Entropy tabulated values

For the electrochemical cell reaction, the reaction free energy AG is the utilizable electrical energy. The reaction enthalpy AH is the theoretical available energy, which is increased or reduced by an amount TAS. The product of the temperature and the entropy describes the amount of heat consumed or released reversibly during the reaction. With tabulated values for the enthalpy and the entropy it is possible to obtain AG. ... 

C14-0056. Using tabulated values of S °, calculate the standard entropy per mole of atoms for He, H2,... 

First-order estimates of entropy are often based on the observation that heat capacities and thereby entropies of complex compounds often are well represented by summing in stoichiometric proportions the heat capacities or entropies of simpler chemical entities. Latimer [12] used entropies of elements and molecular groups to estimate the entropy of more complex compounds see Spencer for revised tabulated values [13]. Fyfe et al. [14] pointed out a correlation between entropy and molar volume and introduced a simple volume correction factor in their scheme for estimation of the entropy of complex oxides based on the entropy of binary oxides. The latter approach was further developed by Holland [15], who looked into the effect of volume on the vibrational entropy derived from the Einstein and Debye models. 

You need tabulated values of standard enthalpies of formation and standard entropies for the three gases, as shown in Table l4-7. 

In this chapter we shall consider the application of tabulated values of affinities, heats and entropies of reaction to the calculation of equilibrium constants. As we have pointed out already it is much more convenient to consider standard affinities of reaction than equilibrium constants. This is because standard affinities can be added and subtracted in just the same way as stoichiometric equations, so that the standard affinity of a reaction not included in the table is easily calculated. This means, as we shall see, that the only reactions which need to be included are those relating to the formation of compounds from their elements. 

Use tabulated values of absolute entropies to calculate the entropy change, AS... 

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-... 

We use the equation for standard entropy change to calculate A5j from the tabulated values of standard molar entropies, 298, for the substances in the reaction. 

Although enthalpies of substances are relatively independent of pressure (for gases) and of concentration (for dissolved species), their entropies, and thus the free energies as well, depend markedly on these variables. Tabulated values for 5 and G usually refer to the idealized state of 1 bar or 1 atm pressure for gases, 1 M concentration for solutes, and to the.pure substances for liquids and solids. Table... 

Finally, although neither G nor H can be measured in absolute terms, so that we are forced always to use differences of these quantities, absolute values of S can be measured calorimetrically. Thus, tables of thermodynamic data for compound i contain values of A/G°, A fH°, and Sf, where S is the entropy of i. If we want a value of A fS°, we must calculate it from the tabulated values of S for the compound and its constituent elements. 

SECTION 19.4 The third law allows us to assign entropy values for substances at different temperatures. Under standard conditions the entropy of a mole of a substance is called its standard molar entropy, denoted S°. From tabulated values of S°, we can calculate the entropy change for any process under standard conditions. For an isothermal process, the entropy change in the surroundings is equal to —AH/T. 

Solution Water at 100 °C, 20 bar is compressed liquid and its entropy is not listed in the steam tables that are provided in the appendk. It may be estimated, however, from the tabulated values at saturation. Since the entropy of liquids is largely independent of pressure and a function of temperature only, we may relate it to entropy on the saturation line in two different paths, one of constant temperature and one of constant pressure (see a very similar calculation of enthalpy in Example, 2.12I. 

Finally, as a state function, entropy can be tabulated. The steam tables in the appendix include the specific entropy of water in the saturated region (liquid, vapor) and in the superheated vapor region. If tabulated values are not available, then entropy changes maybe calculated from eg. (4.8). The calculation requires the amount of heat that is exchanged along the path and this is generally obtained by application of the first law. This methodology is applied below to a number of special cases. 

Problem 4.1 Calculate the entropy change of steam between states Pi = 36 bar, T, = 250 C, and = 22 bar, P2 = 400 °C by direct application of the definition of entropy. Hint devise a path of constant pressure followed by a path of constant volume that connects the two states use tabulated values of U and H to calculate the required heat capacities. 

At the vapor-liquid boundary, a single-phase system splits into two phases,i each with its own properties (molar volume, enthalpy, entropy, etc.). The precise conditions under which phase splitting occurs is an important problem in thermodynamics. Up to this point we have relied on tabulated values and empirical equations, such as the Antoine equation, to establish the relationship between saturation temperature and pressure. In this chapter we develop a connection between the conditions at saturation and the equation of state. The key thermodynamic property that makes this connection possible is the Gibbs energy. 

The fugacity is related to the Gibbs energy, which in turn is related to the enthalpy and entropy. It is possible, therefore, to calculate it from tabulated values of H and S. The calculation is demonstrated with the following example. 

Calculate the standard enthalpy and Gibbs free entropy of reaction from tabulated values. 

The tabulated values for the enthalpy, entropy, and heat capacity are on a molar basis. In order to convert them to the specific property (per unit mass), divide by the molar mass of carbon dioxide (44.010 g/mol). 

The entropy data in this diagram are from program steam, v.2.2, developed by Harvey et al. (2000). This program, in common with many other sources, reports values of entropy which are not third law entropies (Chapter 5), but the difference in entropy between the state of interest and the T and P of the triple point of water. Program SUPCRT92 on the other hand, reports third law entropies, that is, the entropy of water using zero as the entropy of perfectly crystalline ice at 0 K. The third law entropy of water at the triple point is 63.304 Jmol K or 15.130calmol K", so this must be added to many tabulated values to get third law entropies. More detail on steam tables is presented in 13.6.1. 

For most substances, the values of standard entropies are not available for a wide range of temperatures. Most commonly, tables present only data at 25°C. For most purposes, it is sufQcient to use the standard entropies at 25°C to calculate reaction entropy changes at other temperatures because A5 rxr does not generally depend highly on temperature. If accurate work is needed, however, or if the temperature of interest is well removed from the temperature for which data are available, it is necessary to correct the tabulated values for the change in temperature. To do this, we can use a procedure analogous to that outlined in Section 7.7 for the calculation of AT/j n at alternate temperatures. 

According to Joules law, internal energy and enthalpy for ideal gases are functions of temperature only, u = u(T), and h = h(T). For this reason, ideal gas properties are tabulated as functions of temperature only. Entropy for an ideal gas is a function of both pressure and temperature, so property tables include s° (T), which is the entropy at the given temperature and one atmosphere of pressure. To determine entropy at other pressures, it is necessary to apply a correction to the tabulated values. 

Understand the relationship of entropy to the dispersal of energy and dispersal of matter (disorder) in a system Use tabulated values of absolute entropies to calculate the entropy change, AS ... 

What is the absolute entropy of 1 mole of He at 25.0°C and 1.000 atm pressure Compare this with the tabulated value of 126.04 J/(mol-K). Don t forget that proper units are necessary. 

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