Standard state selection

Activity coefficients are dimensionless. With standard states selected as indicated above, activity coefficients will be unity in ideal systems. The degree of departure of a system from the ideal state is described by the departure of the activity coefficients from unity. 

As indicated by the data in Table 1, the conclusions dealing with the influence of solvents on the AG° may differ, depending on the choice of the standard state. Selection of the standard state from column (a) results in relatively high AG° values of the TU adsorption on Hg in water,... 

The activities dj in Eq. (15.13) provide the connection between the equilibm state of interest and the standard states of the individual species, for which di are presumed available, as discussed in Sec. 15.5. The standard states arc arbitra but must always be at the equilibrium temperature T. The standard states select need not be the same for all species taking part in a reaction. However, for particular species the standard state represented by Gt must be the same st represented by the / upon which the activity d,- is based. 

If the chosen standard states are identical, mS and mIs a re the same, since these are the chemical potentials in the standard states consequently a and the activities in the two phases, will be equal. On the other hand, if the standard states selected for the phases I and II are not the same, a and will be different, the difference depending on the corresponding values of /ia a>Dd M >... 

Let us now discuss the pressure dependence of the equilibrium constant in cases where the standard state selected is the pure constituent at the temperature and pressure of the system. From relation (3.22) follows... 

In the following, the standard state selected for each component in air is the partial pressure in dry air at atmospheric pressure. The standard state for water is liquid at 1 atmosphere. The temperature of the surroundings is 25 °C. The exergy of a stream of arbitrary composition can now be calculated by use of Eq. (12). 

Appendix 3D contains a listing of the standard-state reduction potentials for selected species. The more positive the standard-state reduction potential, the more favorable the reduction reaction will be under standard-state conditions. Thus, under standard-state conditions, the reduction of Cu + to Cu E° = -1-0.3419) is more favorable than the reduction of Zn + to Zn (E° = -0.7618). 

When possible, quantitative analyses are best conducted using external standards. Emission intensity, however, is affected significantly by many parameters, including the temperature of the excitation source and the efficiency of atomization. An increase in temperature of 10 K, for example, results in a 4% change in the fraction of Na atoms present in the 3p excited state. The method of internal standards can be used when variations in source parameters are difficult to control. In this case an internal standard is selected that has an emission line close to that of the analyte to compensate for changes in the temperature of the excitation source. In addition, the internal standard should be subject to the same chemical interferences to compensate for changes in atomization efficiency. To accurately compensate for these errors, the analyte and internal standard emission lines must be monitored simultaneously. The method of standard additions also can be used. 

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. 

The standard state chosen for the calculation of controls its magnitude and even its sign. The standard state is established when the concentration scale is selected. For most solution kinetic work the molar concentration scale is used, so A values reported by different workers are usually comparable. Nevertheless, an important chemical question is implied Because the sign of AS may depend upon the concentration scale used for the evaluation of the rate constant, which concentration scale should be used when A is to serve as a mechanistic criterion The same question appears in studies of equilibria. The answer (if there is a single answer) is not known, though some analyses of the problem have been made. Further discussion of this issue is given in Section 6.1. 

For a substance in a given system the chemical potential gi has a definite value however, the standard potentials and activity coefficients have different values in these three equations. Therefore, the selection of a concentration scale in effect determines the standard state. 

Just as the intrinsic energy of a body is defined only up to an arbitrary constant, so also the entropy of the body cannot, from the considerations of pure thermodynamics, be specified in absolute amount. We therefore select any convenient arbitrary standard state a, in which the entropy is taken as zero, and estimate the entropy in another state /3 as follows The change of entropy being the same along all reversible paths linking the states a and /3, and equal to the difference of the entropies of the two states, we may imagine the process conducted in the following two steps ... 

The standard states are selected as m = 1 mol kg-1 and = 1 mol dm-3. In this convention, the ratio m./m is numerically identical with the actual molality (expressed in units of moles per kilogram). This is, however, the... 

It should be noted that the activity appearing in the dissociation constant K is the dimensionless relative activity, and constant K contains the dimensionless relative concentration or molality terms. Constants K and Kf are thus also dimensionless. However, their numerical values correspond to the units selected for the standard state, i.e. moles per cubic decimetre or moles per kilogram. 

THE SELECTION OF THERMOCHEMICAL DATA AND MORE ON STANDARD STATES... 

References (20, 22, 23, 24, 29, and 74) comprise the series of Technical Notes 270 from the Chemical Thermodynamics Data Center at the National Bureau of Standards. These give selected values of enthalpies and Gibbs energies of formation and of entropies and heat capacities of pure compounds and of aqueous species in their standard states at 25 °C. They include all inorganic compounds of one and two carbon atoms per molecule. 

As is customary we select the ideal vapor at unit pressure, P°, as the standard state. The partial molar free energy (chemical potential) of the vapor, p,(v), is... 

A more elegant (although more difficult to visualize) formulation of the procedure for the selection of the standard state for a solute may be made as follows. From Eiquation (16.1)... 

Table 5.13 Selected standard state entropy Sx, p/, T, = 298.15 K, = 1 bar) and Maier-Kelley coefficients of heat capacity function. References as in table 5.12. Data in J/(mole X K).

Keep in mind that at this point, the mixtnres can be either solid or liqnid, depending on the temperature, and that both solid and liqnid mixtnres may coexist at certain temperatures and compositions. Thus, when performing actnal free energy calcnlations using Eqs. (2.34) or (2.35), the standard state free energies for both components mnst be carefully selected. This process is illustrated in Example Problem 2.1. 

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