Gibbs energy standard value

The values of the changes in standard Gibbs energy, standard enthalpy and standard entropy are given for all the stages. The calculation of some of the values depends upon the known values for the standard entropies of the participating species given in Table 4.3. 

Standard thermodynamic constant of a reaction may be calculated from values of free enthalpy (Gibbs energy) standard potentials of the formation of its participating components (AZ°). First is calculated free enthalpy of... 

The standard Gibbs-energy change of reaction AG° is used in the calculation of equilibrium compositions. The standard heat of reaclion AH° is used in the calculation of the heat effects of chemical reaction, and the standard heat-capacity change of reaction is used for extrapolating AH° and AG° with T. Numerical values for AH° and AG° are computed from tabulated formation data, and AC° is determined from empirical expressions for the T dependence of the C° (see, e.g., Eq. [4-142]). 

Integration of this requires a limit to be defined. The limit is taken simply as follows. We define a standard pressure p at which the Gibbs free energy has a standard value G. We have thereby defined a standard state for this component of the system a standard temperature too, is implicit in this since the above equations are treated for constant temperature. 

The Gibbs free energy of a liquid is almost independent of pressure, and so we can replace Gm(l) by its standard value (its value at 1 bar), Gm°(l). The Gibbs free energy of an ideal gas does vary with pressure, and thermodynamics can be used to show that, for an ideal gas,... 

FIGURE 8.4 The variation of the molar Gibbs free energy of an ideal gas with pressure. The Gibbs free energy has its standard value when the pressure of the gas is 1 bar. The value of the Gibbs free energy approaches minus infinity as the pressure falls to zero. 

Note that, because In 1 = 0, Gm(J) has its standard value, Gm°(J), when Pj = 1 bar. Thermodynamic arguments (which we do not reproduce here) show that a similar expression applies to solutes and pure substances. In each case, we can write the molar Gibbs free energy of a substance J as... 

That is, for a pure solid or liquid, the molar Gibbs free energy always has its standard value (provided the pressure is 1 bar). 

Fig. 1.1 (a) The ionization enthalpies of dipositive lanthanide ions with configurations of the type [Xe]4f" (upper plot left-hand axis), (b) The standard Gibbs energy change of reaction 1 (lower plot right-hand axis estimated value ... 

The relationships of the type (3.1.54) and (3.1.57) imply that the standard electrode potentials can be derived directly from the thermodynamic data (and vice versa). The values of the standard chemical potentials are identified with the values of the standard Gibbs energies of formation, tabulated, for example, by the US National Bureau of Standards. On the other hand, the experimental approach to the determination of standard electrode potentials is based on the cells of the type (3.1.41) whose EMFs are extrapolated to zero ionic strength. 

For proton transfer from an acid (HA) to a series of bases (B ) the Gibbs energy of activation for the reaction is predicted to vary with the standard Gibbs energy for the proton transfer according to (18) The value of the... 

The value of this standard molar Gibbs energy, p°(T), found in data compilations, is obtained by integration from 0 K of the heat capacity determined by the translational, rotational, vibrational and electronic energy levels of the gas. These are determined experimentally by spectroscopic methods [14], However, contrary to what we shall see for condensed phases, the effect of pressure often exceeds the effect of temperature. Hence for gases most attention is given to the equations of state. 

The AG symbol refers to the nonstandard Gibbs free energy value, AG° is the standard value, R is the gas constant (8.314 J/mol-K), T is the temperature (K), and Q is the reaction quotient first seen in Chapter 14. At equilibrium, this equation becomes ... 

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. 

Assuming this standard state, the AC° value expresses a change in the Gibbs energy of adsorption of one molecule B upon being moved from the hypothetical ideal solution onto the electrode surface. This enables the particle-particle interactions on the surface to be separated from any other interactions and to be included in the term/(/i). 

Therefore the determination of the standard Gibbs energies of adsorption at various symmetrical or unsymmetrical standard states leads directly to derivation of the particle-particle interaction parameter. The same result may be obtained from the difference of AG"" values calculated at zero surface coverage (0 = 0) and at saturated surface coverage (0=1), using Eqs. (30a) and (30b). 

The Gibbs energy of adsorption is a measure of adsorbate-metal interactions. Its values depend, however, on the choice of standard states for the chemical potentials of the components involved in the process. Therefore AG° values determined for different systems can only be compared if they refer to the same standard-state conditions. AG° values of adsorption of thiourea (TU) on several metallic electrodes, calculated for the most often used standard states, are presented in Table 1. 

The values of the standard Gibbs energy between nitrobenzene and water and the values of the standard potential differences between these two solvents for various ions are given in table 2.1. Equations (2.2.8) and (2.2.10) can be generalized readily for an electrolyte of any type of charge. 

Table 2.1. Values o f standard Gibbs energies of ion transfer from water to nitrobenzene in electron volts. From P. Vanysek, Thesis, J. Heyrovsky Institute of Physical Chemistry and Electrochemistry, Czechoslovak Academy of Sciences, Prague (1982).

The differences in the solvation abilities of ions by various solvents are seen, in principle, when the corresponding values of As ivG° of the ions are compared. However, such differences are brought out better by a consideration of the standard molar Gibbs energies of transfer, AtG° of the ions from a reference solvent into the solvents in question (see further section 2.6.1). In view of the extensive information shown in Table 2.4, it is natural that water is selected as the reference solvent. The TATB reference electrolyte is again employed to split experimental values of AtG° of electrolytes into the values for individual ions. Tables of such values have been published [5-7], but are outside the scope of this text. The notion of the standard molar Gibbs energy of transfer is not limited to electrolytes or ions and can be applied to other kinds of solutes as well. This is further discussed in connection with solubilities in section 2.7. 

The standard molar Gibbs energy of transfer of CA is the sum v AG°(C) -i-v AtG°(A), where the charges of the cation C and anion A " and the designation of the direction of transfer, (aq org), have been omitted. The values for the cation and anion may be obtained from tables [5-7], which generally deal with solvents org that are miscible with water and not with those used in solvent extraction. However, AtG°(C) depends primarily on the (3 solvatochromic parameter of the solvent and AtG°(A) on its a parameter, and these can be estimated from family relationships also for the latter kind of solvents. 

The left-hand-side of the equation is defined as the Gibbs energy relative to a standard element reference state (SER) where is the enthalpy of the element or substance in its defined reference state at 298.IS K, a, b, c and dn are coefficients and n represents a set of integers, typically taking the values of 2, 3 and -1. From Eq. (S.3), further thermodynamic properties can be obtained as discussed in Chapter 6. 

EMF and vapour pressure measurements are dependent on the temperature, the number of phases involved and, importantly, the reference state of the component in question. The problem with the reference state is important as experimentally stated values of partial Gibbs energies will be dependent on this value. The standard states are fixed before optimisation and may actually have values different from those used by the original author. Therefore, as far as possible like should be compared with like. 

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