds are not known. Most of the thermodynamic data now reported in the literature refer to 25° C., which, when combined with the recent international agreement on 273.15° K. for the ice point (319) gives a reference temperature of 298.15° K. The figure 298° K. quoted in the tables and text should be understood to be the reference temperature, 298.15° K. For those who prefer to use 0° K. as the reference temperature, we have included, for cases in which it is known, the heat content at 298.15° K. relative to 0° K.

The value of AS° can be obtained from the absolute entropies of the substances involved at 25°C and 1 atm pressure (both elements and compounds, because the absolute entropy S° of an element is not zero in its standard state). 

By examining the following graphs, predict which element—copper or gold—has the higher absolute entropy at a temperature of 200 K. 

The entropy change is negative because the number of moles of gas has decreased by 1.5. Note that the absolute entropies of the elements are not 0, and that the entropy change for the reaction in which a compound is formed from the elements is also not 0. 

As the temperature of a substance increases, the particles vibrate more vigorously, so the entropy increases (Figure 15-14). Further heat input causes either increased temperature (still higher entropy) or phase transitions (melting, sublimation, or boiling) that also result in higher entropy. The entropy of a substance at any condition is its absolute entropy, also called standard molar entropy. Consider the absolute entropies at 298 K listed in Table 15-5. At 298 K, any substance is more disordered than if it were in a perfect crystalline state at absolute zero, so tabulated values for compounds and elements are always positive. Notice especially that g of an element, unlike its A// , is not equal to zero. The reference state for absolute entropy is specified by the Third Law of Ther-... 

Rubber Company Handbook (Weast, 1987) is one of the more commonly available sources. More complete sources, including some with data for a range of temperatures, are listed in the references at the end of the chapter. Note that many tabulations still represent these energy functions in calories and that it may be necessary to make the conversion to Joules (1 cal = 4.1840J). Because of the definition of the energy of formation, elements in their standard state (carbon as graphite, chlorine as CI2 gas at one bar, bromine as Br2 liquid, etc.) have free energies and enthalpies of formation equal to zero. If needed, the absolute entropies of substances (from which AS may be evaluated) are also available in standard sources. 

Thus the absolute entropies of elements and compounds can be. established. These can be used to determine the entropy changes accompanying chemical reactions. 

As we will see, it is possible to determine the absolute entropy of a substance, something we cannot do for energy or enthalpy. Standard entropy is the absolute entropy of a substance at 1 atm and 25°C. It is this value that is generally used in calculations. (Recall that the standard state refers only to 1 atm. The reason for specifying 25°C is that many processes are carried out at room temperature.) Table 18.1 lists standard entropies of a few elements and compounds Appendix 3 provides a more extensive listing. The units of entropy are J/K or J/K mol for 1 mole of the substance. We use joules rather than kilojoules because entropy values are typically quite small. Entropies of elements and compounds are all positive (that is, S° > 0). By contrast, the... 

Tables 7.1 and 7.2 are copied directly from the thermodynamic compilation of Robie, Hemingway and Fisher (1978), abbreviated as RHF. Many of the other standard thermodynamic data sets discussed later in this chapter are arranged in a similar fashion. We can now begin to examine some of the features of these tables a little more closely. First, we have just observed that A/ G° and Ay H° for the formation of 02(g) from the elements is zero at all temperatures because this is just the difference between the G (or H) of oxygen and the G (or H) of the elements making up oxygen, which is the same thing. We have not yet defined the equilibrium constant K (see Chapter 13), but for completeness we should point out that it is 1.0 and log IT = 0 for the reaction for the formation of oxygen from itself, giving us another column of zeros. Note too that the entropy of 02(g), S°t, given in Table 7.1 is not equal to zero at any temperature shown these are absolute entropies, not entropies of formation from the elements, as discussed in Chapter 6 and again later in this chapter. Table 7.1 is typical of data tables for the elements.

The entropies so computed are termed Third Law, absolute, or conventional entropies, and designated S° or. These are not at all comparable to enthalpies and free energies of formation, AfH° and A/G°, which instead refer to reactions forming the compound from its elements. For example, AfH° and AfG° for an element such as 02(5) at 25°C are both necessarily zero, while the absolute entropy, S Igg, is 205.15 mol (see Table 7.1). 

Srompound = ideal gas absolute entropy of the compound at 298.f5 K and 1 atm, J/mol K n = number of different elements contained in the compound... 

Don t forget that absolute entropies are obtainable for the elements just as well as for compounds, and these numbers are available in tables of data, such as Appendix B. These numbers are... 

As in the case of energy or enthalpy, we are usually interested in differences in entropy rather than absolute values. However, in the case of entropy, it is possible to assign absolute values. This is a consequence of the third law of thermodynamics, which states that the entropy of perfect crystals of all pure elements and compounds is zero at the absolute zero of temperature (OK), Consequently, the absolute entropy of a substance at any temperature T is given by the change in the entropy of the substance in moving from OK to T. The absolute entropies of many substances (generally at 25°C and 1 atm - indicated by 5 for the molar absolute entropy under standard conditions) are... 

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