Standard molar Gibbs energies, enthalpies and entropies

3 Standard molar Gibbs energies, enthalpies and entropies 

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Table VII-15 Standard molar Gibbs energies, enthalpies and entropies for the reactions + wHzOCl) Th COH) - + nit at 25°C.

VII.3.6.3 Standard molar Gibbs energies, enthalpies and entropies... 

Table VH-18 Selected standard molar Gibbs energies, enthalpies and entropies of formation for Th(IV) hydroxide complexes. In order to maintain a high level of numerical consistency, more digits are given than is justified by the precision of the data.

Table 2.1 Change in standard molar Gibbs energy, enthalpy and entropy (all in kj mot ) for the transfer of hydrocarbons from pure liquids into water at 25 °C (Prausnitz, Lichtenthaler and de Azevedo, 1999 Gill and Wadso, 1976). Notice the large negative entropy changes due to the hydrophobic effect, in the case of n-butane, the entropy decrease amounts to 85% of the Gibbs energy of solubilization, while for other hydrocarbons the entropic contribution is even larger...

Besides equilibriumconstants, additional thermodynamic data were included, if available, although little emphasis was put on their completeness. The data for primary master species comprise the standard molar thermodynamic properties of formation from the elements (AfG standard molar Gibbs energy of formation AfH°m standard molar enthalpy of formation ApSm- standard molar entropy of formation), the standard molar entropy (5m), the standard molar isobaric heat capacity (Cp.m), the coefficients Afa, Afb, and Afc for the temperature-dependent molar isobaric heat capacity equation... 

The conventional thermodynamic standard state values of the Gibbs energy of formation and standard enthalpy of formation of elements in their standard states are A(G — 0 and ArH = 0. Conventional values of the standard molar Gibbs energy of formation and standard molar enthalpy of formation of the hydrated proton are ArC (H +, aq) = 0 and Ar// (H +, aq) = 0. In addition, the standard molar entropy of the hydrated proton is taken as zero 5 (H+, aq) = 0. This convention produces negative standard entropies for some ions. 

EFI/PRO] Efimov, M. E., Prokopenko, L V., Tsirelnikov, V. L, Troyanov, S. L, Medvedev, V. A., Berezovskii, G. A., Paukov, L E., Thermodynamic properties of zirconium chlorides. I. The standard molar enthalpy of formation, the low-temperature heat capacity, the standard molar entropy, and the standard molar Gibbs energy of formation of zirconium trichloride, J. Chem. Thermodyn., 19, (1987), 353-358. Cited on pages 163, 164, 333,335,338. 

The standard states correspond to a hypothetical ideal gas at atmospheric pressure (101,325 Pa) and a hypothetical ideal 1 M aqueous solution. The standard molar Gibbs free energy, enthalpy, and entropy changes for the above reaction are donated by symbols AG°, AH°. and AS°, respectively. 

On the other hand, thermodynamic quantities that pertain to the formation of isolated ions from the elements in their standard states are well defined. The standard molar Gibbs energy and the enthalpy of formation, AfG°(F= =, g) and g), of many ions have been reported. The standard molar entropy and constant-pressure heat capacity, 5°(F, g) and Cp(F= =, g), of isolated ions are also well defined quantities and have been reported. Such data are generally available for the standard temperature T° = 298.15 K and pressure P° = 100 kPa, and suitable sources are the NBS tables (Wagman et al. 1982) and the book by Marcus (1997). The standard molar volume of an isolated ion is trivial, being the same for all ions V°(F , g)= RT /P = 0.02479m mor , where/ = 8.31451 J K mor is the gas constant. 

The standard molar Gibbs energy of hydration of an ion, AhydrGi° , can now be obtained from a combination of the standard molar enthalpy and entropy of hydration ... 

AGk, AH, AH thus obtained represent the stoichiometric variations of the Gibbs free energy, enthalpy and entropy, respectively, on the transfer of one mole of solute between the two phases in standard state. AG is the same for the hypothetical ideal state and the real state pro wded that the activity equals unity in both. However AHJ is different in the two cases and reference should be made to the hypothetical ideal state. Because the intermolecular attractions which determine AH are identical in the hypothetical (standard) and reference states, AH refers also to the modification of partial molar enthalpy between the reference states. The same conclusion holds true for the modification of molar heat capacities. A/Sk, like AGk, does not apply to the modification of partial molar entropy between reference states but refers to the hypothetical standard state described above. 

TABLE 2.3 The Standard Molar Gibbs Energy and Enthalpy of formation [1] Standard Molar Entropy [13] and Constant-pressure Molar Heat Capacity [14] of Isolated Ions at the Standard Temperature 7 =298.15 K and Pressure/ °=0.1 MPa... 

Estimation of reasonably correct A,G" values [8] results from the sum of the electrostatic terms, Equations 4.13 and 4.14, and the cavity formation term, Equation 4.10. Such values are shown in Table 4.1. It should be noted that the ionic standard molar Gibbs energies of hydration need to be compatible with the corresponding enthalpies and entropies of hydration (see the following text) according to A G, = A /f,°°-TA Sj . The latter quantities are more directly available from experimental data, so that values adopted from Ref 8 are presented in Table 4.1... 

