Standard molar properties, values

Practically in every general chemistry textbook, one can find a table presenting the Standard (Reduction) Potentials in aqueous solution at 25 °C, sometimes in two parts, indicating the reaction condition acidic solution and basic solution. In most cases, there is another table titled Standard Chemical Thermodynamic Properties (or Selected Thermodynamic Values). The former table is referred to in a chapter devoted to Electrochemistry (or Oxidation - Reduction Reactions), while a reference to the latter one can be found in a chapter dealing with Chemical Thermodynamics (or Chemical Equilibria). It is seldom indicated that the two types of tables contain redundant information since the standard potential values of a cell reaction ( n) can be calculated from the standard molar free (Gibbs) energy change (AG" for the same reaction with a simple relationship... 

We have now answered the fundamental question posed at the beginning of this chapter What determines the value of the equilibrium constant—that is, what properties of nature determine the direction and extent of a particular chemical reaction The answer is that the value of the equilibrium constant is determined by the standard free-energy change, A G°, for the reaction, which depends, in turn, on the standard heats of formation and the standard molar entropies of the reactants and products. 

The calculations of standard thermodynamic properties discussed in the rest of this section are based on the assumption that the standard enthalpies of formation of species are independent of temperature in other words, the heat capacities of species are assumed to be zero. In the future when more is known about the molar heat capacities of species, more accurate calculations can be based on the assumption that the molar heat capacities are independent of temperature. When the heat capacities of species are equal to zero, the standard entropies of formation are also independent of temperature. Under these conditions the values of AfG at other temperatures in the neighborhood of 298.15 K can be calculated using... 

In this expression, ° Ga is the standard (° signifies the value s P= atm) molar Gibbs energy of the pure component A and xa is the mole fraction of component A. The Gibbs energy of the mechanical mixture serves as a reference state for the properties of a solution, in which there is chemical mixing between components on an atomic or molecular level. 

Molar or unit-mass value of any extensive property of pure species i Partial molar property of species i in solution Property change of mixing Standard property change of reaction j Mass... 

As with other thermodynamic variables, we usually compare entropy values for substances in their standard states at the temperature of interest 1 atm for gases, I M for solutions, and the pure substance in its most stable form for solids or liciuids. Because entropy is an extensive property, that is, one that depends on the amount of substance, we are interested in the standard molar entropy (S°) in units of J/moEK (or J mol -K ). The S° values at 298 K for many elements, compounds, and ions appear, with other thermodynamic variables, in Appendix B. 

Understand the meaning of entropy (5) in terms of the number of microstates over which a system s energy is dispersed describe how the second law provides the criterion for spontaneity, how the third law allows us to find absolute values of standard molar entropies (5°), and how conditions and properties of substances influence 5° ( 20.1) (SP 20.1) (EPs 20.4-20.7, 20.10-20.23)... 

We need a way to obtain values for the standard-state chemical potential appearing in (10.3.38). Each standard state is a pure species, so the chemical potential reduces to the pure molar Gibbs energy, and the pure molar property g° is simply related to the Gibbs energy of formation by (10.4.15). So we rewrite (10.4.15),... 

This was not the case for saturated hydrocarbons C H, whose properties—as far as they were known—follow mainly additive schemes which are by and large topography-independent. A good example are their standard molar enthalpies of formation For saturated hydrocarbons in the gas phase and at 298 K, the AfH (C H (g)) values are, in a first approximation, the sum of molar bond increments. Their electronic excitation gives rise to absorption bands in the far-UV region of the spectrum which, at the time, were not only difficult to observe but also to assign, because they are not well defined intra-valence transitions, such as the transitions of n systems, but... 

This standard molar volume provides a handy way to estimate 3S properties or to help judge the reasonableness of a calculated value. 

There is an advantage in using the constant surface pressure standard state since it yields molar properties (enthalpies and entropies of adsorption) analogous to those associated with phase changes evaluated from the Clapeyron equation [80]. The use of the standard state with constant surface concentration provides differential quantities for the enthalpy and entropy changes which are not directly comparable with those calculated using the methods of statistical thermodynamics. The values of AS calculated by these two standard states differ only by the gas constant, B, and are readily interconverted. 

