The standard Gibbs free energy of formation

In order to determine the equilibrimn constant, we need to be able to compute the Gibbs free energy of reaction AG xn This is dependent on the quantities po) — the chemical potential of pure 

The Gibbs free energy of the reaction in Eq. (12.1) can be obtained from Table 3 

From this, we can compute the corresponding value of the equilibrium constant. 

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We obtain K from the standard Gibbs free energies of formation. For reaction (9.85) we get... 

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

FIGURE 7.27 The standard Gibbs free energy of formation of a compound is defined as the standard reaction Gibbs free energy per mole of formula units of the compound when the compound is formed from its elements. It represents a "thermodynamic altitude" with respect to the elements at "sea level." The numerical values are in kilojoules per mole. 

The standard Gibbs free energy of formation of HI is therefore +1.69 kj-mol in good agreement with the value of +1.70 kj-tnol-1 quoted in the text. Note that, because this value is positive, the formation of pure HI from the elements at 1 bar is not spontaneous. 

Use the standard Gibbs free energies of formation in Appendix 2A to calculate AG° for each of the following reactions at 25°C. Comment on the spontaneity of each reaction under standard conditions at 25°C. 

The standard potential of the AI3+/A1 couple is —1.66 V. Calculate the standard Gibbs free energy of formation for Al +(aq). Account for any differences between the standard Gibbs free energy of formation of Tl,+(aq) (see Exercise 14.65) and that of Al +(aq). 

As a thermodynamicist working at the Lower Slobbovian Research Institute, you have been asked to determine the standard Gibbs free energy of formation and the standard enthalpy of formation of the compounds ds-butene-2 and trans-butene-2. Your boss has informed you that the standard enthalpy of formation of butene-1 is 1.172 kJ/mole while the standard Gibbs free energy of formation is 72.10 kJ/mole where the standard state is taken as the pure component at 25 °C and 101.3 kPa. 

Just as there are tables of standard enthalpies of formation, values of the standard Gibbs free energy of formation, AfG, are listed [5—9] for very many compounds and these may be combined in a way analogous to eqn. (10)... 

In a similar manner to that employed for thermochemical AH° of chemical reactions [cf. (3.106)], the reaction free energy AG° can be expressed in terms of the standard Gibbs free energy of formation AGf [AJ for each species A, namely,... 

The standard Gibbs free energies of formation of compounds are based on appropriate synthetic reactions in a manner analogous to the determination of enthalpies of compounds from their elements. For more general reactions ViAi 0 one writes... 

Where, for the ith species, AG is the Gibbs free energy of formation, a,- is the activity, and Zj is the stoichiometric coefficient in the balanced reaction statement (by convention, z,- is negative for reactants and positive for products). The absolute temperature is T R is the gas constant, and P is the absolute pressure. The standard Gibbs free energy of formation, AGf, can be obtained from standard tables, from values of the standard enthalpy AH( and entropy AS of formation for each species via... 

The standard Gibbs free energy of formation, dCj, for gaseous COCIF was calculated to be -412.6 kJ mol , from the relation ... 

Tables of the standard Gibbs free energy of formation allow the calculation of the equilibrium constant at standard conditions (i.e., T = 25°C and p = Ibar). However, in most situations, we require the equilibrium constant at other conditions. In the next section, we discuss how to estimate the equilibrium constant at other temperatures.

The solubility product constant may be determined by direct measnrements or calcnlated from the standard Gibbs free energies of formation (JsGf) of the species involved at their standard states. For the reaction scheme (Equation 8.13) the Gibbs free energy change is ... 

Fig. 5,7. The standard Gibbs free energy of formation of oxides as a function of temperature. This is called an Ellingham diagram.

A common problem is to calculate the composition of a reacting mixture at equilibrium at a specified temperature. To do this, it is always easier if we start with the stoichiometric table of the reaction. The first step is to express all the concentrations in terms of the extent of reaction, . We then calculate the activity of each species and finally, we equate the product of activities to the equilibrium constant. This produces an equation where the only unknown is Once the extent of reaction is known, all the mole fractions can be computed from the stoichiometric table. If the temperature of the calculation is at 25 C, the equilibrium constant is obtained directly from tabulated values of the standard Gibbs free energy of formation. To calculate the equilibrium constant at another temperature, an additional step is needed to obtain the heat of reaction and the Gibbs energy at the desired temperature. This procedure is demonstrated with examples below. 

Graphical data of the standard Gibbs free energy of formation of oxides versus temperature, shown in Fig. 11.2, can be used to predict the conditions under which a metal is oxidized or a metal oxide is reduced [11]. For every reaction in Fig. 11.2, the reactant is 1 mole of O2, so that the reactions are... 

The standard Gibbs free energy of formation, AG°, for any oxide can be read directly off the vertical axis of the graph. For example, at 1000°C, the standard Gibbs free energy of formation of NiO is approximately -250 kJ for two moles of NiO. 

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