Thermodynamic formulas table

Other thermodynamic functions can be obtained in terms of the partition function using standard thermodynamic formulae (Table 9.3). Note that the terras that arise from the N which modify the expressions for S, A, and G for gases are associated only with the translational contribution to the partition function. When evaluating the contributions of vibration and rotation we use the simple expression as given for solids in Table 9.3. 

TABLE 13.3 T-dependent Equilibrium Constant (KT), Gibbs Free Energy of Reaction (AGT), and Overall Entropic Shift (AAG = AG12oo — AG90o) for the Water Gas Shift Reaction (cf. Tables 13.1, 13.2, and Text), as Determined from Theoretically ( B3LYP ) or Empirically ( Hill ) Evaluated Statistical Thermodynamic Formulas Versus Experiment ( Exp. )... 

The fact that a simple formula (such as Zn(OH)2) does not always account for all the chemical properties of the substance it represents may be attributed partly to the occurrence of polymorphous modifications. Differences in crystal structure may indeed cause considerable changes in thermodynamic properties (Table V). 

The extent of dissociation given in the first column of the above table as obs. is derived from this figure that given under " calc. results from the above thermodynamical formula, and leads to the value... 

Table 1.2-1 summarizes important general thermodynamic formulas for the fugacity Equations (1.2-17) and (1.2-18) define the fugacity f,ot a component in solution Eqs. (1.2-19) and (1.2-20) similarly define the fugacity/of a mixture. For a component in an ideai-gas mixture, Eq. (1.2-18) implies that... 

Systems express information not just at the macroscopic level. There are robust states, mechanisms for communication and registration, and uncertainty at the microscopic scale as well. This scale is the complicated domain of quantum mechanics and statistical thermodynamics. Standard tables, formula diagrams, and random walk models, however, provide more immediate handles on information in the statistical sense. 

Kinetic curves of swelling were calculated according to the formula g(t) = m(t)/mE, where m(t), m - current value of the mass of a liquid absorbed by sample and finite one, respectively. Experiments were carried out by swelling at 25°C. Figure 6.6.3 shows the kinetic curves of the samples PDUE swelling in solvents of different thermodynamic quality. Table 6.6.1 shows the experimental values of the parameters characterizing the swelling kinetics. 

Complex chlorides of plutonium (34, 41) do not present such a wide range of formulae as the complex fTuorides but we have at hand thermodynamic information on two important species which have also been characterized with other actinides. In table II we have disregarded the complex halides for which no thermodynamic data are available. The enthalpy of formation of Cs2NaPuClg(c) (55) and Cs2PuClg(c) (56) have been obtained from enthalpy of solution measurements."The selected (8) values are AHf(Cs2NaPuCl6,c) =... 

Tables 3 and 4 contain values of the log water activity and log sulfuric acid activity in molarity units. These can be obtained at any temperature by using the polynomial coefficients supplied by Zeleznik,45 which are based on all of the preexisting thermodynamic data obtained for this medium. The numbers were converted to the molarity scale using the conversion formula given in Robinson and Stokes 46 Molarity-based water activities are given for HCIO4 in Tables 5 and 6. These are calculated from data obtained at 25°C by Pearce and Nelson,17...

A summary of the electrochemical formulae developed above is provided in Table 7.3. AG, pe, E, and K contain virtually the same thermodynamic information. While is the quantity that is analytically measured, pe is preferred by marine chemists as it is temperature independent and numerically easier to work with. AG is often used to compare the relative stability of species because it provides a measure of energy yields in units of calories or joules. A comparison of the three electrochemical scales at 25°C is given in Figure 7.3. The merits of each thermodynamic parameter will become evident in the next section of the chapter where the energetics of some marine redox processes are considered. 

The amount of H2O in amorphous silica (number n of H2O molecules per unit formula) varies between 0.14 and 0.83 (Frondel, 1962). Nevertheless, the thermodynamic properties of the phase are not particularly affected by the value of n (Walther and Helgeson, 1977). The molar volume of opal is 29 cm /mole. The same volume of a-quartz may be adopted for chalcedony see table 5.68 for the other polymorphs. 

This second class of five-membered heterocyclic meso-ionic compounds is represented by the type formula 14 20. So far, only eight representatives (Table II) of type B have been described, whereas acceptable combinations of the groupings a, b, c, d, e, and f derived from suitably substituted carbon, nitrogen, oxygen, or sulfur atoms lead, in principle, to 84 possibilities. However, not all these 84 possible structures are necess y well based because valence tautomerism (see Section VI) might well be associated with thermodynamic preference for the acyclic covalent valence isomer (46) rather than the cyclic meso-ionic alternative (20). 

The values of AHf° and AGf° given in the tables represent the change in the appropriate thermodynamic quantity when one gram formula weight of the substance in its standard state is formed, isothermally at the indicated temperature, from the elements, each in its appropriate standard reference state. The standard reference state at 25 °C for each element has been chosen to be the standard state that is thermodynamically stable at 25 °C and 1 atm pressure. The standard reference states are indicated in the tables by the fact that the values of AHf° and AGf° are exactly zero. 

Reference TDI contains an enthalpy table for ammonia at different pressures. Reference TD2 contains a series of tables in an appendix from which the specific heats of the reaction-gas mixture were calculated. Humidity charts were also useful. Reference TD3 is valuable for its steam tables, while Ref. TD4 contains both thermodynamic and chemical equilibria data for nitric acid. The final reference, Robertson and Crowe (Ref. TD5), contains formulae and tables for the sizing and choice of an air-feed compressor. 

While local codes have different ways of presenting things (even sizing formulas), it can be mathematically proven that their results are practically the same, which is normal given the fact they are all based on hydrodynamic and thermodynamic fundamentals and that the differences are mainly due to the use of different units. (See Appendix A, Relevant Tables And References, where an example shows that the ASME calculations are virtually the same as those required by GOST, the Russian standard.)... 

Here we compare the thermodynamic parameters of trehalose, maltose and sucrose because they have the same chemical formula (C12H22O11) and mass (molecular weight 342.3), but different structures which could be responsible for their different hydration properties. The anomaly of hydration of trehalose is understood from the following observation [10]. Namely, the amount of water used for the preparation of 1.5 M trehalose solution is smaller than the amount used for the preparation of other sugar solutions. In a 1.5 M solution, trehalose itself occupies 37.5% of the volume of the solution. However, in a 1.5 M solution, sucrose occupies 13% and maltose occupies 14%. These data suggest that trehalose has a larger hydrated volume than the other sugars. This hypothesis can be demonstrated from various thermodynamic parameters as shown in Table 12.1. 

The International Practical Temperature Scale of 1968 (IPTS-68) has been replaced by the International Temperature Scale of 1990 (ITS-90). The ITS-90 scale is basically arbitraiy in its definition but is intended to approximate closely the thermodynamic temperature scale. It is based on assigned values of the temperatures of a number of defining fixed points and on interpolation formulas for standard instruments (practical thermometers) that have been cahbrated at those fixed points. The fixed points of ITS-90 are given in Table 1. 

Figure 12-4 shows a psychrometric chart for combustion products in air. The thermodynamic properties of moist air are given in Table 12-1. Figure 12-4 shows a number of useful additional relationships, e.g., specific volume and latent heat variation with temperature. Accurate figures should always be obtained from physical properties tables or by calculation using the formulas given earlier, and these charts should only be used as a quick check for verification. 

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