ELDAR contains data for more than 2000 electrolytes in more than 750 different solvents with a total of 56,000 chemical systems, 15,000 hterature references, 45,730 data tables, and 595,000 data points. ELDAR contains data on physical properties such as densities, dielectric coefficients, thermal expansion, compressibihty, p-V-T data, state diagrams and critical data. The thermodynamic properties include solvation and dilution heats, phase transition values (enthalpies, entropies and Gibbs free energies), phase equilibrium data, solubilities, vapor pressures, solvation data, standard and reference values, activities and activity coefficients, excess values, osmotic coefficients, specific heats, partial molar values and apparent partial molar values. Transport properties such as electrical conductivities, transference numbers, single ion conductivities, viscosities, thermal conductivities, and diffusion coefficients are also included. 

The following data, taken from the National Bureau of Standards compilation. Selected Values of Chemical Thermodynamic Properties gives the standard enthalpy of formation of hydrogen chloride from its elements at 25 °C in kg cal mol (Thus the difference between the first and third results gives the heat of dissolving 1 mol of HCl gas in 2 mol of water.) Show that the partial molar enthalpy of hydrogen chloride in a 10 mol dm solution, relative to the elements, is —36.26 kg cal mol , and that the partial molar enthalpy of water in the same solution, relative to pure liquid water, is —0.43 kg cal mol. ... 

Table 7.5 Real gases expressions for differences between molar properties and standard molar values at the same temperature...

The middle column of Table 7.5 contains an expression for G ip ) — G (g) taken from this equation. This expression contains all the information needed to find a relation between any other molar property and its standard molar value in terms of measurable properties. The way this can be done is as follows. 

This value is one of the many standard molar enthalpies of formation to be foimd in compilations of thermodynamic properties of individual substances, such as the table in Appendix H. We may use the tabulated values to evaluate the standard molar reaction enthalpy AfFf ° of a reaction using a formula based on Hess s law. Imagine the reaction to take place in two steps First each reactant in its standard state changes to the constituent elements in their reference states (the reverse of a formation reaction), and then these elements form the products in their standard states. The resulting formula is... 

The objective of this chapter is, by experimentation or computation, on the basis of the values of the main properties, to determine the value of the equilibrium constant of a reaction, or, which is the same thing by virtue of relation [4.2], that of the standard molar Gibbs energy associated with the... 

Morton and Beckett, in an appendix to their book, present bond dissociation energies and standard electrode potentials. Brown, in his book, which is mainly concerned with the techniques of microcalorimetry, gives values of A/ff, AGf, S°, and C° (for 25 °C) for many biological substances, and partial molar properties for aqueous solutions. He also presents enthalpies and Gibbs energies of formation of adenosine phosphoric acid specimens and thermodynamic quantities for some reactions in solution. 

The dependence of the ionic standard molar enthalpies of transfer on the properties of the solvents and the ions are expressed in a manner similar to Equation 4.22a. For small cations, the operative expression for values at 25°C is [36] ... 

We denote the standard state value of a property by the superscript on the symbol for the property, as in for the standard molar enthalpy of a substance and p for the standard pressure of 1 bar. For example, the standard state of hydrogen gas is the pure gas at 1 bar and the standard state of solid calcium carbonate is the pure solid at 1 bar, with either the calcite or aragonite form specified. The physical state needs to be specified because we can speak of the standard states of the sohd, liquid, and vapor forms of water, for instance, which are the pure sohd, the pure liquid, and the pure vapor, respectively, at 1 bar in each case. The standard states of solutions, which are never pure , need to be treated differently (Section 3.8). 

Data on the enthalpy of formation of many of these compounds are included in the table Standard Thermodynamic Properties of Chemical Substances in Section 5 of this Handbook. Absorption spectra and optical rotation data can be found in Reference 3. Partial molar volume and other thermodynamic properties, including solubility as a function of temperature, are given in References 3 and 5. Most of the pK values come from Reference 7. 

The values of partial molar properties involved in operator [3.5] can be considered under aity conditions thus, we can define a standard Gibbs energy associated with R for which the reactants and the products are selected in their state of reference ... 

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. 

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