Thermodynamic tables, 390, Appendices

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. 

The International Union of Puie and AppUed Chemistry now recommends a standard pressure of 0.1 MPa (1 bar) in place of the previously accepted standard of 101.325 kPa (1 atm). The difference in thermodynamic quantities is not significant for condensed phases, and differences in A// values are not significant even for gases, but the user of thermodynamic tables will have to note carefully the standard state chosen for any compilation of data. See Ref. 1, pp. 2—23 lUPAC Division of Physical Chemistry, Commission on Symbols, Terminology and Units, Manual of symbols and terminology for physico-chemical quantities and units, M. L. McGlashan, M. A. Paul, and D. N. Whiffen, eds., Pure andApp. Chem 51, 1 (1979), and Appendix IV, Pure and Applied Chem. 54, 1239 (1982). 

Appendix C Tables of Thermodynamic Data Appendix D Glossary of Symbols... 

Numerical methods include those based on finite difference calculus. They are ideally suited for tabulated experimental data such as one finds in thermodynamic tables. They also include methods of solving simultaneous linear equations, curve fitting, numerical solution of ordinary and partial differential equations and matrix operations. In this appendix, numerical interpolation, integration, and differentiation are considered. Information about the other topics is available in monographs by Hornbeck [2] and Lanczos [3]. 

Such a series of experiments as has been outlined above., are rarely necessary nowadays. For most compounds the necessary experiments have already been carried out and the thermodynamic properties are tabulated as in Appendix 1. For instance, in the case of the butanes we would merely look up the standard free-energy changes on formation in thermodynamic tables. We find... 

As a state property, the molar (or specific) volume can be determined once as a function of pressure and temperature, and tabulated for future use. Tabulations have been compiled for a large number of pure fluids. In very common use are the steam tables, which contain tabulations of the properties of water. Steam is a basic utility in chemical plants as a heat transfer fluid for cooling or heating, as well as for power generation (pressurized steam), and its properties are needed in many routine calculations. Thermodynamic tables for water are published by the American Society of Mechanical Engineers (ASME) and are available in various forms, printed and electronic. A copy is included in the appendix. We will use them not only because water is involved in many industrial processes but also as a demonstration of how to work with tabulated values in general. 

The third law of thermodynamics (see Appendix E) shows us that at 0.00 K all perfectly regular crystaUine substances have the same value of the entropy, which we assign a datum value of s = 0.00. Entropies based on this value are called absolute entropies. They are used only in the study of chemical equUibrium (Chapter 12). The datum chosen for the steam tables is m = s = 0.00 for the saturated liquid at the triple point (solid, liquid, and gas in equihbrium at 32.018°E and 0.08866 psia). Eor refrigerants the common choice is h=s=0.00 for the saturated liquid at —40°F = —40°C. The light hydrocarbon tables choose h = s = 0.00 for the elements at 0.00 K, which is one of the common reference states for chemical reaction calculations. There are a variety of choices of datums, all of which seem like the right choice for some class of substances or problems. These datum or reference state values can be used in Eqs. 2.9 and 2.14 to calculate those tables, by methods shown below. There is no logical or thermodynamic reason why the values in the datum state must be chosen as 0.00. They could just as well be chosen as... 

Table 1.7 shows typical half reactions for the oxidation of a metal M in aqueous solutions with the formation of aquo cations, solid hydroxides or aquo anions. The equilibrium potential for each half reaction can be evaluated from the chemical potentials of the species involved see Appendix 20.2) and it should be noted that there is no difference thermodynamically between equations 2(a) and 2(b) nor between 3(a) and 3(b) when account is taken of the chemical potentials of the different species involved. 

Appendix 1 includes a review of SI base units as well as tables of thermodynamic data and equilibrium constants. 

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. 

