Standard enthalpy The

The sea level reference point for all enthalpy expressions is called the standard enthalpy of formation AHf), which is defined as the heat change that results when one mole of a compound is formed from its elements at a pressure of 1 atm. Elements are said to be in the standard state at 1 atm, hence the term standard enthalpy. The superscript o represents standard-state conditions (1 atm), and the subscript / stands for formation. Although the standard state does not specify a temperature, we will always use AHf values measured at 25°C. 

Total energies obtained at B3LYP/6-311G(d,p), G3 and G3MP2B3 calculation level are used with isodesmic work reactions having bond conservation, when possible, for the calculation of the standard enthalpies. The total energies obtained with DPT are corrected by zero-point vibration energies (ZPVE), which are scaled by 0.97 as recommended by Scott and Radom [120],... 

The sea level reference point for all enthalpy expressions is called the standard enthalpy of formation (Affy). Substances are said to be in the standard state at 1 atm, hence the term standard enthalpy. The superscript represents standard-state... 

A consequence of the first law of thermodynamics, the conservation of energy, is that we can combine standard enthalpies of reactions to produce the standard enthalpy of another reaction. If a reaction can be accomplished in a set of steps, each a reaction with a known standard enthalpy, the sum of the standard enthalpies of the steps is the standard enthalpy of the overall reaction. This statement is often called Hess s law (Germain Henri Hess, Russia, 1802-1850). Standard enthalpies of formation are available in published tables, and a few selected values are listed in Table 6.1. Enthalpies of formation are reaction enthalpies for which the reactants are pure elemental substances. Thus, if we can develop a set of reaction steps where the reactants in each step are elemental substances, the overall reaction enthalpy will be a combination of enthalpies of formation. Here is an example ... 

Themiodynamic tables usually report at least tln-ee quantities almost invariably the standard enthalpy of fomration at 298 K, Af (298 K) usually the standard entropy at 298 K,, S (298 K) (not AS y298 K), but the... 

In a fiormal analogy to the expressions for the thenuodynamical quantities one can now defiine the standard enthalpy // and entropy ofiactivation. This leads to the second Eyring equation. ... 

Free energy is related to two other energy quantities, the enthalpy (the heat of reaction measured at constant pressure) and the entropy. S. an energy term most simply visualised as a measure of the disorder of the system, the relationship for a reaction taking place under standard conditions being... 

To date there is no evidence that sodium forms any chloride other than NaCl indeed the electronic theory of valency predicts that Na" and CU, with their noble gas configurations, are likely to be the most stable ionic species. However, since some noble gas atoms can lose electrons to form cations (p. 354) we cannot rely fully on this theory. We therefore need to examine the evidence provided by energetic data. Let us consider the formation of a number of possible ionic compounds and first, the formation of sodium dichloride , NaCl2. The energy diagram for the formation of this hypothetical compound follows the pattern of that for NaCl but an additional endothermic step is added for the second ionisation energy of sodium. The lattice energy is calculated on the assumption that the compound is ionic and that Na is comparable in size with Mg ". The data are summarised below (standard enthalpies in kJ) ... 

Calculate the standard enthalpy of formation. AH potassium bromide. 

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. 

Enthalpy of Formation. Once standard enthalpies are assigned to the elements, it is possible to determine standard enthalpies for compounds. For the reaction ... 

Since the elements are in their standard states, the enthalpy change for the reaction is equal to the standard enthalpy of COj less the standard enthalpies of C and Oj, which are zero in each instance. Thus,... 

With all components in the ideal gas state, the standard enthalpy of the process is exothermic by —165 kJ (—39.4 kcal) per mole of methane formed. Biomass can serve as the original source of hydrogen, which then effectively acts as an energy carrier from the biomass to carbon dioxide, to produce substitute (or synthetic) natural gas (SNG) (see Euels, synthetic). 

Krypton Difluoride. Krypton difluoride [13773-81 -4] KrF is a colorless crystalline solid which can be sublimed under vacuum at 0°C but is thermodynamically unstable and slowly decomposes to the elements at ambient temperatures (Table 1). It can, however, be stored for indefinite periods of time at —78° C. The KrF molecule has been shown, like XeF2, to be linear in the gas phase, in the sofld state, and in solution. The standard enthalpy of... 

Sodium Chlorite. The standard enthalpy, Gibbs free energy of formation, and standard entropy for aqueous chlorite ions ate AH° = —66.5 kJ/mol ( — 15.9 kcal/mol), AG = 17.2 kJ/mol (4.1 kcal/mol), and S° = 0.1883 kJ/(molK) (0.045 kcal/(molK)), respectively (107). The thermal decomposition products of NaClO, in the 175—200°C temperature range ate sodium chlorate and sodium chloride (102,109) ... 

