Free Energies of Reactions

Temperature, K Enthalpy of reaction (AH ), kj/mol Free energy of reaction (AG ), kJ/mol Equilibrium cell potential (E ), V... 

Equilibrium concentrations of reactants and products can be calculated from the equilibrium constant, K q, which is related to the free energy of reaction, AGrxn ... 

The Hammett equation is the best-known example of a linear free-energy relationship (LFER), that is, an equation which implies a linear relationship between free energies of reaction or activation for two related processes48. It describes the influence of polar meta-or para-substituents on reactivity for side-chain reactions of benzene derivatives. 

One way to measure the thermodynamics of the reaction is by the ceiling temperatures, Tc (the temperature at which the free energy of reaction 56 is zero). Bowmer and O Donnell74 found that G(S02) increases with decreasing Tc showing the importance of the thermodynamic factor. Although kinetic factors can explain also the increase in G(S02) with temperature, they do not explain the observed correlation with Tc. 

The thermodynamic function used as the criterion of spontaneity for a chemical reaction is the Gibbs free energy of reaction, AG (which is commonly referred to as the reaction free energy ). This quantity is defined as the difference in molar Gibbs free energies, Gm, of the products and the reactants ... 

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. 

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... 

What Do We Need to Know Already The concepts of chemical equilibrium are related to those of physical equilibrium (Sections 8.1-8.3). Because chemical equilibrium depends on the thermodynamics of chemical reactions, we need to know about the Gibbs free energy of reaction (Section 7.13) and standard enthalpies of formation (Section 6.18). Ghemical equilibrium calculations require a thorough knowledge of molar concentration (Section G), reaction stoichiometry (Section L), and the gas laws (Ghapter 4). 

Gibbs free energy of reaction depends on the composition of the reaction mixture and how it changes as the reaction approaches equilibrium. 

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) ... 

Equation 5 shows how the Gibbs free energy of reaction varies with the activities (the partial pressures of gases or molarities of solutes) of the reactants and products. The expression for Q has the same form as the expression for K, but the activities refer to any stage of the reaction. 

EXAMPLE 9.2 Calculating the Gibbs free energy of reaction from the reaction quotient... 

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... 

Because the Gibbs free energy of reaction is negative, the formation of products is spontaneous (as indicated by the green region in the diagram) at this composition and temperature. 

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. 

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. 

Because 1 C-V = l J, we can conclude that the Gibbs free energy of reaction A under these conditions is —201 kj because this value is negative, the reaction is spontaneous in the forward direction for this composition of the cell. 

Redox reactions that have a positive Gibbs free energy of reaction are not spontaneous, but an electric current can be used to make them take place. For example, there is no common spontaneous chemical reaction in which fluorine is a product, and so the element cannot be isolated by any common chemical reaction. It was not until 1886 that the French chemist Henri Moissan found a way to force the... 

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