Compounds standard states

However, the titrations must begin with the neat compound, if one desires to measures excess enthalpies referred to a single-compound standard state. In this case the number of experiments and the data... 

From the difference of the excess Gibbs energies for the groups in the mbcture and in the pure compound (standard state) one can derive an expression for the required activity coefficient y, ... 

Compounds that are products in reactions are sometimes reported in standard states for phases that are not the most stable at the temperature in question. The stable standard state of H2O at 298 K (and 1 atm) is, of course,... 

There are many compounds in existence which have a considerable positive enthalpy of formation. They are not made by direct union of the constituent elements in their standard states, but by some process in which the necessary energy is provided indirectly. Many known covalent hydrides (Chapter 5) are made by indirect methods (for example from other hydrides) or by supplying energy (in the form of heat or an electric discharge) to the direct reaction to dissociate the hydrogen molecules and also possibly vaporise the other element. Other known endothermic compounds include nitrogen oxide and ethyne (acetylene) all these compounds have considerable kinetic stability. 

A more useful quantity for comparison with experiment is the heat of formation, which is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The heat of formation can thus be calculated by subtracting the heats of atomisation of the elements and the atomic ionisation energies from the total energy. Unfortunately, ab initio calculations that do not include electron correlation (which we will discuss in Chapter 3) provide uniformly poor estimates of heats of formation w ith errors in bond dissociation energies of 25-40 kcal/mol, even at the Hartree-Fock limit for diatomic molecules. 

Another problem is that the Nernst equation is a function of activities, not concentrations. As a result, cell potentials may show significant matrix effects. This problem is compounded when the analyte participates in additional equilibria. For example, the standard-state potential for the Fe "/Fe " redox couple is +0.767 V in 1 M 1TC104, H-0.70 V in 1 M ITCl, and -H0.53 in 10 M ITCl. The shift toward more negative potentials with an increasing concentration of ITCl is due to chloride s ability to form stronger complexes with Fe " than with Fe ". This problem can be minimized by replacing the standard-state potential with a matrix-dependent formal potential. Most tables of standard-state potentials also include a list of selected formal potentials (see Appendix 3D). 

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. 

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... 

Entropy of Formation The ideal gas standard entropy of formation (AS°298) of a chemical compound is the increment of entropy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard state definea as the existing phase at a temperature of 298.15 K and one atmosphere (101.325 kPa). Thus ... 

Ideal gas absolute entropies of many compounds may be found in Daubert et al.,"" Daubert and Danner," JANAF Thermochemical Tables,TRC Thermodynamic Tables,and Stull et al. ° Otherwise, the estimation method of Benson et al. " is reasonably accurate, with average errors of 1-2 J/mol K. Elemental standard-state absolute entropies may be found in Cox et al." Values from this source for some common elements are listed in Table 2-389. ASjoqs may also be calculated from Eq. (2-52) if values for AHjoqs and AGJoqs are known. 

If Gf is arbitrarily set equal to zero for all elements in their standard states, then for compounds Gf = AG°, the standard Gibbs-energy change of formation for species i. In addition, the fugacity is eliminated in favor of the fugacity coefficient by Eq. (4-79),/ = yi jP. With these substitutions, the equation for becomes... 

Tables of standard entlialpies of formation, combustion and reaction are available in the literature for a wide variety of compounds. It is important to note that these are valueless imlcss tlie stoicliiomctric equation and tlie standard state of reactants and products are included.

The standard heat of formation ( AH ) of a chemical compound is the standard heat of reaction corresponding to the chemical combination of its constituent elements to form one mole of the compound, each existing in its standard state at 1 atm and 25°C. It has units of cal/g-mole. 

The two elements have similar electronegativity. (Note electronegativity is the power of an element to attract electrons to itself when present in a molecule or in an aggregate of unlike atoms it is a different property from the electrode potential, which depends on the free energy difference between an element in its standard state and a compound or ion in solution (see Section 20.1).) In addition a metal of a lower valency tends to dissolve a metal of a higher valency more readily than vice versa. 

List aU chemical species, both elements and compounds, that are believed to exist at equilibrium. By element we mean the predominant species at standard-state conditions, for example, O2 for oxygen at 1 bar and 298.15 K. 

The standard state entropy change refers to the hypothetical process so conducted as to convert pure 1 and 2 to a uniquely specified array of 1, 2 pairs e.g., to the pure 1, 2 compound.In short, the standard state entropy change is just that portion of A/Siir other than AiS jf. ... 

