Selection of the standard state

Relations (3.22) and (3.28) apply quite in general. However, the selection of the standard state must always be defined in order that it should be possible to express the equilibrium composition by means of convential quantities of concentration. According to the definition of activity 

In principle, there is no limit to the selection of standard states. For practical reasons it is advantageous to make use of one of the following possibilities. 

On substituting the relation (3.35) into the expression for the equilibrium constant, we obtain 

For an ideal mixture of real gases (/ = yJi) we have cpi = 9 . There hold the relation 

As long as the gas mixture behaves in the ideal manner, we have 

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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,... 

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)... 

Adsorption model of HPLC retention mechanism allows clear definition of the column void volume as the total volume of the liquid phase in the column, but this model requires the use of the surface-specific retention and the correlation of the HPLC retention with the thermodynamic (and thus energetic) parameters, which is not well-developed. This model requires the selection of the standard state of given chromatographic system and relation of all parameters to that state. 

In the selection of the standard state enthalpy of formation of monoclinic Zr02... 

The above-mentioned issues also pertain to the selection of the standard state of EASP. As a matter of fact, on LLZ I Li+ electrode, either at x = 0 or at x = 1, no equilibrium conditions corresponding to hthium exchange can be established. The reasoning presented earlier illustrates that the application of the concept of thermodynamic activity to the EASP is impractical and may not be attainable. 

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). 

Figure 3.2. Activity coefficients depend on the selection of the reference state and standard state, (a) On the infinite dilution scale the reference state is an infinitely dilute aqueous solution the standard state is a hypothetical solution of concentration unity and with properties of an infinitely dilute solution. For example, the activity coeffic ent of in a HCl solution, / hcm varies with [HCl] in accordance with a Debye-Hiickel equation (dashed line, left ordinate) (see Table 3.3) only at very great dilutions does /become unity. On the ionic medium scale, for example, in I M KCl, the reference...

Knowledge of the standard states and the adsorbed-phase composition allows the calculation of the selectivity by Equations (16) and the amount of each species adsorbed by Equations (17) and (18). Finally, the entropy and enthalpy of immersion are given by the equations ... 

J-K" -moP quoted by [76VAS/LYT] is based on the standard state enthalpy of formation that is selected in this review (Section V.2.1.2) but is combined with an erroneous value of the standard state Gibbs energy of formation for Zr of... 

Standard enthalpies of reaction are tabulated for the/ormarion reaction of a species. The formation reaction is a balanced chemical equation that produces one mole of the species in its standard state from the pure constituent elements, also at their standard states.3 By convention, the standard enthalpy of pure elements is zero. Tabulated values of the standard enthalpy of formation at 25 °C are available for a large number of components in various handbooks (selected values are given in Appendix C.) These values are accompanied by an indication of the standard state to which the reported value refers. 

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). 

National Institute of Standards and Technology (NIST). The NIST is the source of many of the standards used in chemical and physical analyses in the United States and throughout the world. The standards prepared and distributed by the NIST are used to caUbrate measurement systems and to provide a central basis for uniformity and accuracy of measurement. At present, over 1200 Standard Reference Materials (SRMs) are available and are described by the NIST (15). Included are many steels, nonferrous alloys, high purity metals, primary standards for use in volumetric analysis, microchemical standards, clinical laboratory standards, biological material certified for trace elements, environmental standards, trace element standards, ion-activity standards (for pH and ion-selective electrodes), freezing and melting point standards, colorimetry standards, optical standards, radioactivity standards, particle-size standards, and density standards. Certificates are issued with the standard reference materials showing values for the parameters that have been determined. 

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. 

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 ... 

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