Hilvert s group used the same hapten [26] with a different spacer to generate an antibody catalyst which has very different thermodynamic parameters. It has a high entropy of activation but an enthalpy lower than that of the wild-type enzyme (Table 1, Antibody 1F7, Appendix entry 13.2a) (Hilvert et al., 1988 Hilvert and Nared, 1988). Wilson has determined an X-ray crystal structure for the Fab fragment of this antibody in a binary complex with its TSA (Haynes et al., 1994) which shows that amino acid residues in the active site of the antibody catalyst faithfully complement the components of the conformationally ordered transition state analogue (Fig. 11) while a trapped water molecule is probably responsible for the adverse entropy of activation. Thus it appears that antibodies have emulated enzymes in finding contrasting solutions to the same catalytic problem. 

One cannot resolve all the correlation functions from the experimental (thermodynamic) data. However, by processing the data in the same way that we processed the data as if they were strictly identical sites (see Section 5.9 and Appendix J), we obtain quantities that should be understood only in an average sense, as discussed in Appendix J. The results for benzene-tetracarboxylic acids are reported in Table 6.2. We recall the value of fcj = 1.58 x 10 for benzoic acid. We... 

IV. Appendix Tables of Thermodynamic Properties for Some Chlorine Oxyfluorides. ... 

In addition to a discussion of the individual compounds, a section was added correlating the physical and chemical properties of the chlorine oxyfluorides with their structure. In the Appendix, full tables of thermodynamic properties are given for each compound, where known. 

The thermodynamic properties were computed with the molecular geometry and vibrational frequencies given above assuming an ideal gas at 1 atm pressure and using the harmonic-oscillator rigid-rotor approximation. These properties are given for the range 0-2000°K in the Appendix (Table AI). 

Some of the physical properties of FClOg are summarized in Table XXIX. In the Appendix (Table AIII), the temperature dependence of some of the thermodynamic properties is given (147). In addition to these data, the viscosity of gaseous FClOg between 50 and 150°C was reported... 

Tables of thermodynamic data necessary to apply equations listed by Cook are given in Appendix II of his book. The complete solution of the thermohydrodynamic theory for condensed explosives may then be effected in principle by a simultaneous solution of eqs...

Since this is independent of pH, it is simply a horizontal line at the lower left of Fig. 15.3. The value of E° used in Eq. 15.52 is somewhat more negative than the widely cited —0.409 V derived from the U.S. National Bureau of Standards (now the National Institute of Standards and Technology) thermodynamic data tables (cf. Appendix C). In fact, since various values between —0.409 and —0.475 V have been reported by experienced experimentalists using several different methods, the value selected here is intended to be a conservative compromise.8 The moral is that one should not place blind faith in tabulated data, even from the most authoritative sources. 

Standard potential or "Latimer" diagrams are useful for summarizing a considerable amount of thermodynamic information about the oxidation states of an element in a convenient way. For example, the following half-reactions may be taken from Table F.l. Appendix F ... 

Expressions for the partition function can be obtained for each type of energy level in an atom or molecule. These relationships can then be used to derive equations for calculating the thermodynamic functions of an ideal gas. Table 11.4 or Table A6.1 in Appendix 6 summarize the equations for calculating the translational, rotational, and vibrational contributions to the thermodynamic functions, assuming the molecule is a rigid rotator and harmonic oscillator.yy Moments of inertia and fundamental vibrational frequencies for a number of molecules are given in Tables A6.2 to A6.4 of Appendix 6. From these values, the thermodynamic functions can be calculated with the aid of Table 11.4. 

The integral in equation (11.137) must be evaluated numerically. Table A6.7 of Appendix 6 gives the heat capacity and other thermodynamic properties as a function of 0d/T. It can be used to obtain values for the thermodynamic properties as a function of the temperature. 

P14.5 (a) Use thermodynamic data in Table A5.4 of Appendix 5 to determine if you would expect benzene (CftHg) to be more or less soluble in CS2 than in n-octane (CgHig). Justify your choice. 

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