Solid thermodynamic properties

X-ray measurements normally give information on the structure of the system studied. In special cases however, such as the lyotropic and the thermotropic smectic-A phases of liquid crystals or two dimensional solids, thermodynamic properties can be obtained reliably from the analysis of the shape of the structure factor. 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

Table 2. Physical and Thermodynamic Properties of Solid Hydrogen...

Anhydrous Hydrogen Chloride. Anhydrous hydrogen chloride is a colorless gas that condenses to a colorless liquid and freezes to a white crystalline solid. The physical and thermodynamic properties of HCl are summarized in Table 2 for selected temperatures and pressures. Figure 1 shows the temperature dependence of some of these properties. 

Vapor pressure is the most important of the basic thermodynamic properties affec ting liquids and vapors. The vapor pressure is the pressure exerted by a pure component at equilibrium at any temperature when both liquid and vapor phases exist and thus extends from a minimum at the triple point temperature to a maximum at the critical temperature, the critical pressure. This section briefly reviews methods for both correlating vapor pressure data and for predicting vapor pressure of pure compounds. Except at very high total pressures (above about 10 MPa), there is no effect of total pressure on vapor pressure. If such an effect is present, a correction, the Poynting correction, can be applied. The pressure exerted above a solid-vapor mixture may also be called vapor pressure but is normallv only available as experimental data for common compounds that sublime. 

The thermodynamic properties of the solid silicates show the expected entropy change of formation from the constituent oxides of nearly zero, which is typical of the reaction type... 

The thermodynamic properties of thiophene,2-methylthiophene, ° and 3-methylthiophene have been computed from careful measurements of the heat capacity of the solid, liquid, and vapor states, the heat of fusion, the heat of vaporization, and the heat of combustion. From the heat of combustion of thiophene and from thermochemical bond energies, the resonance energy of thiophene has been re-estimated to be only 20 kcal/mole. 

R.C. Oliver et al, USDeptCom, Office Tech-Serv ..AD 265822,(1961) CA 60, 10466 (1969) Metal additives for solid proplnts formulas for calculating specific impulse and other proplnt performance parameters are given. A mathematical treatment of the free-energy minimization procedure for equilibrium compn calcns is provided. The treatment is extended to include ionized species and mixing of condensed phases. Sources and techniques for thermodynamic-property calcns are also discussed... 

The thermodynamic properties of a chemical substance are dependent upon its state and, therefore, it is important to indicate conditions when writing chemical reactions. For example, in the burning of methane to form carbon dioxide and water, it is important to specify whether each reactant and product are solid, liquid, or gaseous since different changes in the thermodynamic property will occur depending upon the state of each substance. Thus, different volume and energy changes occur in the reactions... 

We are interested in describing and calculating AmixZ, the change in the thermodynamic variable Z, when liquids (or solids) are mixed to form a solution. We will begin by deriving the relationship for calculating Amjx<7. Changes in the other thermodynamic properties can then be obtained. 

Statistical thermodynamics provides the relationships that we need in order to bridge this gap between the macro and the micro. Our most important application will involve the calculation of the thermodynamic properties of the ideal gas, but we will also apply the techniques to solids. The procedure will involve calculating U — Uo, the internal energy above zero Kelvin, from the energy of the individual molecules. Enthalpy differences and heat capacities are then easily calculated from the internal energy. Boltzmann s equation... 

One of the first attempts to calculate the thermodynamic properties of an atomic solid assumed that the solid consists of an array of spheres occupying the lattice points in the crystal. Each atom is rattling around in a hole at the lattice site. Adding energy (usually as heat) increases the motion of the atom, giving it more kinetic energy. The heat capacity, which we know is a measure of the ability of the solid to absorb this heat, varies with temperature and with the substance.8 Figure 10.11, for example, shows how the heat capacity Cy.m for the atomic solids Ag and C(diamond) vary with temperature.dd ee The heat capacity starts at a value of zero at zero Kelvin, then increases rapidly with temperature, and levels out at a value of 3R (24.94 J-K -mol-1). The... 

Once equation (10.158) has been obtained for relating Cy. m to T for a Debye solid, equations relating (Um - U0 m), (Hm - Uo.m), and Sm to T can be derived. Tables of values, expressed in terms of 9d/T. can be found in Table A4.7, Appendix 4, with more extensive tables found in the literature1 to calculate these thermodynamic properties. 

Table A4.7 summarizes the thermodynamics properties of monatomic solids as calculated by the Debye model. The values are expressed in terms of d/T, where d is the Debye temperature. See Section 10.8 for details of the calculations. Tables A4.5 to A4.7 are adapted from K. S. Pitzer, Thermodynamics, McGraw-Hill, New York, 1995.

Chapter 10, the last chapter in this volume, presents the principles and applications of statistical thermodynamics. This chapter, which relates the macroscopic thermodynamic variables to molecular properties, serves as a capstone to the discussion of thermodynamics presented in this volume. It is a most satisfying exercise to calculate the thermodynamic properties of relatively simple gaseous systems where the calculation is often more accurate than the experimental measurement. Useful results can also be obtained for simple atomic solids from the Debye theory. While computer calculations are rapidly approaching the level of sophistication necessary to perform computations of... 

The kinetics of decomposition of these solids may be classified according to the process which has been identified as rate-limiting. This criterion allows a more concise presentation but is not completely satisfactory since some reactions show a sensitivity of behaviour to the conditions prevailing [1270]. Furthermore, certain of the reactions discussed are reversible. Reference to the extensive literature devoted to the thermodynamic properties of these solids and phase stabilities and interactions will only be made where kinetic observations or arguments have been used. 

Manes L, Benedict U (1985) Structural and Thermodynamic Properties of Actinide Solids and Their Relation to Bonding. 59/60 75-125... 

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. 

Phase changes, which convert a substance from one phase to another, have characteristic thermodynamic properties Any change from a more constrained phase to a less constrained phase increases both the enthalpy and the entropy of the substance. Recall from our description of phase changes in Chapter 11 that enthalpy increases because energy must be provided to overcome the intermolecular forces that hold the molecules in the more constrained phase. Entropy increases because the molecules are more dispersed in the less constrained phase. Thus, when a solid melts or sublimes or a liquid vaporizes, both A H and A S are positive. Figure 14-18 summarizes these features. 

Fig. 2.37. Phase diagram for Ca0-Na20 Si02-(Al203)-H20 system in equilibrium with quartz at 400°C and 400 bars. Plagioclase solid solution can be represented by the albite and anorthite fields, whereas epidote is represented by clinozoisite. Note that the clinozoisite field is adjacent to the anorthite field, suggesting that fluids with high Ca/(H+) might equilibrate with excess anorthite by replacing it with epidote. The location of the albite-anorthite-epidote equilibrium point is a function of epidote and plagioclase composition and depends on the model used for calculation of the thermodynamic properties of aqueous cations (Berndt et al., 1989).

The purpose of this compilation is to tabulate the densities of compounds, hence only minimal description of experimental methods used to measure the density of liquids or solids appears. Detailed descriptions of methods for density determination of solids, liquids and gases, along with appropriate density reference standards, appear in a chapter by Davis and Koch in Physical Methods of Chemistry, Volume VI, Determination of Thermodynamic Properties [86-ros/bae],... 

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