Energy of reactions

Although it is not universally true that the activation energies of reactions parallel their heats of reaction, this is approximately true for the kind of addition reaction we are discussing. Accordingly, we can estimate E = k AH, with k an appropriate proportionality constant. If we consider the difference between two activation energies by combining this idea with Eq. (7.21), the contribution of the nonstabilized reference reaction drops out of Eq. (7.21) and we obtain... 

A reactor system is shown in Figure 2 to which the HAZOP procedure can be appHed. This reaction is exothermic, and a cooling system is provided to remove the excess energy of reaction. If the cooling flow is intermpted, the reactor temperature increases, leading to an increase in the reaction rate and the heat generation rate. The result could be a mnaway reaction with a subsequent increase in the vessel pressure possibly leading to a mpture of the vessel. 

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 ... 

Which cation benefits more from the solvent Recalculate the energy of reaction (1) taking account of hydration of the two cations (only). 

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. 

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