Thermodynamic properties standard state values

In Chapter 10. we will calculate the thermodynamic properties of gases from the molecular parameters, and these calculations, which provide the standard state values, are most easily done for the ideal gas. 

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. 

The values given in the following table for the heats and free energies of formation of inorganic compounds are derived from a) Bichowsky and Rossini, Thermochemistry of the Chemical Substances, Reinhold, New York, 1936 (h) Latimer, Oxidation States of the Elements and Their Potentials in Aqueous Solution, Prentice-Hall, New York, 1938 (c) the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards and (d) the tables of Selected Values of Chemical Thermodynamic Properties of the National Bureau of Standards. The reader is referred to the preceding books and tables for additional details as to methods of calculation, standard states, and so on. 

Compiled from Daubert, T. E., R. R Danner, H. M. Sibiil, and C. C. Stebbins, DIPPR Data Compilation of Pure Compound Properties, Project 801 Sponsor Release, July, 1993, Design Institute for Physical Property Data, AlChE, New York, NY and from Thermodynamics Research Center, Selected Values of Properties of Hydrocarbons and Related Compounds, Thermodynamics Research Center Hydrocarbon Project, Texas A M University, College Station, Texas (extant 1994). The compounds are considered to be formed from the elements in their standard states at 298.15 K and 101,325 P. These include C (graphite) and S (rhombic). Enthalpy of combustion is the net value for the compound in its standard state at 298.15K and 101,325 Pa. 

As the Gibbs function is a thermodynamic property, values of AG do not depend on the intermediate chemical reactions that have been used to transform a set of reactants, under specified conditions, to a series of products. Thus, one can add known values of a Gibbs function to obtain values for reactions for which direct data are not available. The most convenient values to use are the functions for the formation of a compound in its standard state from the elements in their standard states, as given in Tables 7.2... 

We can summarize our conclusions about the thermodynamic properties of the solute in the hypothetical 1-molal standard state as follows. Such a solute is characterized by values of the thermodynamic functions that are represented by p2. 77m2. and 5m2- Frequently a real solution at some molality m2(j) also exists (Fig. 16.4) for which p.2 = that is, for which the activity has a value of 1. The real solution for which // i2 is equal to H 2 is the one at infinite dilution. Furthermore, 5 n,2 has a value equal to 5 2 for some real solution only at a molahty m2(k) that is neither zero nor m2( j). Thus, three different real concentrations of the solute exist for which the thermodynamic qualities p,2, //mi. and S a respectively, have the same values as in the hypothetical standard state. 

The left-hand-side of the equation is defined as the Gibbs energy relative to a standard element reference state (SER) where is the enthalpy of the element or substance in its defined reference state at 298.IS K, a, b, c and dn are coefficients and n represents a set of integers, typically taking the values of 2, 3 and -1. From Eq. (S.3), further thermodynamic properties can be obtained as discussed in Chapter 6. 

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 ... 

Absolute values of many thermodynamic properties cannot be obtained. This difficulty is overcome by choosing a reference or standard state so that properties can be given in terms of die difference between die state of interest and the reference or standard state. 

For the standard state of gaseous substances, we want to calculate thermodynamic properties in the 1.0-bar ideal gas state from measured values of properties at the measurement pressure, P. The calculation consists of the following three steps ... 

It appears that there are two temperatures of a universal nature that describe the thermodynamic properties for the dissolution of liquid hydrocarbons into water. The first of these, 7h is the temperature at which the heat of solution is zero and has a value of approximately 20°C for a variety of liquids. The second universal temperature is Ts, where the standard-state entropy change is zero and, as noted, Ts is about 140°C. The standard-state free energy change can be expressed in terms of these two temperatures, requiring knowledge only of the heat capacity change for an individual substance... 

A standard thermodynamic value occurs with all components at 25 °C and 100 kPa. This thermodynamic standard state is slightly different from the standard temperature and pressure (STP) often used for gas law problems ( 0 °C and 1 atm=101.325 kPa). Standard properties of common chemicals are listed in tables. 

