Enthalpy comparison

By comparison, Fig. 13.36 shows an exothermic reactor integrated below the pinch. Although heat is being recovered, it is being recovered into part of the process which is a heat source. The hot utility requirement cannot be reduced because the process above the pinch needs at least Q//m-,n to satisfy its enthalpy imbalance. 

A more useful quantity for comparison with experiment is the heat of formation, which is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The heat of formation can thus be calculated by subtracting the heats of atomisation of the elements and the atomic ionisation energies from the total energy. Unfortunately, ab initio calculations that do not include electron correlation (which we will discuss in Chapter 3) provide uniformly poor estimates of heats of formation w ith errors in bond dissociation energies of 25-40 kcal/mol, even at the Hartree-Fock limit for diatomic molecules. 

In estimating the enthalpy of polymerization, the physical state of both starting monomer and polymer must be specified. Changes in state are accompanied by ethalpy changes. Therefore, they also affect the level of the polymerization enthalpy. The AfT forN ylylene previously mentioned is apphcable to the monomer as an ideal gas. To make comparisons with other polymerization processes, most of which start with condensed monomer, a heat of vaporization for N ylylene is needed. It is assumed herein that it is the same as that for N ylene, 42.4 kJ /mol (10.1 kcal/mol). Thus the AfT of the hquid monomer -xylylene is 192.3 kJ/mol (46.0 kcal /mol). 

As a check on the assumptions made, a comparison can be made to a different method of checking the derivation of the head. Enthalpy difference, as a function of temperature change, for an adiabatic pro is... 

Table 1.19. Comparison of Ab Initio and DFT Enthalpies with Experimentai Values in kcal/mol for the Isodemie Reaction " C H + (3 - )CH4 -> (2 - /2)CjH,...

Reductions by NaBKt are characterized by low enthalpies of activation (8-13kcal/mol) and large negative entropies of activation (—28 to —40eu). Aldehydes are substantially more reactive than ketones, as can be seen by comparison of the rate data for benzaldehyde and acetophenone. This relative reactivity is characteristic of nearly all carbonyl addition reactions. The reduced reactivity of ketones is attributed primarily to steric effects. Not only does the additional substituent increase the steric restrictions to approach of the nucleophile, but it also causes larger steric interaction in the tetrahedral product as the hybridization changes from trigonal to tetrahedral. 

An important question for chemists, and particularly for biochemists, is, Will the reaction proceed in the direction written J. Willard Gibbs, one of the founders of thermodynamics, realized that the answer to this question lay in a comparison of the enthalpy change and the entropy change for a reaction at a given temperature. The Gibbs free energy, G, is defined as... 

Theoretical studies of the relative stabilities of tautomers 14a and 14b were carried out mostly at the semiempirical level. AMI and PM3 calculations [98JST(T)249] of the relative stabilities carried out for a series of 4(5)-substituted imidazoles 14 (R = H, R = H, CH3, OH, F, NO2, Ph) are mostly in accord with the conclusion based on the Charton s equation. From the comparison of the electronic spectra of 4(5)-phenylimidazole 14 (R2 = Ph, R = R3 = H) and 2,4(5)-diphenylimidazole 14 (R = R = Ph, R = H) in ethanol with those calculated by using ir-electron PPP method for each of the tautomeric forms, it follows that calculations for type 14a tautomers match the experimentally observed spectra better (86ZC378). The AMI calculations [92JCS(P1)2779] of enthalpies of formation of 4(5)-aminoimidazole 14 (R = NH2, R = R = H) and 4(5)-nitroimidazole 14 (R = NO2, R = R = H) point to tautomers 14a and 14b respectively as being energetically preferred in the gas phase. Both predictions are in disagreement with expectations based on Charton s equation and the data related to basicity measurements (Table III). These inconsistencies may be... 

A Mollier Diagram is useful for the expansion of a specific gas/vapor or multicomponent vapor fluid. See Figure 12-91 for comparison of (1) constant enthalpy (Joule-Thompson effect), isenthalpic, and (2) isentropic (constant entropy), which provides the colder temperature. Note that the expander indicated on the figure is somewhere between isenthalpic and isentropic or polytropic. See Figure 12-92. ... 

