Calculation of AH

The lattice energy of a molecular crystal is defined as the energy for formation of the crystal lattice from molecules that are infinitely separated in the gas phase, can be decomposed into two components  

---

The following diagram (Fig. 11) shows the original DTA melting curve of indium and the inserted calibration rectangle which is required for the manual evaluation. The experimental parameters which were used for the calculation of AH are given below, and also the evaluation of /uV sec for the peak area. 

At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs free energy. Some reactions are spontaneous because they give off energy in the form of heat (AH<0). Other reactions are spontaneous because they lead to an increase in the disorder of the system (AS>0). Calculations of AH and AS can be used to probe the driving force behind a particular reaction. 

MNDO calculation of AH for 3-amino-1,2,4-dithiazole-5-thione indicated that, of its possible isomeric forms (7), (8), and (9) (R = H), (7) is the most favorable. This structure had been found experimentally in the crystal and in solution but the differences are small and structures (8) and (9) may also take part in reactions. In fact, methylation of (7 R = H) gives (9 R = Me) shown by MNDO calculation to possess the lowest AHf <82JCR(S)65>. The MNDO method was used to calculate the structure and energy of 3-amino-1,2,4-dithiazole-5-one, its molecular cation and also its fragmentation ions <82MI 4i3-oi>. 

The calculation of AH° and AS° values from the pK-temperature data in each solvent mixture was performed by the nonempirical method of Clarke and Glew (26) as simplified by Bolton (27). In this method the thermodynamic parameters are considered to be continuous, well-behaved functions of temperature, and their values are expressed as perturbations of their values at some reference temperature 0 by a Taylor s series expansion. The basic equation is ... 

Thermochemical data for the solvation of ions as used in the preceding calculations are difficult to measure and even to estimate. Therefore this kind of calculation of AH° for ionic reactions involving organic molecules in solution usually cannot be made. As a result, we have considerably fewer possibilities to assess the thermodynamic feasibility of the individual steps of polar reactions in solution than we do of vapor-phase radical processes. Bond energies are not of much use in predicting or explaining reactivity in ionic reactions unless we have information that can be used to translate gas-phase AH°. values to solution AH° values. Exercise 8-3 will give you a chance to see how this is done. 

In the most common thermodynamic case, the Clapeyron equation is used with pure components to obtain the heat of vaporization from pure component two-phase (vapor pressure) data. The Clapeyron equation is one of the primary successes of thermodynamics, because it enables the calculation of AH, which is difficult to measure, from easily available properties of pressure and temperature. 

The heat absorbed or evolved when liquids or solutions are mixed or diluted is obtained from the calculation of AH for the solution process.kk The calculation of AH is usually obtained from the relative partial molar enthalpy defined as... 

As described in Sections III.A.l and III.A.2, organotin compounds which are complexed with polar solvents or are auto-associated usually show a change in chemical shift to high frequency as the temperature is increased, and this allows the calculation of AH values. On the other hand, Mitchell has observed (37) a low-frequency chemical shift change as the temperature is increased in di- and tri-isopropyltin bromides. These molecules are unlikely to be self-associated under the conditions used. 

Example 5. Calculation of AH° of C3H8 Using an Isodesmic Scheme... 

The calculation of AH0 from enthalpies of formation applies, strictly speaking, only to the reaction of reactants in standard states to form products in standard states. Nonetheless, calculations of AH° are very useful in the general case because AH is usually not very sensitive to conditions so that AH° provides us with a good semi-quantitative estimate of the reaction energy in most situations. 

Calculation of AH, the enthalpy change involved when the temperature of a substance with heat capacity,... 

The energy balance for this flow process gives AH = Q, where AH is the enthalpy of the product streams minus the total enthalpy of the feed stream, the problem reduces to finding AH from the available data. Since enthalpy is a s function, the path used for the calculation of AH is immaterial and may be sele as convenience dictates and without reference to the actual path followed in evaporator. The data available are heats of solution of UC1 in H20 at 25°C (see 13.7), and the calculational path, shown in Fig. 13.9, allows their direct use. 

In order to meet the requirements of a practical application, a metal hydride must first satisfy the thermodynamic requirements operation temperature and hydrogen pressure. As the entropy term of Eq. (1.11) is effectively the same for all compounds, this means that the heat of formation (AH) is the principal parameter of a given alloy for hydrogen storage applications. Unfortunately, first principles calculations of AH for ternary alloys are still lacking [47]. However, semi-empirical models can be applied for some systems and give useful physical insight on the hydride formation. 

This result can be compared with the calculation of AH for this reaction from the standard enthalpy of formation for HF (-271 kj/mol) ... 

Liquids are usually moved by pumps, generally rotating equipment. The same equations apply to adiabatic pumps as to adiabatic compressors. Thus, qs. (7.25) through (7.27) and (7.29) are valid. However, application of Eq. (7.26) for the calculation of - -AH requires values of the enthalpy of compressed liquids, and these are seldom available. The fundamental property relation, Eq. (6.8), provides an alternative. For an isentropic process,... 

When performing energy balances on a reactive chemical process, two procedures may be followed in the calculation of AH (or AH or AH) that differ in the choice of reference states for enthalpy or internal energy calculations. In the heat of reaction method, the references are the reactant and product species at 25 C and 1 atm in the phases (solid, liquid, or gas) for which the heat of reaction is known. In the heat of formation method, the references are the elemental species that constitute the reactant and product species [e.g., C(s), 02(g), H2(g), etc.] at 25°C and 1 atm. In both methods, reference slates for nonreactive species may be chosen for convenience, as was done for the nonreactive processes of Chapters 7 and 8. 

P. Bourre-Maiadi re. Compt. rend. 230, 640-2 (1950). Theory H bond in nylon, electrostatic calculation of AH. 

The regression equation can be used for the calculation of AH°(CnH2nt2) for arbitrary values of n using a correlation equation (see also rel. 2.2.30). The results shown in... 

We are now equipped to include in the calculation of ah enthalpy change the occurrence of a phase change. Because enthalpy is a state variable, any arbitary path from the initial to the final state will suffice for the actual computation. Simply choose the simplest possible path. 

In the case depicted in Fig. 3.3. The c-value amounts to 80 and falls well within the range of 5-500 that displays clear sigmoidal curvature and is best suited for the calculation of AH, Kassoc and n in a single experiment. 

Several theoretical studies were performed on the FO2 radical. The best and more recent one is that by Francisco et al (56). References to previous work on the subject are given there. The calculation of AH o for the direct reaction proved to be exceedingly difficult and inaccurate. Therefore, the authors studied also some other isodesmic and/or isogyric reactions, namely FO2 + HO —> HO2 + FO... 

Calculation of AHs. The solubility data presented in the preceding section can be used to calculate AHs from Equation 1, where T is the... 

---