Free enthalpy of formation

Just as the standard enthalpy change for a reaction can be calculated from the standard free enthalpies of formation of the reactants and products, the standard free energy... 

Thermodynamic calculations based on compiled [36] Gibbs free enthalpies of formation result in an equilibrium composition of ca. 40 mole-% 1-M-Np and 60 mole-% 2-M-Np in the temperature range from 200 to 300 C. Attempts to determine the position of equilibrium experimentally [37, 38] indicated that 30 mole-% 1-M-Np and 70 mole-% 2-M-Np is a more... 

It is assumed further that the contribution of f.s.s.e. to the free enthalpy of formation of a bond is linear with the total number of preexisting bonds in the first shell, n i.e. 

Enzymes are a class of macromolecules with the ability both to bind small molecules and to effect reaction. Stabilizing forces such as hydrophobic effects only slightly dominate destabilizing forces such as Coulombic forces of equal polarity thus the Gibbs free enthalpy of formation of proteins, AGformation, is only weakly negative. 

The balance of favorable minimization of hydrophobic area and unfavorable reduction of conformational states upon folding will determine the stability of the protein. As these forces tend to be large and comparable in magnitude, the free enthalpy of formation of a protein is the sum of two large opposing forces and may thus be negative or positive. In any case, a folded and catalytically active protein is always just a few kilojoules away from instability. 

The free enthalpy of formation of a protein can be written as a difference in the Gibbs free enthalpy between folded and unfolded states, Gu and Gf [Eq. (17.2)]. 

The relation observed between regioselectivity and number of Clar sextets of reactants and products is not unexpected for a reaction that is controlled by thermodynamics i.e. by the difference between free enthalpy of formation of reactants and products. Conversely, however, no conclusions regarding the mechanism of the reaction can be derived from the relation. 

It follows, in general, that the standard chemical potential p) of a chemical compound i corresponds to the free enthalpy of formation for one mole of the compound substance i at the standard state, the value of which is tabulated in chemical handbooks as shown for a few compounds in Table 5.1. For ions in electrolytic solutions the chemical potential in their pure state can not be defined, but we may use the standard state of an ion in which the ionic activity is equal to unity (a, = 1) to define the unitary chemical potential of the ion as will be discussed in chapter 9. 

Thermodynamics provides the relation between the equilibrium constant and the free enthalpy of formation (AG°)... 

This change of free enthalpy may also be written as a difference in free enthalpies of formation of the compounds considered ... 

Therefore, if the free enthalpies of formation of the compounds participating in any reaction are known, it is possible to calculate the position of the equilibrium of this reaction. 

From the preceding it follows that it is of great practical importance, for polymerisation as well as for degradation and substitution reactions, to know the numerical value of the free enthalpy of formation. 

TABLE 20.1 Free enthalpy of formation of some small molecules and related group contributions... 

In the system of Van Krevelen and Chermin the free enthalpy of formation is calculated from group contributions, with some corrections due to structural influences ... 

It is not possible to describe accurately the temperature dependence of the free enthalpy of formation by the simple Eq. (20.18) over a very large temperature interval, by it is sufficiently accurate in the temperature interval of 300-600 K. 

All group contributions and structural corrections are based on experimental data of Rossini et al. (1953), the free enthalpies of formation calculated agree with the literature values within 3 kj. For non-hydrocarbons the accuracy is less good and deviations up to 12 kj may occur. 

All values for the free enthalpy of formation are as a rule standardised for the ideal gaseous state of 1 (bar), (Standard State this ideal state is called fugacity). This also holds for the group contributions given. 

Estimate the free enthalpy of formation of gaseous 1,3-butadiene and of the (imaginary) gaseous polybutadiene. 

Thermo chemical properties (Chaps. 20-22) molar free enthalpy of formation... 

Fractionation of chain molecules according to their chain length, 727 Fracture mechanics, 472 Free enthalpy of formation, 753, 754 Freely jointed chain model, 247 Free-rotation model, 246 Free surface energy, 229 Free volume fraction, 537 Freeze-off time, 806 Freezing-in process, 151 Frequency doubling, 349 factor, 751... 

Molar elastic wave functions, 383,391 Molar free enthalpy of formation, 792 Molar functions, classification, 62 Molar heat... 

The desired unsaturated hydrocarbons only appear to be stable in relation to the saturated structures from which they are derived at relatively elevated temperatures. This fact is illustrated by Fig. 2.1, which shows the variation of the free enthalpy of formation as a function of temperature, related to a carbon atom, of a number... 

From eq, (15.10) it can be seen that AH03 (the partial free enthalpy of formation) and AS02 (the partial free entropy of formation) may be derived from curves of the types shown in Fig. 15.2. AHqz/R may be obtained from the slopes of the curves and ASoz/R ff m the intercepts. 

Figure 153, The partial free enthalpy of formation, -AHq2, as a function of log(s) in for y = 0.0.1 and 0.2. The daia are taken from a literature review, ...

The sole cathodic deposition of Na from NalEtjAl-F-AlEtj] with mercury cathodes [118] was initially thought to support the reaction mechanism in Scheme 2, where alkali metal is always initially deposited. However, this reaction is easily explained by the great driving force for the formation of sodium amalgam. For a 0.2% sodium amalgam, the free enthalpy of formation is = — 81.9kJ/mol, cor-... 

The product of activity coefficients /and the mole fraction x is often called activity a. It is noteworthy that the chemical equilibrium constant can only be calculated if the acitivity coefficients are known. In the case of reactive distillation, this information is available. It should be mentioned that the equilibrium constant can be calculated from the pure free enthalpies of formation that have to be corrected to the reaction state depending on the model (activity coefficients or fugacity) used. 

The estimation of the free enthalpy of formation using the data from Tables 2.2.8 to 2.2.10 leads to values for the gaseous state of the molecule (in some instances hypothetical state). However, few compounds and no polymers are in gas phase. For this reason, correction must be made to the gaseous state of a compound in order to estimate the free enthalpy for a specific reaction involving compounds in liquid or solid (crystalline or amorphous) state. A number of empirical rules are available for the change from gas phase to a condensed phase, and a selection of such corrections is given in Table 2.2.11 [35]. 

The ions shown on the Fig. 18 all have seven carbon atoms. We observe that the formation enthalpy depends neither on the position of the charge nor on the neighbouring groups, but only on the primary,15 secondary or tertiary character of the ion. The single-events theory accepts that observations made for formation enthalpy are also true for the intrinsic free enthalpy of formation. 

Assumption 1. For a given number of carbon atoms, the intrinsic free enthalpy of formation of an ion depends only on its type (secondary or tertiary). 

The free enthalpies of formation and therefore the equilibrium constants between paraffins, olefins and ions are known we can therefore calculate the olefin and ion concentrations. Given the operating conditions (high temperature and high hydrogen pressures), the quantities of olefins and ions are always negligible compared with those of paraffins.17... 

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