The standard enthalpy of formation AH°f of a compound is defined as the enthalpy change when one mol of the compound is formed from its constituent elements in the standard state. The enthalpy of formation of the elements is taken as zero. The standard heat of any reaction can be calculated from the heats of formation —AH of the products and reactants if these are available or can be estimated. 

At pulp and paper mills, air emissions from both process and combustion units are regulated under the National Ambient Air Quality Standards (NAAQS) and the State Implementation Plans (SIP) that enforce the standards. States may implement controls to limit emissions of particulate matter (PM), nitrogen oxides (NO ), volatile organic compounds (VOCs), and sulfur dioxide (S02). 

As a thermodynamicist working at the Lower Slobbovian Research Institute, you have been asked to determine the standard Gibbs free energy of formation and the standard enthalpy of formation of the compounds ds-butene-2 and trans-butene-2. Your boss has informed you that the standard enthalpy of formation of butene-1 is 1.172 kJ/mole while the standard Gibbs free energy of formation is 72.10 kJ/mole where the standard state is taken as the pure component at 25 °C and 101.3 kPa. 

Fig. 12.4. Vapor-to-water transfer data for saturated hydrocarbons as a function of accessible surface area, from [131]. Standard states are 1M ideal gas and solution phases. Linear alkanes (small dots) are labeled by the number of carbons. Cyclic compounds (large dots) are a = cyclooctane, b = cycloheptane, c = cyclopentane, d = cyclohexane, e = methylcyclopentane, f = methylcyclohexane, g = cA-l,2-dimethylcyclohexane. Branched compounds (circles) are h = isobutane, i = neopentane, j = isopentane, k = neohexane, 1 = isohexane, m = 3-methylpentane, n = 2,4-dimethylpentane, o = isooctane, p = 2,2,5-tri-metbylhexane. Adapted with permission from [74], Copyright 1994, American Chemical Society...

Table 5 lists equilibrium data for a new hypothetical gas-phase cyclisation series, for which the required thermodynamic quantities are available from either direct calorimetric measurements or statistical mechanical calculations. Compounds whose tabulated data were obtained by means of methods involving group contributions were not considered. Calculations were carried out by using S%g8 values based on a 1 M standard state. These were obtained by subtracting 6.35 e.u. from tabulated S g-values, which are based on a 1 Atm standard state. Equilibrium constants and thermodynamic parameters for these hypothetical reactions are not meaningful as such. More significant are the EM-values, and the corresponding contributions from the enthalpy and entropy terms. 

Thermochemical data from the compilation of Stull et at., 1969. Entropy values are based on a 1 M standard state. The asterisk denotes symmetry-corrected quantities. Symmetry numbers were chosen as follows 18 for the n-alkanes, cis-3-hexene, dibuthyl sulphide, diethyl ether, and diethyl amine 2n for the cycloalkanes and 2 for all of the remaining ring compounds 3 for the alkanols, alkanethiols and alkyl amines 9 for the methyl alkyl sulphides... 

Standard enthalpy of formation, AHJ, is the enthalpy change when one mole of a compound is formed, under standard conditions, from its elements in their standard states. 

Polynomial expressions are conveniently used to represent a condensed phase which is stable in the whole temperature range of interest and which does not undergo any structural, electronic or magnetic transformations. The Gibbs energy of a compound is in the CALPHAD approach represented relative to the elements in their defined standard state at 298.15 K as a power series in terms of temperature in the form of [16] ... 

Here Hm is the sum (in the stoichiometric ratio of the compound in question) of A298-15tf° of the elements in their defined standard state, a, b, c and dn are coefficients and n integers. This form of expression is useful for storing thermodynamic information in databases. A number of such expressions are often required for a given phase to cover the whole temperature range of interest. From eq. (2.41) all other thermodynamic functions can be derived, e.g. 

The standard enthalpy of formation, A fH, of a compound at 0 K reflects the strength of the chemical bonds in the compound relative to those in the constituent elements in their standard state. The standard enthalpy of formation of a binary oxide such as CaO is thus the enthalpy change of the reaction... 

It will be immediately clear from Table 3.1 that several values of A Hi are zero. This value arises from the definition we chose, above as A Hi relates to forming a compound from its constituent elements, it follows that the enthalpy of forming an element can only be zero, provided it exists in its standard state. Incidentally, it also explains why A//f(Br2,1) = 0 but A//f(Br2, g) =... 

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