Thermochemical solution cycle

The total enthalpy change that occurs when a solution forms from solute and solvent is the heat of solution (Affsoin)> we combine the three individual enthalpy changes to find it. The overall process is called a thermochemical solution cycle and is yet another application of Hess s law ... 

In a thermochemical solution cycle, the heat of solution is the sum of the endothermic separations of solute and of solvent and the exothermic mixing of their particles. 

Finally, a number of solution calorimetric techniques can be used to measure Af//°v For example, q for the solution of a metal in acid can be measured. Additional thermochemical results are then used to complete a cycle that yields AfH°m for the metallic salt. The process adds ArH° for the following reactions ... 

However, the adduct is not stable enough to exist in significant amounts at a temperature of 116 °C, the boiling point of pyridine. As a result, such interactions are studied in solutions, although it is the strength of the bond that would be produced in the gas phase that is desired. A thermochemical cycle... 

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.

D. D. M. Wayner, V D. Parker. Bond Energies in Solution from Electrode Potentials and Thermochemical Cycles. A Simplified and General Approach. Acc. Chem. Res. 1993, 26, 287-294. 

In the liquid phase, the equivalents of IPs and EAs are the electrochemical oxidation and reduction potentials and analogous thermochemical cycles have been used in the literature to calculate pK values. However, oxidation and reduction potentials of RsSi radicals are not yet established experimentally and, therefore, the solution thermochemical cycles suffer from these limitations. 

Figure 1. Thermochemical cycle for the solvation of ions from the gas phase into aqueous solution.

For dissociative electron transfer, an analogous thermochemical cycle can be derived (Scheme 2). In this case the standard potential includes a contribution from the bond fragmentation. Using equations (40) and (41) one can derive another useful expression for BDFEab-, equation (42). While direct electrochemical measurements on solutions may provide b. b, for example, of phenoxides and thiophenoxides (Section 4), the corresponding values for alkoxyl radicals are not as easily determined. Consequently, these values must be determined from a more circuitous thermochemical cycle (Scheme 3), using equation (43). The values of E°h+/h io a number of common solvents are tabulated elsewhere. Values of pKa in organic solvents are available from different sources. " A comparison of some estimated E° values with those determined by convolution voltammetry can be found in Section 3. 

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. 

Figure 2.11 A thermochemical cycle for the solution of sodium sulfate...

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 ... 

Three thermochemical cycles are required for the solution of the problem, (i) One (not shown, but similar to that in Figure 2.11) is for the formation of NH4 + (aq) and CI04 (aq) from the solid compound, and the splitting of the lattice into the gaseous ions followed by their hydration. This leads to the equations ... 

The French decision in 2006 to realise a Generation IV nuclear reactor prototype by year 2020 has led to promote the sodium fast reactor as the reference solution. The maximum temperature available with this type of nuclear reactor is around 500°C. If such a reactor is used to produce hydrogen, using a thermochemical cycle, it is necessary to find a thermochemical cycle compatible with this level of temperature. 

The lattice enthalpy U at 298.20 K is obtainable by use of the Born—Haber cycle or from theoretical calculations, and q is generally known from experiment. Data used for the derivation of the heat of hydration of pairs of alkali and halide ions using the Born—Haber procedure to obtain lattice enthalpies are shown in Table 3. The various thermochemical values at 298.2° K [standard heat of formation of the crystalline alkali halides AHf°, heat of atomization of halogens D, heat of atomization of alkali metals L, enthalpies of solution (infinite dilution) of the crystalline alkali halides q] were taken from the compilations of Rossini et al. (28) and of Pitzer and Brewer (29), with the exception of values of AHf° for LiF and NaF and q for LiF (31, 32, 33). The ionization potentials of the alkali metal atoms I were taken from Moore (34) and the electron affinities of the halogen atoms E are the results of Berry and Reimann (35)4. 

The data given in Tables 2 and 3 are, of course, related to one another through a thermochemical cycle. AHi0n(g) and AHaq differ only by the heats of solvation (hydration in aqueous solution) of the reactants and product, and therefore these heats of solvation must affect the absolute bond energies in the gas phases in such a manner as to cause an inversion in the order of stability in cases of class (b) behaviour (see below). 

For a certain ionic compound, MX, the lattice energy is 1220 kJ mol-1 and the heat of solution in water is -90 kJ mol-1. If the heat of hydration of the cation is 1.50 times that of the anion, what are the heats of hydration of the ions Use the thermochemical cycle developed in question 2. 

Taube and Bray noted in 1940 that the standard potential for the F(g)/F couple is 4.04 V (310). Berdnikov and Bazhin obtained a solution-phase potential by use of a thermochemical cycle that involves estimating the free energy of hydration of the fluorine atom (45) this led to a calculated E° of 3.6 V for the F/F couple and a corresponding AfG° of 68 kJ/mol for F. The chemistry of F2 and HOF has been discussed in Thompson s review (315), but there is no evidence of fluorine-containing radicals in the reactions of these species. There does not seem to be any reported evidence for the existence of F2 in aqueous solution, although the species has been detected in irradiated crystals. In the reversible reaction of H with F to give e q and HF, it has been argued that HF" does not exist as an intermediate but only as a transition state (16). 

Despite the importance of keto/enol tautomers [57] only a small amount of work has been devoted to the study of enol radical cations in condensed phase. This is directly related to the fact that simple enols as the thermodynamically less stable tautomers [58] are usually not isolable, sinre the kinetic barrier for ketonization is rather low [59,60]. Much more is known about the chemistry of enol and keto radical cations in the gas-phase [61]. For details the reader is referred to recent comprehensive reviews [62]. The only available data on the thermodynamics of enol/keto radical cations in solution stem from a recent study [63]. Using stable dimesityl substituted enols the relative stabilities were determined by a thermochemical cycle approach. 

Fig 1. Thermochemical cycle used for the evaluation of the relative stabilities for enol and keto radical cations in solution [63]... 

Many transition-metal hydrides exhibit significant equilibrium acidities [12]. This applies in particular to those that have electron-withdrawing ancillary ligands and/ or a positive charge. This section presents a thermochemical cycle that uses these acidity (pAa) data, when available, as an anchoring point to derive absolute BDE data. In principle the method is applicable to the investigation of BDEs of any M-X bond. In practice, applications have been limited to M-H because data on the prerequisite equilibrium dissociation of M-X to M and X+ in solution have been limited to metal hydrides. 

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