Standard entropy, table

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. 

Themiodynamic tables usually report at least tln-ee quantities almost invariably the standard enthalpy of fomration at 298 K, Af (298 K) usually the standard entropy at 298 K,, S (298 K) (not AS y298 K), but the... 

Because of the Nemst heat theorem and the third law, standard themrodynamic tables usually do not report entropies of fomiation of compounds instead they report the molar entropy 50 7 for each element and... 

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. 

The heat capacity of thiazole was determined by adiabatic calorimetry from 5 to 340 K by Goursot and Westrum (295,296). A glass-type transition occurs between 145 and 175°K. Melting occurs at 239.53°K (-33-62°C) with an enthalpy increment of 2292 cal mole and an entropy increment of 9-57 cal mole °K . Table 1-44 summarizes the variations as a function of temperature of the most important thermodynamic properties of thiazole molar heat capacity Cp, standard entropy S°, and Gibbs function - G°-H" )IT. 

Table 17.1 can be used to calculate the standard entropy change, AS°, for reactions, using the relation... 

AS° for this system at 25°C and 1 atm can be calculated from a table of standard entropies it is found to be —358.4 J/K. The negative sign of AS° is entirely consistent with the second law. All the law requires is that the entropy change of the surroundings be greater than 358.4 J/K, so that ASunIverse > 0. 

Tables of standard free energies of formation at 25°C of compounds and ions in solution are given in Appendix 1 (along with standard heats of formation and standard entropies). Notice that, for most compounds, AG is a negative quantity, which means that the compound can be formed spontaneously from the elements. This is true for water ...

Self-Test 7.6A Calculate the standard entropy of vaporization of argon at its boiling point (see Table 6.3). 

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... 

TABLE 7.1 Standard Entropy of Vaporization at the Normal Boiling Point ... 

Use data in Table 7.3 or Appendix 2A to calculate the standard entropy change for each of the following reactions at 25°C. For each reaction, interpret the sign and magnitude of the reaction entropy, (a) The synthesis of carbon disulfide from natural gas (methane) CH4(g) + 4 S(s, rhombic) - CS2(1) +... 

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. 

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. 

The procedure followed in the use of the tables of Andersen et al. [1], and Yoneda [4] is illustrated below for the estimation of standard entropies. These tables also include columns of base structure and group contributions for estimating fHm,298.i5K> thc Standard enthalpy of formation of a compound, as well as columns for a, b, and c, the constants in the heat capacity equations that are quadratic in the temperature. Thus it is possible to estimate AfGm gg.isK by appropriate summations of group contributions to Af7/ 298.i5K and to 5m,298.i5K- Then, if information is required at some other temperature, the constants of the heat capacity equations can be inserted into the appropriate equations for AG, as a function of temperature and AGm can be evaluated at any desired temperature (see Equation 7.68 and the relation between AG and In K). 

Table 9.8 Standard molar enthalpies (Ai7°) and standard entropies (A5 ) of solution of noble gases in silicate melts, after Lux (1987). (1) leucite-basanite (2) tholeiite (3) alkali-olivine basalt.

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

Interestingly, the standard entropies (and in turn heat capacities) of both phases were found to be rather similar [69,70]. Considering the difference in standard entropy between F2(gas) and the mixture 02(gas) + H2(gas) taken in their standard states (which can be extracted from general thermodynamic tables), the difference between the entropy terms of the Gibbs function relative to HA and FA, around room temperature, is about 6.5 times lower than the difference between enthalpy terms (close to 125 kJ/mol as estimated from Tacker and Stormer [69]). This indicates that FA higher stability is mostly due to the lower enthalpy of formation of FA (more exothermic than for HA), and that it is not greatly affected by entropic factors. Jemal et al. [71] have studied some of the thermodynamic properties of FA and HA with varying cationic substitutions, and these authors linked the lower enthalpy of formation of FA compared to HA to the decrease in lattice volume in FA. 

The conventional standard entropies of some main group cations are given in Table 2.13, which also includes the standard entropies of the elements. 

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. 

We shall discuss now the variation of the three main thermodynamic functions with solvent composition for the case of n-Bu4NBr-water-acetone system and shall extend this discussion to the n-Bu4NBr-water-THF system. Figure 4 and Table IV present the results obtained. The figure was constructed as follows first the standard enthalpy of transfer AH°t, obtained by Ahluwalia and co-workers (12) from pure water to Z2 = 0.30, was used in order to get the standard entropy of transfer function from the relation ... 

TABLE 9.2 PER MOLE STANDARD ENTROPIES OF SELECTED SUBSTANCES AT 298 K (25°C)... 

During a chemical reaction there is a change in the identity of substances as reactants transform to products. If the sum of the standard entropies of the products is greater than the sum of the standard entropies of the reactants, then there is a net increase in entropy and the reaction is favored. The difference in entropies can be calculated using data such as is given in Table 9.2 by the same... 

The standard heat of sorption, Afl°, can then be interpreted in terms of appropriate energy contributions and the corresponding entropy, AS°, in terms of various degrees of freedom of the guest molecules relative to the host lattice (Table II) (10). An example of the use of the above method is given elsewhere in this volume (11). In comparing observed standard entropies with those based on the models of Table II, only empirical methods (12) are available for a priori estimates of the frequencies v. Nevertheless, comparisons have been of considerable interest (10). 

To calculate the standard entropy of vaporization of acetone at its boiling point of 329.4 K (corresponding to 56.2°C), we note from Table 6.2 that its standard enthalpy of vaporization at its boiling point is 29.1 kjmol-1. - Therefore, from Eq. 5, its standard entropy of vaporization at its boiling point is... 

The standard entropies of vaporization of a number of liquids are given in Table 7.1. When these and other data are considered, a striking feature is that many are reasonably close to 85 J-K -mol-1. This obser-... 

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