Thermodynamic properties of ions in nonaqueous solvents are described in terms of the transfer from water as the source solvent to nonaqueous solvents as the targets of this transfer. These properties include the standard molar Gibbs energies of transfer (Table 4.2), enthalpies of transfer (Table 4.3), entropies of transfer (Table 4.4) and heat capacities of transfer (Table 4.5) as well as the standard partial molar volumes (Table 4.6) and the solvation numbers of the ions in non-aqueous solvents (Table 4.10). The transfer properties together with the properties of the aqueous ions yield the corresponding properties of ions in the nonaqueous solvents. 

We cannot calculate AjG from the standard molar Gibbs energies themselves because these quantities are not known. One practical approach is to calculate the standard reaction enthalpy from standard enthalpies of formation (Section 1.11), the standard reaction entropy from Third-Law entropies (Section 2.5), and then to combine the two quantities by using... 

In the case of a pure solid, the chemical potential is quite simply its standard molar Gibbs energy and is expressed according to its standard molar enthalpy and entropy, both functions of the temperature only, as follows ... 

The standard partial molar Gibbs free energy of solution is related to the enthalpy and entropy functions at the column temperature T by the expression... 

Because it applies mostly to electrolytes, it is discussed in Chapter 15. Briefly, Helgeson models the behavior of solutes by developing equations for the standard state partial molar volume (Helgeson and Kirkham 1976) and standard state partial molar heat capacity (Helgeson et al. 1981) as a function of P and T, with adjustable constants such that they can be applied to a wide variety of solutes. If you know these quantities (V°, C°p), you can calculate the variation of the standard state Gibbs energy, and that leads through fundamental relationships to equilibrium constants, enthalpies, and entropies. 

In these equations, the real-gas properties are expressed relative to the standard state values, H°, S°, and G°, which are, respectively, the molar enthalpy, the molar entropy, and the molar Gibbs energy values which the gas would have at a standard pressure p° (1.013 25 bar) if it were ideal. 

Calculate the standard Gibbs free energy of formation of HI(g) at 25°C from its standard molar entropy and standard enthalpy of formation. 

The standard enthalpy difference between reactant(s) of a reaction and the activated complex in the transition state at the same temperature and pressure. It is symbolized by AH and is equal to (E - RT), where E is the energy of activation, R is the molar gas constant, and T is the absolute temperature (provided that all non-first-order rate constants are expressed in temperature-independent concentration units, such as molarity, and are measured at a fixed temperature and pressure). Formally, this quantity is the enthalpy of activation at constant pressure. See Transition-State Theory (Thermodynamics) Transition-State Theory Gibbs Free Energy of Activation Entropy of Activation Volume of Activation... 

It is necessary to specify zero ionic strength here because Debye-HUckel adjustments for ionic strength depend on the temperature. Heat capacities and transformed heat capacities are discussed in an Appendix to this chapter. However, since there is not very much information in the literature on heat capacities of species or transformed heat capacities of reactants, the treatments described here are based on the assumption that heat capacities of species are equal to zero. When molar heat capacities of species can be taken as zero, both standard enthalpies of formation and standard entropies of formation of species are independent of temperature. When Af H° and Af 5° are independent of temperature, standard Gibbs energies of formation of species at zero ionic strength can be calculated using... 

As mentioned in Sections 1.1 and 2.9, the third law of thermodynamics makes it possible to obtain the standard Gibbs energy of formation of species in aqueous solution from measurements of the heat capacity of the crystalline reactant down to about 10 K, its solubility in water and heat of solution, the heat of combustion, and the enthalpy of solution. According to the third law, the standard molar entropy of a pure crystalline substance at zero Kelvin is equal to zero. Therefore, the standard molar entropy of the crystalline substance at temperature T is given by... 

Combining the selected molar standard enthalpy of formation and entropy yields the selected molar standard Gibbs energy of formation ... 

In thermodynamic data tables (standard enthalpies or Gibbs energies of formation and standard molar entropies) which relate to compounds other than ions in a solution, the common convention that is applied involves setting the values of standard enthalpy and standard Gibbs energy of formation (or chemical potential) equal to OJmor for all simple pure elements in their stable physical state at the temperature in question. The data therefore refer to the formation of substances from simple elements. 

Because partial molar volume, enthalpy, and heat capacity are the same anywhere on the Henry s law tangent, including both the state of infinite dilution and the ideal one molal solution, either of these states can serve as the standard state for these properties. We have chosen to say that the infinitely dilute solution is the standard state, but many treatments prefer to say that the standard state for these properties, as well as for the Gibbs energy and entropy, is the ideal one molal solution. For some reason, these treatments (e.g., Klotz, 1964, p. 361) then define the reference state for enthalpy, volume and heat capacity... 

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