Enthalpy thermodynamic properties’ plots

Molar diagram A plot of the thermodynamic properties of a substance that has specific enthalpy as one of its coordinates. 

The thermodynamic properties of a number of compounds are shown in Appendix D as pressure-enthalpy diagrams with lines of constant temperature, entropy, and specific volume. The vapor, liquid, and two-phase regions are clearly evident on these plots. The conditions under which each compound may exhibit ideal gas properties are identified by the region on the plot where the enthalpy is independent of pressure at a given temperature (i.e., the lower the pressure and the higher the temperature relative to the critical conditions, the more nearly the properties can be described by the ideal gas law). 

The plot in Fig. 3.2 of the acid dissociation constant for acetic acid was calculated using equation 3.2-21 and the values of standard thermodynamic properties tabulated by Edsall and Wyman (1958). When equation 3.2-21 is not satisfactory, empirical functions representing ArC[ as a function of temperature can be used. Clark and Glew (1966) used Taylor series expansions of the enthalpy and the heat capacity to show the form that extensions of equation 3.2-21 should take up to terms in d3ArCp/dT3. 

Component activity is a direct measure of the slope of the Gibbs energy surfaces of the stable phases from the direction of the component reference state. The variation of the logarithm of activity with inverse temperature gives the partial molar enthalpy and entropy of mixing of the alloy component A, using the second-law method. A well-defined reference state that can be routinely measured is critical for activity measurements. In addition to these thermodynamic quantities, phase transformation temperatures can be determined from changes in the slopes of these plots. The extraction of the various thermodynamic properties from KEMS measurements is discussed later. 

The 1981 article summarizes the development of a thermodynamic surface for water with which all thermodynamic properties for the fluid states can be calculated from the freezing line to 1000 K and up to 1 GPa in pressure. The discussion is very brief, but gives references to earlier work and indicates that a more detailed publication Is forthcoming. Given are coefficients of the Helmholtz function which define the surface. Plots of heat capacity, enthalpy, and speed of sound are included. 

The capability of this rate expression to describe the data is illustrated in Figures 7.17 and 7.18. The optimized rate parameters at various temperatures are listed in Table 7.13, and Arrhenius plots of these values yield the thermodynamic properties in Table 7.14. The enthalpies and entropies of adsorption are consistent with the rules in Table 6.9, eonsidering the uncertainty of the numbers. Again, this does not prove that the proposed model is correct, but only that it is consistent and should not be rejeeted at this time. This same model was also capable of providing satisfactory fits of the data... 

An important correlation between trivalent f-block ions and their Trivalent atoms (f" ds ) is the P(M) function proposed by Nugent et al. [29]. This function has been utilized for predicting enthalpies of sublimation of metals and enthalpies of formation of aqueous ions. David et al. [27] used heavy-actinide thermodynamic properties to establish a P(M) function relating all of the actinide metals and their 3 + aquo ions. Morss and Sonnenberger [ 103] used newer data to refine this P(M) and to develop similar P(M) plots relating f-block metals and their sesquioxides and trichlorides (Figs 17.5 and 17.6). 

The data obtained were used to calculate enthalpy, entropy and the Gibbs functions for the seq-IPNs synthesis. It was shown that the isotherms of diverse thermodynamic properties of interpenetrating polymer networks plotted versus their composition, in particular the molar fraction of the CPU per conditional mole, can be described by straight lines. This made it possible to estimate the thermodynamic behavior of the seq-IPNs of any compositions at standard pressure within a wide temperature range. It was determined [50] that at molar content > 0.50 of PCN in seq-IPNs studied AG°p (AG° of process) < 0 and this has allowed authors to conclude about thermodynamical miscibility of the components for seq-IPNs of these composition... 

