Standard Gibbs free energy reaction

The assessment of the driving force follows from the reaction standard Gibbs free energies A Go, calculated by using the corresponding energies of formation of the reactant CX (AGr) and the products (AGp) in reactions (4.11a,b). 

Having calculated the standai d values AyW and S" foi the participants in a chemical reaction, the obvious next step is to calculate the standard Gibbs free energy change of reaction A G and the equilibrium constant from... 

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

The standard Gibbs free energy of reaction, AG°, is defined like the Gibbs free energy of reaction but in terms of the standard molar Gibbs energies of the reactants and products ... 

STRATEGY We write the chemical equation for the formation of HI(g) and calculate the standard Gibbs free energy of reaction from AG° = AH° — TAS°. It is best to write the equation with a stoichiometric coefficient of 1 for the compound of interest, because then AG° = AGf°. The standard enthalpy of formation is found in Appendix 2A. The standard reaction entropy is found as shown in Example 7.9, by using the data from Table 7.3 or Appendix 2A. 

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. 

Just as we can combine standard enthalpies of formation to obtain standard reaction enthalpies, we can also combine standard Gibbs free energies of formation to obtain standard Gibbs free energies of reaction ... 

EXAMPLE 7.15 Sample exercise Calculating the standard Gibbs free energy of reaction... 

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. 

Notice that the combination of the first four terms in the final equation is the standard Gibbs free energy of reaction, AGr° (Eq. 19 of Chapter 7) ... 

STRATEGY Calculate the reaction quotient and substitute it and the standard Gibbs free energy of reaction into Eq. 5. If AGr < 0, the forward reaction is spontaneous at the given composition. If AGr > 0, the reverse reaction is spontaneous at the given composition. If AGr = 0, there is no tendency to react in either direction the reaction is at equilibrium. At 298.15 K, RT = 2.479 kJ-moF h... 

The reaction quotient, Q, has the same form as K, the equilibrium constant, except that Q uses the activities evaluated at an arbitrary stage of the reaction. The equilibrium constant is related to the standard Gibbs free energy of reaction by AG° = —RT In K. 

Example 9.4 deals with a system at equilibrium, but suppose the reaction mixture has arbitrary concentrations. How can we tell whether it will have a tendency to form more products or to decompose into reactants To answer this question, we first need the equilibrium constant. We may have to determine it experimentally or calculate it from standard Gibbs free energy data. Then we calculate the reaction quotient, Q, from the actual composition of the reaction mixture, as described in Section 9.3. To predict whether a particular mixture of reactants and products will rend to produce more products or more reactants, we compare Q with K ... 

We are free to choose either K or Kc to report the equilibrium constant of a reaction. However, it is important to remember that calculations of an equilibrium constant from thermodynamic tables of data (standard Gibbs free energies of formation, for instance) and Eq. 8 give K, not Kc. In some cases, we need to know Kc after we have calculated K from thermodynamic data, and so we need to be able to convert between these two constants. 

The effect of temperature on the equilibrium composition arises from the dependence of the equilibrium constant on the temperature. The relation between the equilibrium constant and the standard Gibbs free energy of reaction in Eq. 8 applies to any temperature. Therefore, we ought to be able to use it to relate the equilibrium constant at one temperature to its value at another temperature. 

A catalyst speeds up both the forward and the reverse reactions by the same amount. Therefore, the dynamic equilibrium is unaffected. The thermodynamic justification of this observation is based on the fact that the equilibrium constant depends only on the temperature and the value of AGr°. A standard Gibbs free energy of reaction depends only on the identities of the reactants and products and is independent of the rate of the reaction or the presence of any substances that do not appear in the overall chemical equation for the reaction. 

Calculate the standard Gibbs free energy for each of the following reactions ... 

A certain enzyme-catalyzed reaction in a biochemical cycle has an equilibrium constant that is 10 times the equilibrium constant of the next step in the cycle. If the standard Gibbs free energy of the first reaction is —200. k -mol 1, what is the standard Gihhs free energy of the second reaction ... 

From values in Appendix 2A, determine the standard Gibbs free energy and the standard entropy for the reaction. 

Sodium metal is produced from the electrolysis of molten sodium chloride in the Downs process (Section 12.13). Determine (a) the standard Gibbs free energy of the reaction... 

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