The Enthalpy of Formation

A combined application of direct calorimetric measurements and thermochemical investigations has made possible to obtain a number of important thermochemical quantities characterizing the interaction of the N—H bond of the amine with the epoxy ring 53). Combustion and evaporation enthalpies of phenylglycidyl ether and its condensation products with aniline and butylamine have been determined. Standard enthalpies of the formation of these compounds, strain energies of the epoxy ring in the phenylglycidyl ether molecule and — AH values for the three-phase states, which are most important for the determination of the true thermodynamic reaction characteristics, have been estimated. 

One real value of tables of standard enthalpies of formation is that they permit the calculation of the standard enthalpy of any reaction for which all the reactants and products are listed it is not necessary to do an experimental measurement. Based on Hess s law, the basic premise of the use of tables is that the enthalpy of reaction is the difference between the sum of the enthalpies of the formation of the products and the sum of the enthalpies of formation of the reactants. That is,... 

AHa, will be solvent-dependent unless IA//3I = IA Hi + AH2, where A Hi and A H2 are the heats of solvation of the electron donor and the hydrogen compound, respectively, and AH3 is the heat of solvation of the complex. The enthalpy of the formation of the adduct in the gas phase, which would give the actual strength of the hydrogen bond, will be different from that in solution unless the solvation energies cancel. In many cases, this is questionable because of the electron donor properties of the solvent. There is no doubt that many of the hydrogen bond enthalpies reported in the literature may be in error because of this. Moreover, it has been shown that the extent of self-association of... 

Thus, when the surface is predominantly covered by intermediate K formed before the rate-limiting step, the apparent activation energy equals the activation energy of the rate-limiting step plus the standard enthalpy of the formation of intermediate Kl from intermediate K. ... 

Thus, the molar enthalpy of i in solution and in the pure phase are the same, so that the enthalpy of the formation of the solution from its components is zero. 

Chemical equations can be manipulated using rules of algebra to get a desired equation. When equations are added or subtracted, enthalpy changes must be added or subtracted. And when equations are multiplied by a constant, the enthalpy changes must also be multiplied by that constant. For example, the enthalpy of the formation of CO, when CO2 and solid carbon are reactants, is found using the equations below. 

The standard enthalpy of the formation (previously known as the heat of formation) of B at p = 1 bar is defined by... 

Five reliable reports are available for the reaction enthalpies of the formation of Ni(SCN) (x = 1 - 3) complexes. The reported values are collected in Table V-33. 

The authors also discuss the relationship between the standard enthalpies of the formation reactions of the various zircon-type orthosilicates MSi04 from the binary oxides and the ionic radii of the tetravalent M cations. 

Free enthalpy characterizes maximum useful work, which is performed between atoms and molecules on the account of potential energy of only electrons. In this coimection it may be assumed that the free enthalpy of elements per se is equal to zero. Then the values of median (molar) free enthalpy and of any compounds may be characterized as energy of its formation in the amoimt of 1 mole. In order to compare free enthalpy of the formation of different compounds, it is necessary to measure the energy of their formation from individual elements under some identical conditions. 

Free enthalpy of the formation of 1 mole of any substance imder standard conditions from atoms and up to the standard state is called standard free enthalpy (Gibbs energy) of formation. This potential is determined by way of subtle physicochemical experiments and measurements. Its values are continuously fine-tuned and published in articles, monographs and reference publications. In composite Tables the standard potential is usually provided for temperature of 298.15 K (25 °C) and denoted as AZp29s or AGp 298> its value, as a rule, is negative and has the dimension kcal mole or J mole Standard potential serves a measure of potential energy of inter-atomic or inter-molecular bonds in individual chemical compounds. Knowing its values, it is possible to determine free enthalpy of substances under any nonstandard conditions. 

Dissociation constant of this reaction under standard conditions (25 °C) may be calculated from values of standard free enthalpy of the formation of H, OH" and H O ... 

A pair of cation and anion is capable of forming k complex compounds, which coexist. Strength, therefore concentrations of these compounds are proportionate to value of their stability constants or standard free enthalpy of the formation of 1 mole ... 

Relative measurements of the enthalpy of the formation of Zn3P2 si est that this compound is predominantly ionic. According to our data, 60% of the bonding in this compound is of the covalent-metallic type and the ionic component represents only 40%. Our view is supported also by the measurements of the forbidden band width of this compound, which is of the order 1.2 eV [17, 18] and does not exceed the values typical of A B semiconductors with predominantly covalent-metallic bonds. 

Thermodynamic data are one of the sources of information on the strength of chemical bonds. This is particularly true of the enthalpies of the formation of compounds. Unfortunately, no thermodynamic data are available for most of the rare-earth mono- and sesquichalcogenides. 

The errors in such calculations were probably not greater than the errors in the experimental values of AH and AS. The enthalpy of the formation of CoTe2 from its components... 

Scheme 7. Enthalpies (kcal mor ) of formation and Si-Si bond cleavage reactions of some coordinated disilenes, calculated at the B3LYP/6-31 l+G //B3LYP/6-31 l+G level values in parentheses refer to the reaction enthalpy of the formation of the coordinated disilene from disilene and 1 or 2 molecules of ammonia bond lengths in pm.

FICU RE 17.12 Temperature (o) and enthalpy ( ) of the formation of AI12M0 intermetallic compound in mechanically alloyed Al-10 at.% Mo powders as a function of milling time. 

The chemical enthalpy of the formation of sulfobelitic clinkers is lower than that of ordinary Portland clinkers and even of belitic clinkers. This is due mainly to a lower overall CaO content in the clinker to be produced, as well as to the fact that a fraction of the needed CaO is introduced in the form of calcium sulfate rather than calcium carbonate. The thermal losses are also reduced because of the lower burning temperature... 

The nudeation process can be regarded as a succession of the addition of growth units to an aggregate. To derive the nudeation rate, the free enthalpy of the formation of a droplet with a radius r, Aj Gr, has to be calculated (Figure 2.20). Two terms contribute to the free enthalpy - the enthalpy of condensation and the enthalpy necessary for creating the new surface (Equation 2.5) ... 

Nucleation can also occur on the surface of a foreign particle. The free enthalpy of the formation of a droplet on a surface is decreased. A factor relates the free enthalpy ofnucleation on a surface Ay G to that in the volume (Equation 2.11). Fora flat surface, the qualitative dependence of on the contact angle is shown in Figure... 

We have reported in all cases the values as published, and where necessary we list on the second line the values taking as reference state the pure solid elements. When an element possesses allotropic forms we have referred the enthalpy of the formation to the aggregation state at room temperature. 

The solvation (including hydration) of ions in the gas phase is described in Section 2.1.2 in terms of the stepwise Gibbs energies and enthalpies of the formation of ion/solvent clusters. The absolute values of these quantities diminish as the number... 

Formation of a nucleus on a foreign surfaee involves a creation of a new interface, similar to the case of homogeneous nucleation. However, a pre-existing foreign surface greatly reduces the free enthalpy of the formation of a critical nucleus, A4>. This lowers the critical size of the nucleus and results in the formation of heterogeneous nuclei at lower undercooling. 

Thus, the molar enthalpy of i in solution and in the pure phase are the same, so that the enthalpy of the formation of the solution from its components is zero. (3) From the constraints for equilibrium between liquid and vapor for each species (2.4.15) and (2.5.1) we obtain... 

---