Enthalpy of Formation The ideal gas standard enthalpy (heat) of formation (AHJoqs) of chemical compound is the increment of enthalpy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard states, defined as the existing phase at a temperature of 298.15 K and one atmosphere (101.3 kPa). Sources for data are Refs. 15, 23, 24, 104, 115, and 116. The most accurate, but again complicated, estimation method is that of Benson et al. " A compromise between complexity and accuracy is based on the additive atomic group-contribution scheme of Joback his original units of kcal/mol have been converted to kj/mol by the conversion 1 kcal/mol = 4.1868 kJ/moL... 

Equation (1) can be viewed in an over-simplistic manner and it might be assumed that it would be relatively easy to calculate the retention volume of a solute from the distribution coefficient, which, in turn, could be calculated from a knowledge of the standard enthalpy and standard entropy of distribution. Unfortunately, these properties of a distribution system are bulk properties. They represent, in a single measurement, the net effect of a large number of different types of molecular interactions which, individually, are almost impossible to separately identify and assess quantitatively. 

It is clear that a graph of ln(V j-) or In(k ) against 1/T will give straight line. This line will provide actual values for the standard enthalpy (AH ), which can be calculated from the slope of the graph and the standard entropy (AS ), which can be calculated from the intercept of the graph. These types of curves are called van t Hoff curves and their important characteristic is that they will always give a linear relationship between In(V r) and (1/T). However, it is crucial to understand that the distribution... 

Summarizing, the greater the forces between the molecules, the greater the energy (enthalpy) contribution, the larger the distribution coefficient, and the greater the retention. Conversely, any reduction in the random nature of the molecules or any increase in the amount of order in the system reduces the distribution coefficient and attenuates the retention. In chromatography, the standard enthalpy and standard entropy oppose one another in their effects on solute retention. Experimentally it has... 

The curves provide relative values for the standard enthalpy (Methylene Group)... 

Different portions of the standard free energy of distribution can he allotted to different parts of a molecule and, thus, their contribution to solute retention can be disclosed. In addition, from the relative values of the standard enthalpy and standard entropy of each portion or group, the nianner in which the different groups interact with the stationary phase may also be revealed. 

Finally, another important and interesting fact is established from the data treated in this manner. All the examples given confirm that the standard entropy term tends to increase with the standard enthalpy term. Consequently, the increase in retention is not as great as that which would be expected from the increase in standard enthalpy alone. 

It is seen from equation (22) that there will, indeed, be a temperature at which the separation ratio of the two solutes will be independent of the solvent composition. The temperature is determined by the relative values of the standard free enthalpies of the two solutes between each solvent and the stationary phase, together with their standard free entropies. If the separation ratio is very large, there will be a considerable difference between the respective standard enthalpies and entropies of the two solutes. As a consequence, the temperature at which the separation ratio becomes independent of solvent composition may well be outside the practical chromatography range. However, if the solutes are similar in nature and are eluted with relatively small separation ratios (for example in the separation of enantiomers) then the standard enthalpies and entropies will be comparable, and the temperature/solvent-composition independence is likely be in a range that can be experimentally observed. 

The amonnt of energy that can be released from a given chemical reaction is determined from the energies (enthalpies of formation) of the individnal reactants and prodncts. Enthalpies are nsnally given for snbstances in their standard states, which are the stable states of pnre snbstances at atmospheric pressnre and at 25°C. The overall heat of reaction is the difference between the snms of the standard enthalpies of formation of the prodncts... 

Figure 7.7 Trends in the standard enthalpies of formation AH] for Groups 3 and 13 trihalides as illustrated by data for MF3 and MBrj.

The atom and bond concepts dominate chemistry. Dalton postulated that atoms retained their identities even when in chemical combinations with other atoms. We know that their properties are sometimes transferable from one molecule to another for example, the incremental increase in the standard enthalpy of formation of a normal hydrocarbon per CHj group is —20.6 1.3 kJmol . We also know that more often there are subtle modifications to the electron density. 

Standard Heat of Reaction. This is the standard enthalpy change accompanying a chemical reaction under the assumptions that the reactants and products exist in their standard states of aggregation at the same T and P, and stoichiometric amounts of reactants take part in the reaction to completion at constant P. With P = 1 atm and T = 25°C as the standard state, AH (T,P) can be written as... 

The standard enthalpies of formation of ions in aqueous solution listed at the bottom of Table 8.3 are relative values, established by taking... 

The standard enthalpy change, Aff°, for a given thermochemical equation is equal to the sum of the standard enthalpies of formation of the product compounds minus the sum of the standard enthalpies of formation of the reactant compounds. 

Enthalpy changes for reactions in solution can be determined using standard enthalpies of formation of aqueous ions, applying the general relation... 

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