Phase enthalpy

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. 

In Equation (15), the third term is much more important than the second term. The third term gives the enthalpy of the ideal liquid mixture (corrected to zero pressure) relative to that of the ideal vapor at the same temperature and composition. The second term gives the excess enthalpy, i.e. the liquid-phase enthalpy of mixing often little basis exists for evaluation of this term, but fortunately its contribution to total liquid enthalpy is usually not large. 

Figure 1 gives an enthalpy-concentration diagram for ethanol(1)-water(2) at 1 atm. (The reference enthalpy is defined as that of the pure liquid at 0°C and 1 atm.) In this case both components are condensables. The liquid-phase enthalpy of mixing... 

Fig. 9. Vapor-phase enthalpy of anhydrous HF where the numbers represent the partial pressure of HF in kPa (1,17,20,31,33). The critical point occurs at 188°C. To convert kPa to psi, multiply by 0.145. To convert kJ/kg to Btu/lb, multiply by 4.302 x 10 . ...

A tabulation of the partial pressures of sulfuric acid, water, and sulfur trioxide for sulfuric acid solutions can be found in Reference 80 from data reported in Reference 81. Figure 13 is a plot of total vapor pressure for 0—100% H2SO4 vs temperature. References 81 and 82 present thermodynamic modeling studies for vapor-phase chemical equilibrium and liquid-phase enthalpy concentration behavior for the sulfuric acid—water system. Vapor pressure, enthalpy, and dew poiat data are iacluded. An excellent study of vapor—liquid equilibrium data are available (79). 

The observed equilateral triangular 3-centre, 2-electron structure is more stable than the hypothetical linear structure, and the comparative stability of the species is shown by the following gas-phase enthalpies ... 

TABLE 6.1. Gas-Phase Enthalpies that Can Be Used to Determine the Energies of the Different Configurations Involved in the Catalytic Reaction of Lysozyme3... 

Fig. 8. Correlation between Pearson s hardness parameter (7P) derived from gas-phase enthalpies of formation of halide compounds of Lewis acids (19), and the hardness parameter in aqueous solution (/A), derived from formation constants of fluoride and hydroxide complexes in aqueous solution (17). The Lewis acids are segregated by charge into separate correlations for monopositive ( ), dipositive (O), and tripositive ( ) cations, with a single tetrapositive ion (Zr4+, ). The /P value for Tl3+ was not reported, but the point is included in parentheses to show the relative ionicity of Tl(III) to ligand bonds. 

As in Section II,A,l,a, the thermal conductivities are assumed to be constant, and the liquid enthalpy is assumed to be only a function of temperature. The gas phase enthalpy term can be separated into two parts ... 

So far we have not touched on the fact that the important topic of solvation energy is not yet taken into account. The extent to which solvation influences gas-phase energy values can be considerable. As an example, gas-phase data for fundamental enolisation reactions are included in Table 1. Related aqueous solution phase data can be derived from equilibrium constants 31). The gas-phase heats of enolisation for acetone and propionaldehyde are 19.5 and 13 keal/mol, respectively. The corresponding free energies of enolisation in solution are 9.9 and 5.4 kcal/mol. (Whether the difference between gas and solution derives from enthalpy or entropy effects is irrelevant at this stage.) Despite this, our experience with gas-phase enthalpies calculated by the methods described in this chapter leads us to believe that even the current approach is most valuable for evaluation of reactivity. 

We start with a discussion of allene (propadiene), the simplest diene of all. Its gas phase enthalpy of formation is 190.5 1.2 kJmol-1. We wish to compare this quantity with that of related monoenes. The first comparison addresses the relative stability of one and two double bonds in a 3-carbon chain. Conceptually, this may be expressed as the enthalpy of the formal reaction 9... 

The liquid phase enthalpy of formation of this species is from Pedley the necessary enthalpy of vaporization was estimated. 

We admit to comparatively little experience in quantitatively understanding solvent and entropic effects. For example, consider the 1,2,3,4-tetramethylbutadienes presented in Table 2. From Reference 23, we find the relative solution phase Gibbs energies for the ( , )-, (E,Z)- and (Z,Z)-isomers (34-36, respectively) increase in the order (E, E) < (E, Z) (Z, Z). By contrast, the gas phase enthalpies of formation increase in the order (Z, Z) < (E, E) < (E, Z). Somehow it seems inappropriate to include the other CsHi4 hydrocarbons of Reference 23 in the current study when we only know their relative Gibbs energies in solution29. 

