Entropy standard values, table

Standard Gibbs free energies of formation can be determined in various ways. One straightforward way is to combine standard enthalpy and entropy data from tables such as Tables 6.5 and 7.3. A list of values for several common substances is given in Table 7.7, and a more extensive one appears in Appendix 2A. 

Boyer et al. [20] have measured the heat capacity of crystalline adenine, a compound of biologic importance, with high precision, from about 7 K to over 300 K, and calculated the standard entropy of adenine. Table 11.8 contains a sampling of their data over the range from 7.404 K to 298.15 K. Use those data to calculate the standard entropy of adenine at 298.15 K, which assume the Debye relationship for Cp. The value for 298.15 K is calculated by the authors from a function fitted to the original data. 

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. 

If the temperature is not too far removed from 298-16 °K we may, to a first approximation, replace the heat and entropy terms in (10.51) by their standard values at 298 16° which may be calculated from the data in table 8.1. Thus we have, approximately, at 1 atm. pressure,... 

The standard values of the enthalpy, H, entropy. S , and specific heat capacity, C , for COCIF (ideal gas state, atmospheric pressure, 25 C) have been calculated from molecular data. The data reported by various authors are recorded in Table 16.4. 

Tables 9-11 list the predicted thermodynamic functions for the hydration of divalent, trivalent and tetravalent lanthanides as calculated by Bratsch and Lagowski (1985b). Values for yttrium hydration are also included when available. The formation values refer to the reaction Ln, Ln"a while the hydration values relate to the use of eqs. (28)-(30). The standard state ionic entropies given in table 10 are corrected for...

Table 2, containing results derived from measurements of heat capacities of some pure organic compounds published since 1961, gives values of temperatures, enthalpies, and entropies of phase transitions, and also of standard entropies. In the Table, (t) refers to crystal-crystal transitions (m) to crystal-liquid transitions (c), (1), and (g) to crystal, liquid, and gas G to glass transition and m, s to metastable, stable crystal. 

The entropy of a pure crystalline solid at absolute zero is zero. As energy is added, the randomness of the molecular motion increases. Measurements of energy absorbed and calculations are used to determine the absolute entropy or standard molar entropy, and values are then recorded in tables. These molar values are reported as kJ/(mol K). Entropy change, which can also be measured, is defined as the difference between the entropy of the products and the reactants. Therefore, an increase in entropy is represented by a positive value for AS, and a decrease in entropy is represented by a negative value for AS. 

There are several important ramifications of equation 3.26. First, it introduces the concept that an absolute entropy can be determined. Entropy thus stands alone among state functions as the only one whose absolute values can be determined. Therefore, in large thermodynamic tables of At/ and AH values, parallel entries for entropy are for S, not AS. It also implies that the entropies found in tables are not zero for elements under standard conditions, because we are now tabulating absolute entropies, not entropies for formation reactions. We can determine changes in entropies, AS s, for processes up to now we have dealt exclusively with changes in entropy. But Boltzmann s equation 3.26 means that we can determine absolute values for entropy. 

Note that to use this formula we use the enthalpy of vaporization at the boiling temperature. Table 2.1 lists the entropy of vaporization of several substances at 1 atm. For the standard value, AyapS, we use data corresponding to 1 bar. Because vaporization is endothermic for all substances (with one exception of little relevance to biology helium), all entropies of vaporization are positive. The increase in entropy accompanying vaporization is in line with what we should expect when a compact liquid turns into a gas. To calculate the entropy of phase transition at a temperature other than the transition temperature, we have to do additional calculations, as shown in the following brief illustration. 

If we only consider systems of pure substances in their standard state, eqn. (5.28), it is immediately possible to use table data for thermodynamic standard values. However, we have already learned that, for example, the entropy S of an ideal gas depends on the pressure (see for example 4.26) therefore, the molar free energy of the gas must also depend on the pressure. 

A lustrous metal has the heat capacities as a function of temperature shown in Table 1-4 where the integers are temperatures and the floating point numbers (numbers with decimal points) are heat capacities. Print the curve of Cp vs. T and Cp/T vs. T and determine the entropy of the metal at 298 K assuming no phase changes over the interval [0, 298]. Use as many of the methods described above as feasible. If you do not have a plotting program, draw the curves by hand. Scan a table of standard entropy values and decide what the metal might he. 

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. 

Table 7.1 lists the standard entropies of vaporization of a number of liquids. These and other data show a striking pattern many values are close to 85 J-K 1-mol h This observation is called Trouton s rule. The explanation of Trouton s rule is that approximately the same increase in positional disorder occurs when any liquid is converted into vapor, and so we can expect the... 

Using data from Table 9.2 and standard graphing software, determine the enthalpy and entropy of the equilibrium N204(g) — 2 N02(g) and estimate the N—N bond enthalpy in N204. How does this value compare with the mean N—N bond enthalpy in Table 6.8 ... 

The use of direct electrochemical methods (cyclic voltammetry Pig. 17) has enabled us to measure the thermodynamic parameters of isolated water-soluble fragments of the Rieske proteins of various bci complexes (Table XII)). (55, 92). The values determined for the standard reaction entropy, AS°, for both the mitochondrial and the bacterial Rieske fragments are similar to values obtained for water-soluble cytochromes they are more negative than values measured for other electron transfer proteins (93). Large negative values of AS° have been correlated with a less exposed metal site (93). However, this is opposite to what is observed in Rieske proteins, since the cluster appears to be less exposed in Rieske-type ferredoxins that show less negative values of AS° (see Section V,B). 

