Standard Molar Thermodynamic Properties

Besides equilibriumconstants, additional thermodynamic data were included, if available, although little emphasis was put on their completeness. The data for primary master species comprise the standard molar thermodynamic properties of formation from the elements (AfG standard molar Gibbs energy of formation AfH°m standard molar enthalpy of formation ApSm- standard molar entropy of formation), the standard molar entropy (5m), the standard molar isobaric heat capacity (Cp.m), the coefficients Afa, Afb, and Afc for the temperature-dependent molar isobaric heat capacity equation... 

Standard Molar Thermodynamic Properties of Th2CrN3 and Th2MnN3, Calculated by the Authors of this Article from Estimated Entropy and Heat Capacity Data of Analogous Compounds [7, 8]. 

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

Practically in every general chemistry textbook, one can find a table presenting the Standard (Reduction) Potentials in aqueous solution at 25 °C, sometimes in two parts, indicating the reaction condition acidic solution and basic solution. In most cases, there is another table titled Standard Chemical Thermodynamic Properties (or Selected Thermodynamic Values). The former table is referred to in a chapter devoted to Electrochemistry (or Oxidation - Reduction Reactions), while a reference to the latter one can be found in a chapter dealing with Chemical Thermodynamics (or Chemical Equilibria). It is seldom indicated that the two types of tables contain redundant information since the standard potential values of a cell reaction ( n) can be calculated from the standard molar free (Gibbs) energy change (AG" for the same reaction with a simple relationship... 

USNBS 1982. United States National Bureau of Standards tables of molar thermodynamic properties. J. Phys. Chem Ref. Data, 11 (Supp. 2). World Wide Web Addresses http //www.ualberta.ca/ jplambec/che/data/p00404.htm and http // www.ucdsb.on.ca/tiss/stretton/cheml/data3.htm. 

Table 2.3 Test of the different equations for the standard partial molar volume of aqueous ions (Reproduced from Chemical Geology, A new equation of state for correlation and prediction of standard molal thermodynamic properties of aqueous species at high temperatures and pressures with permission from Elsevier)...

This table contains standard state thermodynamic properties of positive and negative ions in aqueous solution. It includes enthalpy and Gibbs energy of formation, partial molar entropy, and partial molar heat capacity. The standard state is the hypothetical ideal solution with molality equals 1 mol/kg. 

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. 

P. A. G. O Hare, G. A. Hope. Thermodynamic Properties of Tungsten Ditelluride (WTe2) II. Standard Molar Enthalpy of Formation at the Temperature of298.15 K. J. Chem. Thermodynamics 1992, 24, 639-647. 

O Hare, P.A.G. (1993) Calorimetric measurements of the specific energies of reaction of arsenic and of selenium with fluorine. Standard molar enthalpies of formation Af7/°m at the temperature 2.98.15 K of AsFs, SeF6, As2Se3, AS4S4, and As2S3. Thermodynamic properties of AsFs and SeF6 in the ideal-gas state. Critical assessment of AfH°m (AsF3, 1)), and the dissociation enthalpies of As-F bonds. Journal of Chemical Thermodynamics, 25, 391-402. 

O Hare, P.A.G., Lewis, B.M., Susman, S. and Volin, K.J. (1990) Standard molar enthalpies of formation and transition at the temperature 298.15 K and other thermodynamic properties of the crystalline and vitreous forms of arsenic sesquiselenide (As2S3). Dissociation enthalpies of As-Se bonds. Journal of Chemical Thermodynamics, 22, 1191-206. 

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 calculations of standard thermodynamic properties discussed in the rest of this section are based on the assumption that the standard enthalpies of formation of species are independent of temperature in other words, the heat capacities of species are assumed to be zero. In the future when more is known about the molar heat capacities of species, more accurate calculations can be based on the assumption that the molar heat capacities are independent of temperature. When the heat capacities of species are equal to zero, the standard entropies of formation are also independent of temperature. Under these conditions the values of AfG at other temperatures in the neighborhood of 298.15 K can be calculated using... 

