Standard molar entropy table

Standard molar entropies of elements, compounds, and aqueous ions are listed in Table 17.1 (p. 456). Notice that—... 

TABLE 7.2 Standard Molar Entropy of Water at Various Temperatures... 

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 14-2 Standard Molar Entropies (S°) of Selected Substances at 298 K...

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). 

By applying equation 9.97 to plots of the type shown in figure 9.15B, Lux (1987) obtained standard molar enthalpies AH° and standard molar entropies ASf of solution of noble gases in melts, as listed in table 9.8. Enthalpies of solution are positive but close to zero, within error approximation. 

Table 2.13 Standard molar entropies of some main group elements and the conventional standard molar entropies of their aqueous cations at 25 C (in J K 1 mol- )...

The conventional standard molar entropies of some anions and some elements are given in Table 2.14. 

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). 

Self-Test 7.6B Calculate the standard molar entropy of freezing of benzene at its freezing point (see Table 6.2). 

If we want to calculate the entropy of a liquid, a gas, or a solid phase other than the most stable phase at T =0, we have to add in the entropy of all phase transitions between T = 0 and the temperature of interest (Fig. 7.11). Those entropies of transition are calculated from Eq. 5 or 6. For instance, if we wanted the entropy of water at 25°C, we would measure the heat capacity of ice from T = 0 (or as close to it as we can get), up to T = 273.15 K, determine the entropy of fusion at that temperature from the enthalpy of fusion, then measure the heat capacity of liquid water from T = 273.15 K up to T = 298.15 K. Table 7.3 gives selected values of the standard molar entropy, 5m°, the molar entropy of the pure substance at 1 bar. Note that all the values in the table refer to 298 K. They are all positive, which is consistent with all substances being more disordered at 298 K than at T = 0. 

We can use the data in Table 7.3 and Appendix 2A to calculate the entropy change when reactants change into products. The standard reaction entropy, ASr°, is the difference in standard molar entropies of the products and reactants, taking into account their stoichiometric coefficients ... 

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]. 

Standard molar entropies make it possible to compare the entropies of different substances under the same conditions of temperature and pressure. It s apparent from Table 17.1, for example, that the entropies of gaseous substances tend to be larger than those of liquids, which, in turn, tend to be larger than those of solids. Table 17.1 also shows that S° values increase with increasing molecular complexity. Compare, for example, CH3OH, which has S° = 127 J/(K mol), to CH3CH2OH, which has S° = 161 J/(K mol). 

To calculate A S° for the reaction, subtract the standard molar entropies of all the reactants from the standard molar entropies of all the products. Look up the S° values in Table 17.1 or Appendix B and remember to multiply the S° value for each substance by its coefficient in the balanced chemical equation. 

To determine the sign of AStotai = ASsys + ASsurr/ we need to calculate the values of ASsys and ASsurr. The entropy change in the system equals the standard entropy of reaction and can be calculated using the standard molar entropies in Table 17.1. To obtain ASsurr = —AH°/T, first calculate AH° for the reaction from standard enthalpies of formation (Section 8.10). 

These are the properties of the monatomic gas at a pressure of 1 bar. It should be pointed out that this standard molar Gibbs energy is not the AfG° of thermodynamic tables because there the convention in thermodynamics is that the standard formation properties of elements in their reference states are set equal to zero at each temperature. However, the standard molar entropies of monatomic gases without electronic excitation calculated using equation 2.8-11 are given in thermodynamic tables. 

The standard molar entropies at 298.15 K derived from the low-temperature heat capacity measurements are summarized in table 3. Similar to the heat capacity, the entropy can be described as the sum of the lattice and excess components (Konings, 2001, 2002) ... 

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. 

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)). 

A long time ago chemists realized that the most efficient way to store thermodynamic data on chemical reactions is by making tables of standard thermodynamic properties of species. The NBS Tables of Chemical Thermodynamic Properties (4) gives AfG°, Af// and Sm° for species at 298.15 K at xero ionic strength. Since the standard molar entropy is not available for many species of biochemical interest, the standard entropies of formation Af S" are used. This property of a species is calculated by using... 

A eiei is the number of atoms of element i in the crystalline substance and (j m (298.I5 is the standard molar entropy of element i in its thermodynamic reference state. This equation makes it possible to calculate Af5 ° for a species when Sm ° has been determined by the third law method. Then Af G° for the species in dilute aqueous solution can be calculated using equation 15.3-2. Measurements of pATs, pA gS, and enthalpies of dissociation make it possible to calculate Af G° and Af//° for the other species of a reactant that are significant in the pH range of interest (usually pH 5 to 9). When this can be done, the species properties of solutes in aqueous solution are obtained with respect to the elements in their reference states, just like other species in the NBS Tables (3). 

In this case the hydrogen ion is added to the left side to balance the formation reaction. For more complicated organic weak acids it is useful to remember that the atomic composition to be used in calcentropy298 for each species is that shown for the uncharged form in the Merck Index (9). The standard molar entropies of species in kJ K" mol are calculated using theAf5 ° in Table 15.1. 

Using the table of standard molar entropies in Appendix D, calculate A.S° for the chemical reaction... 

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-... 

Figure 5.5 The standard molar entropies of boron and hydrogen from 0 to 4500 K. Note the large increase on vaporization. (Data from JANAF Thermochemical Tables, Dow Chemical Company, Midland, Michigan.)...

Table 2.14 Conventional standard molar entropies of some elements and the Group 17 anions at 25 "C (in J K" morh...

Molar entropies for substances in their standard states are known as standard molar entropies and denoted S°. The standard state for any substance is defined as the pure substance at 1 atm pressure. TABLE 19.1 lists the values of S° for a number of substances at 298 K Appendix C gives a more extensive list. 

Plan We can make this calculation using Equation 19.8 and the standard molar entropy values in Table 19.1 and Appendix C. 

On the other hand, thermodynamic quantities that pertain to the formation of isolated ions from the elements in their standard states are well defined. The standard molar Gibbs energy and the enthalpy of formation, AfG°(F= =, g) and g), of many ions have been reported. The standard molar entropy and constant-pressure heat capacity, 5°(F, g) and Cp(F= =, g), of isolated ions are also well defined quantities and have been reported. Such data are generally available for the standard temperature T° = 298.15 K and pressure P° = 100 kPa, and suitable sources are the NBS tables (Wagman et al. 1982) and the book by Marcus (1997). The standard molar volume of an isolated ion is trivial, being the same for all ions V°(F , g)= RT /P = 0.02479m mor , where/ = 8.31451 J K mor is the gas constant. 

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