We wish to argue that experimental error is the case. Pedley cites liquid phase enthalpies of formation of —12.7 and —58.7 kJmol-1 for the isomeric 3-methylenecyclohexene and 2-methyl-l,3-cyclohexadiene. The difference of these two numbers, -46 kJ mol-1, is meaningfully... 

While there is some dispute about how universal the universal methylene increment really is (cf Reference 1), it is nonetheless generally conceded that a methylene group affixed to two carbons usually contributes ca — 21 kJ mol-1 to the gas phase enthalpy of formation. 

Observation of the empirically linear equation 2 for the gas-phase enthalpy-of-formation data implies that AH(3) is constant for the series of compounds ML 20a b. AH°(3) can also be expressed in terms of the bond dissociation enthalpies (equation 5) by again using Scheme 1. 

The calculated standard gas-phase enthalpies (AH0) and Gibbs free energies (AG°) corresponding to eq 33 are given in Scheme 1. The spontaneity... 

Omitting the liquid-phase enthalpy of formation for 2-nitrodecane gives a slope of —27.2, which is somewhat larger. This third enthalpy of formation for the liquid phase probably mitigates the effect of the incorrect value in the regression analysis. 

Let us now turn to compounds with more than one benzenoid ring. The first species are the isomeric a- and /J-naphthylamincs, 18a and 18b. The archival enthalpies of formation are found to be 157.6 6.9 and 133.8 5.1 kJmol-1. The 24 9 kJmol-1 difference of these two numbers is incompatible with the near-zero difference of the enthalpies of formation for the isomeric naphthols, methyl- and bromonaphthalenes32. Which or either naphthylamine has the correct enthalpy of formation The gas-phase enthalpies of formation of the naphthols differ from their single benzene ring analog, phenol, by 66 kJmol-1 in close agreement with the difference between the methylnaphthalenes and toluene, 63, and between the brominated and parent hydrocarbons, 69 6 and 68 2 kJmol-1 respectively. That is, it is plausibly asserted33 that the difference quantities 17 are nearly constant and equal. 

If two amino groups geminal- to each other provide stabilization, what about vicinal- to each other The archetype here is 1,2-diaminoethane or ethylenediamine, (Cl I2)2(NI I2)2 (23) with a gas-phase enthalpy of formation of —17.6 0.6 kJmol-1. Reaction 26... 

We now consider heteroaromatic diamines with the condition that an amino group is not a to a heterocyclic nitrogen. The only thermochemical data we can find are for 2,8-diamino acridine for which the solid-phase enthalpy is 127 7 kJmol-1. In the absence of significant substituent and solid state effects, thermoneutrality is expected for the conproportionation reaction 40 that produces diaminoarenes from monoamine derivatives. 

The first tetramine we will discuss is the acyclic AfW -bis-(2-aminoethyl)propane-1,3-diamine (36) with an accompanying gas-phase enthalpy of formation58 of 0.0 3.3 kJmol-1. In the absence of intramolecular hydrogen bonding and any vie- and more distant diamine effects, this value could be estimated by summing the enthalpy of formation of w-undecane, 2- 4 and 2-85. The calculated value is —17 kJmol-1. Because the calculated enthalpy of formation is more negative than the experimentally measured... 

The solid-phase enthalpy-of-formation data for the 1,2,4- and 1,3,5-trinitrobenzenes are wildly discrepant. Whichever of them are compared, the 1,2,4-trinitrobenzene isomer is less stable than the 1,3,5-isomer. The dominant destabilization of the 1,2,4-isomer is probably due to the ortho dinitro interaction. We would welcome enthalpy-of-formation data on the 1,2,3-trinitrobenzene isomer. 

As was the case for dinitrobenzene, the meta and para nitroaniline isomers have essentially the same gaseous enthalpy of formation. In the gaseous phase, it is surprising to find that despite the more attractive quinonoid resonance structures92 for the para isomer (58) than for the meta (59) the met a and para nitroaniline have essentially the same gas-phase enthalpy of formation. In the solid and liquid states the intermolecular stabilization lowers the enthalpy of formation of the para isomer relative to the meta. Interestingly, the gas-phase intramolecularly hydrogen-bonded ortho isomer is of comparable stability to its isomers. In contrast, it is considerably less stable than its isomers in the solid state because it can form fewer intermolecular hydrogen bonds. All isomers of nitroaniline are more stable than calculated by additivity. 

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