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. 

Table 5 lists equilibrium data for a new hypothetical gas-phase cyclisation series, for which the required thermodynamic quantities are available from either direct calorimetric measurements or statistical mechanical calculations. Compounds whose tabulated data were obtained by means of methods involving group contributions were not considered. Calculations were carried out by using S%g8 values based on a 1 M standard state. These were obtained by subtracting 6.35 e.u. from tabulated S g-values, which are based on a 1 Atm standard state. Equilibrium constants and thermodynamic parameters for these hypothetical reactions are not meaningful as such. More significant are the EM-values, and the corresponding contributions from the enthalpy and entropy terms. 

By convention, the standard Gibbs function for formation AfG of graphite is assigned the value of zero. On this basis, AfG gg of diamond is 2900 J mol Entropies and densities also are listed in Table 8.2. Assuming that the entropies and densities are approximately constant, determine the conditions of temperature and pressure under which the manufacture of diamonds from graphite would be thermodynamically and kinetically practical [2]. 

As we mentioned, it is necessary to have information about the standard enthalpy change for a reaction as well as the standard entropies of the reactants and products to calculate the change in Gibbs function. At some temperature T, A// j can be obtained from Af/Z of each of the substances involved in the transformation. Data on the standard enthalpies of formation are tabulated in either of two ways. One method is to list Af/Z at some convenient temperature, such as 25°C, or at a series of temperatures. Tables 4.2 through 4.5 contain values of AfZ/ at 298.15 K. Values at temperatures not listed are calculated with the aid of heat capacity equations, whose coefficients are given in Table 4.8. 

Standard entropies for many substances are available in tables such as Tables 11.2 through 11.6. Generally, the values listed are for 298.15 K, but many of the original sources, such as the tables of the Thermodynamics Research Center, the JANAF tables, or the Geological Survey tables, give values for other temperatures also. If heat capacity data are available, entropy values for one temperature can be converted to those for another temperature by the methods discussed in Section 11.4. 

Table 3.6 Comparison of predictive capacities of various equations in estimating standard molar entropy T = 298.15 K, P = 1 bar). Column I = simple summation of standard molar entropies of constituent oxides. Column II = equation 3.86. Column III = equation 3.86 with procedure of Holland (1989). Column IV = equation 3.85. Values are in J/(mole X K). Lower part of table exchange reactions adopted with equation 3.85 (from Helgeson et al., 1978) and Sj finite differences for structural oxides (Holland, 1989). 

Standard state entropy values and Maier-Kelley coefficients of heat capacity at constant P, with respective T limits of validity, are listed for the same components in table 5.13. The adopted polynomial expansion is the Haas-Fisher form ... 

Chemists have found it possible to assign a numerical quantity for the entropy of each substance. When measured at 25° C and 1 atm, these are called standard entropies. Table l4-4 lists 12 such values, symbolized by S° where the superscript denotes the standard state. 

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

The entropy change in a process is given by eqn. (14) and it follows that entropies can be assigned to individual substances. As entropy is a state function, its value will depend on the state of the substance and, with the aid of eqn. (14), the entropy difference between any two states can be calculated. The third law enables a zero to be fixed for the entropy scale and there are tables [5—9] which give the entropies of many substances in their standard states at the reference temperature of 298 K. As long as there is no change of phase, the entropy at any other temperature can be calculated using... 

Barrer (3) makes similar calculations for the entropies of occlusion of substances by zeolites and reaches the conclusion that the adsorbed material is devoid of translational freedom. However, he uses a volume, area or length of unity when considering the partition function for translation of the adsorbed molecules in the cases where they are assumed to be capable of translation in three, two or one dimensions. His entropies are given for the standard state of 6 = 0.5, and the volume, area or length associated with the space available to the adsorbed molecules should be of molecular dimensions, v = 125 X 10-24 cc., a = 25 X 10-16 cm.2 and l = 5 X 10-8 cm. When these values are introduced into his calculations the entropies in column four of Table II of his paper come much closer together, as is shown in Table I. The experimental values for different substances range from zero to —7 cals./deg. mole or entropy units, and so further examination is required in each case to decide... 

Table 3 provides entropies for those species that are needed to determine the temperature dependence of standard potentials for alkali metal redox couples. AU of these entropies were obtained from values published by NIST [11]. The resulting temperature dependences agree well with values tabulated by Bratsch [17]. 

Using equation (41), and the values of E roor/ro, ro determined as described above, values for BDFE can be determined if E°ro7ro is known. In fact, in favorable conditions, the standard potential for the RO /RO couple can be determined through analysis of the voltammetric oxidation of the RO anion. In this way, reasonable estimates of solution 0—0 BDFEs were obtained for some peroxides. The data are also reported in Table 4 and are the same within experimental error. Since the entropy term for this series of compounds is not expected to be very different, this implies that the BDE of these compounds is also the same consistent with what is known about the substituent effects on BDE for simple peroxides." " " Using a common entropy correction for the acyclic peroxides, the BDE of the peroxides is in the range 34-37 kcal moU. ... 

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). 

The values of the changes in standard Gibbs energy, standard enthalpy and standard entropy are given for all the stages. The calculation of some of the values depends upon the known values for the standard entropies of the participating species given in Table 4.3. 

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