Standard state data

Figure 3.7 The activity of Ni of molten Fe-Ni at 1850 K using both a Raoultian and a Henrian standard state. Data are taken from reference [3].

Figure 3.12 The integral molar Gibbs energy of liquid Ge-Si at 1500 K with pure liquid Ge and solid Si as standard states. Data are taken from reference [4].

Thus the equilibrium constant can be calculated for any reaction for which we have standard state data for each product and reactant. Note that this does not necessarily mean that the reaction is important, or that it has reached equilibrium in our natural system, or perhaps any natural system it tells us the ratio of product and reactant activities ( concentrations) if the reaction does reach equilibrium. 

The following measured or apparent (not standard-state) data at 25°C are available for this binding reaction, AbndG = —30.8 kJ mol , AbndH = —13.1 kJ mol , and AbndCp 0, where these apparent changes are for the following equilibrium constant ... 

Numbers for and in the standard state are available for many substances (for instance Stull et al. [14], Reid et al. [8], Frenkel et al. [15, 16]). Numbers for and at other conditions can be obtained from the standard state data using information on heat capacities and enthalpies of vaporization, which are also available in many cases, for instance in the sources cited above. It should be noted that the accuracy of chemical equilibrium constants obtained by this way is limited and may not be sufficient for a given application. This is mainly caused by the fact that due to the summation of the chemical potentials in equations such as equation (4.13) or (4.15), even small errors in the numbers for the pure component chemical potentials may become very important in the calculation of the equilibrium constant from equations such as equations (4.13) and (4.15). Therefore, the chemical equilibrium constants generally have to be determined from direct experimental investigations. A comparison of some chemical equilibrium constants of esterifications and transesterifications as obtained from direct measurements and from estimated numbers for is given in Table 4.1, underlining the need for accurate experimental data on chemical equilibrium constants. 

Figure 8.9 The pressure on the gas phase is 1 bar, but the partial pressure of CH4 in the gas is 0.01 bar. The Gibbs energy (ju) of CH4 is the same in each phase, and a variety of standard state data may be used.

Newton (accompanying paper) has found positive values of for this solid solution series, confirming the general form of the activity-composition relationships discussed here. It is doubtful, however, whether calorimetric results on the solid solutions provide a good constraint on the standard state data because of lack of knowledge of excess entropy contributions to G . The author s results on Ca0-Al203-Si02 lead him to prefer the upper curve for G s in Fig. 7 and lower activity curves in Fig. 6. 

In some cases, the temperature of the system may be larger than the critical temperature of one (or more) of the components, i.e., system temperature T may exceed T. . In that event, component i is a supercritical component, one that cannot exist as a pure liquid at temperature T. For this component, it is still possible to use symmetric normalization of the activity coefficient (y - 1 as x - 1) provided that some method of extrapolation is used to evaluate the standard-state fugacity which, in this case, is the fugacity of pure liquid i at system temperature T. For highly supercritical components (T Tj,.), such extrapolation is extremely arbitrary as a result, we have no assurance that when experimental data are reduced, the activity coefficient tends to obey the necessary boundary condition 1... 

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

Correlations for standard-state fugacities at 2ero pressure, for the temperature range 200° to 600°K, were generated for pure fluids using the best available vapor-pressure data. 

At temperatures above those corresponding to the highest experimental pressures, data were generated using the Lyckman correlation all of these were assigned an uncertainty of 5% of the standard-state fugacity at zero pressure. Frequently, this uncertainty amounts to one half or more atmosphere for the lowest point, and to 1 to 5 atmospheres for the highest point. 

The standard state of an electrolyte is the hypothetical ideally dilute solution (Henry s law) at a molarity of 1 mol kg (Actually, as will be seen, electrolyte data are conventionally reported as for the fonnation of mdividual ions.) Standard states for non-electrolytes in dilute solution are rarely invoked. 

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. 

Enthalpy of Formation The ideal gas standard enthalpy (heat) of formation (AHJoqs) of chemical compound is the increment of enthalpy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard states, defined as the existing phase at a temperature of 298.15 K and one atmosphere (101.3 kPa). Sources for data are Refs. 15, 23, 24, 104, 115, and 116. The most accurate, but again complicated, estimation method is that of Benson et al. " A compromise between complexity and accuracy is based on the additive atomic group-contribution scheme of Joback his original units of kcal/mol have been converted to kj/mol by the conversion 1 kcal/mol = 4.1868 kJ/moL... 

The activities in Eq. (4-342) provide the connection between the equilibrium states of interest and the standard states of the constituent species, for which data are presumed available. The standard states are alwavs at the equihbrium temperature. Although the standard state need not be the same for all species, or Sipaliicular species it must be the state represented by both Gf and thej ° upon which the activity dj is based. 

The heal of reaction (see Section 4.4) is defined as tlie enthalpy change of a system undergoing chemical reaction. If the retictants and products are at tlie same temperature and in their standard states, tlie heat of reaction is temied tlie standard lieat of reaction. For engineering purposes, the standard state of a chemical may be taken as tlie pure chemical at I atm pressure. Heat of reaction data for many reactions is available in tlie literature. ... 

Standard-State Enthalpy Changes (AH°). To expedite calculations, thermochemical data are ordinarily presented in the form of standard-state enthalpy changes of the system AH°(T,P), with the requirement that materials start and end at the same temperature (T) and pressure (P) and in their standard states of aggregation, i.e.,... 

The entropy of C02 in its standard state is 51.08 e.u., while that of water at 25° is 16.75 e.u. From the experimental data it has been found that... 

A variety of procedures can be used to determine Z, as a function of composition.2 Care must be taken if reliable values are to be obtained, since the determination of a derivative or a slope is often difficult to do with high accuracy. A number of different techniques are employed, depending upon the accuracy of the data that is used to calculate Z, and the nature of the system. We will now consider several examples involving the determination of V,- and Cpj, since these are the properties for which absolute values for the partial molar quantity can be obtained. Only relative values of //, and can be obtained, since absolute values of H and G are not available. For H, and we determine H, — H° or — n°, where H° and are values for H, and in a reference or standard state. We will delay a discussion of these quantities until we have described standard states. 

An enthalpy of reaction also depends on the conditions (such as the pressure). All the tables in this book list data for reactions in which each reactant and product is in its standard state, its pure form at exactly 1 bar. The standard state of liquid water is pure water at 1 bar. The standard state of ice is pure ice at 1 bar. A solute in a liquid solution is in its standard state when its concentration is 1 mol-L". The standard value of a property X (that is, the value of X for the standard state of the substance) is denoted X°. 

Most thermochemical data are reported for 25°C (more precisely, for 298.15 I<). Temperature is not part of the definition of standard states we can have a standard state at any temperature 298.15 K is simply the most common temperature used in tables of data. All reaction enthalpies used in this text are for 298.15 K unless another temperature is indicated. 

It is possible to choose a different standard state (after all, molecules don t know what their standard state is) for the pressure or concentration of chemical species. The standard state corresponding to data presented in Appendix 2A is for... 

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