In brief, a DSC instrument comprises two cells fixed in an adiabatic chamber. One cell contains the sample to be tested, the second cell contains a reference solution or an empty DSC pan. The adiabatic chamber is maintained under pressure to avoid the evaporation of the sample (Plum, 2009). A DSC-thermogram represents the plot of heat capacity difference ACp (between the sample and the reference) as a function of temperature. Thermodynamic parameters, such as T, AH and AS, could be determined by the DSC curve analysis. T is the temperature at which the concentration of denatured and native forms of the protein are equal. This specific temperature is also called the midpoint of the thermal transition. AH represents the enthalpy of thermal transition determined from the integration of the DSC curve. The entropy (AS) of the thermodynamic transition of the protein may be calculated from the integrated area under the curve of AC /T vs. T. The free energy (AG), which gives an indication of the protein stability, can also be determined at any temperature from the values of AH and AS (O Brien and Haq, 2004 Plum, 2009). Thermal and thermodynamic properties of proteins analyzed by DSC are greatly affected by the experimental conditions used, such as pH, salts, alcohols, and the presence of other food components (e.g., lipids, polysaccharides) (Grinberg et al, 2009). 

Somewhat better data are available for the enthalpies of hydration of transition metal ions. Although this enthalpy is measured at (or more property, extrapolated to) infinite dilution, only six water molecules enter the coordination sphere of the metal ion lo form an octahedral aqua complex. The enthalpy of hydration is thus closely related to the enthalpy of formation of the hexaaqua complex. If the values of for the +2 and +3 ions of the first transition elements (except Sc2, which is unstable) are plotted as a function of atomic number, curves much like those in Fig. 11.14 are obtained. If one subtracts the predicted CFSE from the experimental enthalpies, the resulting points lie very nearly on a straight line from Ca2 lo Zn2 and from Sc to Fe3 (the +3 oxidation state is unstable in water for Ihe remainder of the first transition series). Many thermodynamic data for coordination compounds follow this pattern of a douUe-hunped curve, which can be accounted for by variations in CFSE with d orbital configuration. 

FIG. 2-7 Enthalpy-concentration diagram for aqueous ammonia. From Thermodynamic and Physical Properties NH3-H20, Int Inst. Refrigeration, Paris, France, 1994 (88 pp.). Reproduced by permission. In order to determine equilibrium compositions, draw a vertical from any liquid composition on any boiling line (the lowest plots) to intersect the appropriate auxiliary curve (the intermediate curves). A horizontal then drawn from this point to the appropriate dew line (the upper curves) will establish the vapor composition. The Int. Inst. Refrigeration publication also gives extensive P-v-xtah es from —50 to 316°C. Other sources include Park, Y. M. and Sonntag, R. E., ASHRAE Trans., 96,1 (1990) 150-159 x, h, s, tables, 360 to 640 K) Ibrahim, O. M. and S. A. Klein, ASH E Trans., 99, 1 (1993) 1495-1502 (Eqs., 0.2 to 110 bar, 293 to 413 K) Smolen, T. M., D. B. Manley, et al.,/. Chem. Eng. Data, 36 (1991) 202-208 p-x correlation, 0.9 to 450 psia, 293-413 K)i Ruiter, J. P, 7nf. J. R rig., 13 (1990) 223-236 gives ten subroutines for computer calculations. 

This is a rather more complex problem because the interfacial layer is not infinitesimally thin and some free energy is stored in this layer. There is a gradient of molecular density, composition, enthalpy, entropy, electrical potential (for charged molecules) and many other properties in this interfacial transition layer, as shown in Figure 3.1 a as a property-distance plot. Actually, Us is located in a layer of certain thickness, Ax, and some assumption must be made if we want to define Us in thermodynamical terms, because it is impossible to decide physically where phase a ends and phase ft begins. The thickness of this transition layer, Axp for any two immiscible phases is shown in Figure 3.2 a and is dependent on the molecular nature of phases a and /), and also on external factors such as temperature and pressure. It has been found experimentally that this interfacial layer is usually a few molecules in thickness for most non-electrolytes. 

NIST/ASME Steam Properties Database versiou 2.21 http //www.nist.gov/srd/nistlO.cfm (accessed November 10, 2010) (purchase required). Thermophysical properties include in the STEAM Database temperature, Helmholtz energy, thermodynamic derivatives, pressure, Gibbs energy, density, fugacity, thermal conductivity, volume, isothermal compressibility, viscosity, dielectric constant, enthalpy, volume expansivity, dielectric derivatives, internal energy, speed of sound, Debye-Hlickel slopes, entropy, Joule-Thomson coefficient, refractive index, heat capacity, surface tension. The STEAM database generates tables and plots of property values. Vapor-liquid-solid saturation calculations with either temperature or pressure specified are available. 

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