Virtually all chemical reactions in soils are studied as isothermal, isobaric processes. It is for this reason that the measurement of the chemical potentials of soil components involves the prior designation of a set of Standard States that are characterized by selected values of T and P and specific conditions on the phases of matter. Unlike the situation for T and P, however, there is no strictly Ihermodynamic method for determining absolute values of the chemical potential of a substance. The reason for this is that p represents an intrinsic chemical property that, by its very conception, cannot be identified with a universal scale, such as the Kelvin scale for T, which exists regardless of the chemical nature of a substance having the property. Moreover, p cannot usefully be accorded a reference value of zero in the complete absence of a substance, as is the applied pressure, because there is no thermodynamic method for measuring p by virtue of the creation of matter. 

The Standard-State chemical potentials of substances in the gas, liquid, and .olul phases, as well as of solutes in aqueous solution, can be determined by a v.uiely of experimental methods, among them spectroscopic, colorimetric, mi 11 ib i lily, colligative-property, and electrochemical techniques.817 The accepted values of these fundamental thermodynamic properties are and should be undergoing constant revision under the critical eyes of specialists. It is not the puipose of this book lo discuss the practice of determining values of /i° for all < (impounds of interest in soils. This is best left lo. specialized works on... 

The compilations by Wagman et al. and Robie et al. are quite extensive, including many solids as well as ionic solutes in aqueous solution. Since a compound may be written as the product of a chemical reaction that involves only chemical elements as reactants, and since pP for an element is equal to zero, pP for a compound can be considered to be a special example of ArG° for a reaction that forms the compound from its constituent chemical elements. Thus pP values also are termed standard Gibbs energies of formation and given the symbol AfG°. In addition to p° (or AfG°) values, Wagman et al. and Robie et al. list H° and S° for many substances. These Standard-State thermodynamic properties are related to ArH° and ArS° in Eq. 1.42 15... 

Standard-State chemical potentials for aqueous and solid A1(III) species are discussed carefiilly in the context of dissolution-precipitation reactions by B. S. Hemingway, R. A. Robie, and J. A. Apps, Revised values for the thermodynamic properties of boehmite, A10(OH), and related species and phases in the system Al-H-O, Am. Mineralog. 76 445 (1991). 

One should not adhere to the mistaken notion that the analysis of subsection (a) can be used in the upper range of xA values and that the analysis of subsection (b) for the same solution can then be used in the lower range. The two approaches are based on different standard states (i.e. P versus P, as discussed earlier) and therefore are not interchangeable or interrelated. Further, one must stay with one scheme or the other to obtain internally consistent results. It is just more convenient to apply methodology (b) if one is interested primarily in the thermodynamic characterization of solutes in dilute solution, and methodology (a) if one wishes to analyze the properties of solvents. This discussion again points to the fact (see also subsection (e) below) that it is only the differences in the chemical potential themselves that are unique in value all other quantities must be determined self-consistently. 

Using such a standard state, the thermodynamic feasibility calculations were expected to become much easier as only the value of the weight percent of the constituent was required to be used in place of activity values. But, at the same time, values of thermodynamic properties would need to be obtained as per this new standard and tabulated. 

The superscript zero on a thermodynamic function (for example, AH0) indicates that the corresponding process has been carried out under standard conditions. The standard state for a substance is a precisely defined reference state. Because thermodynamic functions often depend on the concentrations (or pressures) of the substances involved, we must use a common reference state to properly compare the thermodynamic properties of two substances. This is especially important because for most thermodynamic properties, we can measure only changes in that property. For example, we have no method for determining absolute values of enthalpy. We can measure only enthalpy changes (AH values) by performing heat flow experiments. 

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. 

Thermodynamic properties taken from Robie, Hemingway, and Fisher are based on a reference state of the elements in their standard states at 1 bar (10 P = 0.987 atm). This change in reference pressure has a negligible effect on the tabulated values for the condensed phases. [For gas phases only data from NBS (reference state = 1 atm) are given.]... 

Absolute values of some thermodynamic quantities are unknown. Only changes in values caused by changes in parameters such as temperature and pressure can be determined. It is therefore important to define a base line for substances, to which the effect of such variations may be referred. The standard state is such a base line. The properties of these standard states are indicated by use of the symbol ... 

In addition to these reference state tables, we have tabulated the thermodynamic properties of all but a few of the ideal gaseous species over the entire range from 298.15 K. to 3000 K. These values can be readily calculated from molecular constant and spectroscopic data by methods described in standard texts (155, 555, 571). Pertinent data were mainly taken from the compilations of Moore (541), Herzberg (155), and Landolt-Bornstein Tabellen 208). Estimates were made for a few molecules for which spectroscopic data were not available. 

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