Thermochemical cycle enthalpies

The enthalpy of formation of a compound is a so-called thermodynamic state function, which means that the value depends only on the initial and final states of the system. When the formation of crystalline NaCl from the elements is considered, it is possible to consider the process as if it occurred in a series of steps that can be summarized in a thermochemical cycle known as a Born-Haber cycle. In this cycle, the overall heat change is the same regardless of the pathway that is followed between the initial and final states. Although the rate of a reaction depends on the pathway, the enthalpy change is a function of initial and final states only, not the pathway between them. The Born-Haber cycle for the formation of sodium chloride is shown as follows ... 

Figure 2.1 Thermochemical cycle, showing how to relate the enthalpy of the experimental reaction 2.1 with reaction 2.2, where reactants and products are in their standard states.

Figure 2.2 Thermochemical cycle relating the enthalpies of reaction 2.2 at 298.15 Kand 310 K.

We have illustrated how standard enthalpy of formation values can be handled to yield data for practical conditions. The procedure always involves thermochemical cycles, relating the standard state processes with those observed in... 

Figure 5.1 Thermochemical cycle (f = 298.15 K), showing how solution and gas-phase bond dissociation enthalpies are related. AS0 VH° are standard enthalpies of solvation.

Figure 5.3 Thermochemical cycle, illustrating how the enthalpy of reaction 5.10 can be given as a bond dissociation enthalpy balance.

Figure 5.5 Thermochemical cycles relating O-H bond enthalpy contributions ( s) with bond dissociation enthalpies (DH°) in phenol and ethanol. ER are reorganization energies (see text).

Let us concentrate on the thermochemical cycle of figure 5.6 that involves the disruption of the complex Cr(CO)3(C6H6). The enthalpy of this reaction, previously calculated as 497.9 10.3 kJ mol-1 from standard enthalpy of formation data, can be related (equation 5.24) to the bond enthalpy contributions EsfCr-CO ) andE s(Cr (V.He) through the reorganization energies ER(C() ) and ER(C(tHf )- Two asterisks indicate that the fragment has the same structure as... 

Figure 5.6 Thermochemical cycles to estimate the Cr-CgHg bond enthalpy contribution (fs) in Cr(CO)3(C6hl6). ER are reorganization energies. One asterisk indicates that the fragment has the same structure as in Cr(CO)6, and two asterisks mean that the fragment has the same structure as in Cr(CO)3(CgH6)-...

We are now left with the evaluation of E s (Cr—CO), the Cr-CO bond enthalpy contribution in Cr(CO)6. The third thermochemical cycle in figure 5.6 shows how this bond enthalpy contribution can be evaluated from the Cr-CO mean bond dissociation enthalpy (107.0 0.8 kJ mol-1 see section 5.2) and the reorganization energy ER(CO ). 

Figure 8.6 Thermochemical cycle used to derive the enthalpy of formation of Mo(r 5-C5hl5)2(C2H4) in the crystalline state.

Finally, the R-H bond dissociation enthalpy in the gas phase can be obtained by using the general thermochemical cycle shown in figure 5.1 (R = A and H = B), which includes the solvation enthalpies of RH and R ... 

The relationships between the two different states and between the enthalpy of formation from the elements at standard state (H°) and the lattice energy (U) are easily understood by referring to the Born-Haber-Fayans thermochemical cycle. In this cycle, the formation of a crystalline compound from isolated atoms in the gaseous state is visualized as a stepwise process connecting the various transformations. Let us follow the condensation process of a crystal MX formed from a metal M and a gaseous molecule X2 ... 

We have also seen (in chapter 1) that enthalpy and lattice energy are related through the Born-Haber-Fayans thermochemical cycle, on the basis of the energy additivity principle of Hess. The enthalpy or heat content of a phase H) is composed of the internal energy U at the T of interest and the PV product ... 

Table 5.12 reports a compilation of thermochemical data for the various olivine components (compound Zn2Si04 is fictitious, because it is never observed in nature in the condition of pure component in the olivine form). Besides standard state enthalpy of formation from the elements (2) = 298.15 K = 1 bar pure component), the table also lists the values of bulk lattice energy and its constituents (coulombic, repulsive, dispersive). Note that enthalpy of formation from elements at standard state may be derived directly from bulk lattice energy, through the Bom-Haber-Fayans thermochemical cycle (see section 1.13). 

As described above, everything is converted to the gas phase leading to the following thermochemical cycle in Fig. 1 which contains the important enthalpy contributions to the equilibrium written in Eq. (1) ... 

The enthalpy change of the reaction in Equation (1.18) is minus the proton affinity of ammonia, -P(NH3,g). This could be calculated from the thermochemical cycle shown in Figure 1.58, provided the lattice energy of ammonium chloride is known. 

Table 2.12 gives the absolute enthalpies of hydration for some anions. The values are derived from thermochemical cycle calculations using the enthalpies of solution in water of various salts containing the anions and the lattice enthalpies of the solid salts. 

The data given in Table 3.2 may be interpreted for a general acid H-A, using thermochemical cycles, in terms of the enthalpy changes accompanying the reactions ... 

Hydrogen fluoride in aqueous solution is a weak acid, characterized by its pKa value of 3.2. By comparison, the other hydrogen halides are extremely strong acids in aqueous solution all three are fully dissociated in dilute solution, and their pA", values may be estimated by thermochemical cycle calculations. The thermochemical cycle shown in Figure 3.1 represents the various processes as the aqueous hydrogen halide, HX, is converted to a solution containing hydrated protons and hydrated halide ions. The enthalpy of acid dissociation of the HX(aq) compound is given by ... 

The standard enthalpy change for the reduction of M + (aq) to M(s) may be estimated from the above data by carrying out a calculation using the thermochemical cycle shown in Figure 6.1 for the overall reaction ... 

Figure 7.1 A thermochemical cycle for the calculation of the enthalpy of hydration of...

Figure 7.2 A thermochemical cycle lor the calculation of ihe enthalpy of hydration of the Cr3 ion...

The validity of the Kirchhoff integration formula (3.111) can be verified graphically by consideration of the thermochemical cycle shown in Fig. 3.14. As shown in the figure, the enthalpy change AH(1 ) for the direct reaction path at T must match the total enthalpy change for the alternative path of... 

Thermochemical cycles (Figure 2) involving the formation of compounds (a-quartz, gibbsite, amines, tetrapropylammonium bromide, etc.), the dissolution of these compounds and of the HFI-type samples in 25% HF, and the dilution of aqueous HF allow the calculation of the standard enthalpy of formation of the samples. 

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