The enthalpy of formation of PuB c) rests on three concordant sets of data for the enthalpy of solution of this compound in 02-free 6 M HCl (66), 1 M HC1 and 0.1 M HCl (67) and comparison with the enthalpy of solution of PuCl3(c) in the same media (18). These data yield virtually identical values for the enthalpy of formation of PuBr3(c) and can be averaged as AHf(PuBr3,c) =... 

Stability constants as a function of temperature and the calculated complexation enthalpies and entropies of the associated reactions are given in Table II. The results of duplicate experiments at 2.0 M acidity and ionic strength are shown as the last entry in the table. Comparison of the results at 25°C, and 1.0 and 2.0 M acidity indicate an approximate inverse first order stoichiometry in [IT "] for the Kj and acid independence for K2. 

Table 14. Observed (AH obs) and calculated (AH ) heats of formation of cations R + in the gas phase and comparison of heats of formation with enthalpy differences AA (AA = AH°(R+) — AH°(R—F)) in the gas phase and in solution (CH2C12) (all values in kJ mol-1)...

The solvent influence, calculated with the Huron-Claverie method, reverses the qualitative graduation of the reaction enthalpies of the propagation steps as the chain length increases, in comparison to the gas phase. The same results were obtained using the same model system by Basilevski et al.125), while using a fundamentally different model for the solvent influence. 

Reliable information on the thermodynamic stability of group 13/15 adducts is usually obtained by gas phase measurements. However, due to the lability of stibine and bismuthine adducts in the gas phase toward dissociation, temperature-dependent H-NMR studies are also useful for the determination of their dissociation enthalpies in solution [41b], We focussed on analogously substituted adducts t-BusAl—E(f-Pr)3 (E = P 9, As 10, Sb 11, Bi 12) since they have been fully characterized by single crystal X-ray diffraction, allowing comparisons of their thermodynamic stability in solution with structural trends as found in their solid state structures. 

The surface-catalyst composition data for the silica-supported Ru-Rh cuid Ru-Ir catalyst are shown in Figure 1. A similcir plot for the series of silica-supported Pt-Ru bimetallic catalysts taken from ref. P) is included for comparison purposes. Enthalpies of sublimation for Pt, Ru, Rh and Ir are 552, 627, 543, and 648 KJ/mole. Differences in enthalpies of sublimation (a<75 KJ/mole) between Pt and Ru cind between Rh and Ru are virtually identical, with Pt euid Rh having the lower enthalpies of sublimation. For this reason surface enrichment in Pt for the case of the Pt-Ru/Si02 bimetallic clusters cannot be attributed solely to the lower heat of sublimation of Pt. Other possibilities must also be considered. 

A few compounds wili be chosen to test the method with various types of structures. Compounds wiil be chosen for which enthalpy can, for the purpose of comparison, be found in the tables and the enthalpy calculated in the liquid state oniy when this value is needed to be known. 

The comparison of the experimental and estimated enthalpies of decomposition according to CHETAH shows that the latter are almost always overestimated. This is why AWd is calculated using AHf of the substance in the physical state at 25°C. 

Unfortunately, the above thermodynamic approach has only been followed for two systems, namely As-Pt(lll) and Bi-Pt(lll) [Blais et al., 2001, 2002]. Table 7.3 summarizes the main results. Thermodynamic data about the bulk formation of As(OH)s and Bi(OH)2 are not available for comparison. The only data available is the standard enthalpy for the bulk formation of Bi(OH)3 (A/7 = 711.3kJ/mol). 

Considering that the standard enthalpies of formation of various oxides, sulfides, and halides of As, Sb, and Bi are very close to each other, the similarity between this value and the standard enthalpy for the surface formation of As(OH)3, A//f = —680 + 20 kJ/mol, was taken as an indication that, indeed, the As redox process on Pt(l 11) involves the formation of hydroxide species [Blais et al., 2001]. For comparison with A/7 for the surface formation of Bi(OH)2, the strategy followed... 

Comparison of the BDEs and enthalpies of formation obtained from different experimental approaches can be used to assess the quality of the measurements. Berkowitz, et al. have compared the results of positive ion and negative ion methods for determining BDEs of stable molecules with those obtained from kinetics studies. They found that for most systems, the agreement in the results from the three approaches was excellent. In this section, the results that have been obtained for the enthalpies... 

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