Standard molar free enthalpy

The only thermodynamic condition then required for this reaction to be driven from left to right is that the standard molar free enthalpy of the reaction be negative, that is, the following inequality must hold E pq < E ac, where E ac represents the standard redox potential of the A/C couple. 

This standard chemical potential is a characteristic of the reaction A - B it corresponds to the standard molar free enthalpy of reaction and its definition is the value taken by the chemical potential when equality between substance amounts is realized... 

This mathematical relationship expresses Latimer-Luther s rule. We infer from it the fact that it is unnecessary to calculate the standard molar free enthalpy changes, but this result is not general. The rule is valid only for processes that involve only redox phenomena. This was not the case in the examples given before. 

The terms on the right-hand side of the first line represent the difference between the molar free enthalpies of the solid and liquid solutions at composition X Mb. In addition, a standard result for binary systems (e.g., Swalin, 1962) states for G and n the following relationship... 

Then according to thermodynamics one can obtain the change in the standard molar free energy (at constant pressure), in the enthalpy and in the entropy for adsorptional exchange (21) ... 

In chemical thermodynamics the standard chemical potential ut of a compound i is defined as the molar free enthalpy Ag° for the formation of the compound from its constituent elements j in their stable molecular form in the standard state, and their chemical potential values are set zero in the standard state fit-Ag°f. In exergy engineering the standard molar exergy e° of a compound i is defined as consisting of the molar free enthalpy Ag°f for the formation of the compound in the standard state from its constituent elements and the stoichiometrical sum of the standard chemical exergy values e° of the constituent elements j in their stable state at the standard temperature T° and pressure p° ef- Ag°f + 2 vy e°. 

The molar free enthalpies and enthalpies of combustion at standard conditions will be termed Ag°. and Ah , respectively. 

Standard partial molar free enthalpies, enthalpies, and entropies of vaporization from infinitely dilute solutions in Apiezon M were calculated from retention volumes determined over a range of temperatures data are listed for many organic and a few MR4 compounds (M = Si, Ge, and Sn), including Ge(C2H5)4 [29]. Apiezon L and two polar stationary phases were used in similar studies on a variety of MRr,R4 n compounds, yielding relative molar enthalpies and entropies of solution at 100°C referred to Si(CH3)4 as the standard [43]. Retention volumes and heats of solutions on two stationary phases have also been compared for M(C2H5)4 and M(C2H5)3H compounds with M = Si, Ge, and Sn [38]. 

The quantity that appears in the argument of the exponential at the numerator is the molar free enthalpy of reaction of the reaction intermediate that is identified with the molar activation energy Eg and with the opposite of the standard chemical potential pf. The pre-exponential term is the intrinsic rate constant /(° that is equal to the scaling chmical potential ju divided by the Avogadro constant and by the Planck constant h or what amounts to the same, by dividing numerator and denominator by to keep only the Boltzmann constant (the values of these constants are given in Appendix 2). 

The standard value is the molar free enthalpy of grain boimdary formation ArG, i.e., the G-change during the reaction ... 

One mole of matter is assumed, and unless explicitly noted on the first data card the reference state is the ideal gas at one atmosphere pressure. The enthalpy reference is chosen such that includes the enthalpy of formation as in Eq. (9) of the text. This means that values of H°/RT calculated from the polynomials can be used directly to compute enthalpies of reaction. (See text for discussion of absolute enthalpy). The usual thermochemical manipulations can be done on these polynomials to compute other thermochemical quantities such as standard molar free energies. 

To find a numerical value for AHi, we need to know ArH° at one temperature, while evaluation of I requires ArG° at one temperature. The usual choice is to obtain ArH° and ArG° at T = 298.15 K from standard molar enthalpies of formation and standard molar Gibbs free energies of formation. Earlier in this chapter we referred to examples of these quantities. It is now time to define AfH° and AfG° explicitly and describe methods for their measurement. 

Standard molar enthalpies of formation, AfH°m, and standard molar Gibbs free energies of formation, Af(7, are useful, since they can be used to calculate ArH° and ArG°. The relationships are... 

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

These equations are not very useful in practice because, as remarked earlier, we do not know the absolute values of the molar free energies of substances. However, we can use the same technique we used to find the standard reaction enthalpy in Section 6.19, where we assigned each compound a standard enthalpy of formation, AHf°. We can also tabulate free energies of formation of substances and then use them to calculate AGr°. The standard free energy of formation, AGf°, of a substance is the standard reaction free energy per mole for the formation of a compound... 

Write a chemical equation for the formation reaction and then calculate the standard free energy of formation of each of the following compounds from the enthalpies of formation and the standard molar entropies, using AGr° = AH° — TAS° (a) NH3(g) ... 

Just as we can define a standard enthalpy of formation (AH°f) and a standard free energy of formation (AG°f), we can define an analogous standard entropy of formation (AS°f) as being the entropy change for formation of a substance in its standard state from its constituent elements in their standard states. Use the standard molar entropies given in Appendix B to calculate AS°f for the following substances ... 

However, it is customary to express the concentration of electrolytes in water solutions not in molar fractions but in molalities. That is why standard potential of free enthalpy for dissolved electrolytes is determined at the concentration 1 mole per 1 kg of solvent, and their relative activity is... 

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. 

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