The preceding sections have used standard molar concentration units for RNA and ions, indicated by brackets or the abbreviation M. Thermodynamic definitions of interaction coefficients are made in terms of molal units, abbreviated m, the moles of solute per kilogram of solvent water. Molal units have the convenient properties that the concentration of water is a constant 55.5 m regardless of the amount ofsolute(s) present, and the molality of one solute is unaffected by addition of a second solute. For dilute solutions, M and m units are interchangeable. We use molal units for the thermodynamic derivations in this section, and indicate later (Section 3.1) the salt concentrations where a correction for molar-molal conversion is required. 

Recall that the partial molar free energy or chemical potential of a component in a solution is independent of the standard state chosen. In other words, it is an absolute thermodynamic property of the component in the solution. 

The two primary reference works on inorganic thermochemistry in aqueous solution are the National Bureau of Standards tables (323) and Bard, Parsons, and Jordan s revision (30) (referred to herein as Standard Potentials) of Latimer s Oxidation Potentials (195). These two works have rather little to say about free radicals. Most inorganic free radicals are transient species in aqueous solution. Assignment of thermodynamic properties to these species requires, nevertheless, that they have sufficient lifetimes to be vibrationally at equilibrium with the solvent. Such equilibration occurs rapidly enough that, on the time scale at which these species are usually observed (nanoseconds to milliseconds), it is appropriate to discuss their thermodynamics. The field is still in its infancy of the various thermodynamic parameters, experiments have primarily yielded free energies and reduction potentials. Enthalpies, entropies, molar volumes, and their derivative functions are available if at all in only a very small subset. 

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). 

Also, it is customary to refer all thermodynamic properties to chemical potentials of all species, whether in the pure state or in solution, to their values under standard conditions. In that case the equilibrium constant will be designated, as before, by fCx and the pressure in the above equations is set at P = bar. Finally, it is possible to specify compositions in terms of molarity c, or molality m, leading to the specification of Kc and Km or Kc and Km - The resulting analysis becomes somewhat involved and will not be taken up here interested readers should read Section 3.7 for a full scale analysis of the treatment of nonideal solutions. 

The values in these tables were generated from the NIST REFPROP software (Lemmon, E. W., McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23 Reference Fluid Thermodynamic and Transport Properties—REFPROP, National Institute of Standards and Technolo, Standard Reference Data Program, Gaithersburg, Md., 2002, Version 7.1). The primary source for the thermodynamic properties is Magee, J. W., Outcalt, S. L., and Ely, J. F., Molar Heat Capacity C(u), Vapor Pressure, and (p, Rho, T) Measurements from 92 to 350 K at Pressures to 35 MPa and a New Equation of State for ChlorotrifluorometEiane (R13), Int. J. Thermophys. 21(5) 1097-1121, 2000. Validated equations for the viscosity and thermal conductivity are not currently available for this fluid. 

The standard state is here a purely hypothetical one, just as is the case with gases ( 30b) it might be regarded as the state in which the mole fraction of the solute is unity, but certain thermodynamic properties, e.g., partial molar heat content and heat capacity, are those of the solute in the reference state, he., infinite dilution (cf. 37d). If the solution behaved ideally over the whole range of compodtion, the activity would always be equal to the mole fraction, even when n = 1, i.e., for the pure solute (cf. Fig. 24,1). In this event, the proposed standard state would represent the pure liquid solute at 1 atm. pressure. For nonideal solutions, however, the standard state has no reality, and so it is preferable to define it in terms of a reference state. 

As with other thermodynamic variables, we usually compare entropy values for substances in their standard states at the temperature of interest 1 atm for gases, I M for solutions, and the pure substance in its most stable form for solids or liciuids. Because entropy is an extensive property, that is, one that depends on the amount of substance, we are interested in the standard molar entropy (S°) in units of J/moEK (or J mol -K ). The S° values at 298 K for many elements, compounds, and ions appear, with other thermodynamic variables, in Appendix B. 

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