Enthalpy change estimation

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. 

An estimate of the enthalpy change which conesponds to the activation energy of the collision theory analysis of 167kJmoP may be made by assuming that the formation of tire dimer from two molecules of the monomer is energetically equivalent to tire dipole-dipole and dispersion interactions of two HI molecules. These exothermic sources of interaction are counterbalanced... 

Because these various quantities are characteristics of the reactants and products but are independent of the reaction path, they cannot provide insight into mechanisms. Information about AG, AH, and AS does, however, indicate the feasibility of any specific reaction. The enthalpy change of a given reaction can be estimated from tabulated thermochemical data or from bond-energy data such as those in Table 1.3 (p. 14) The exan le below illustrates the use of bond-energy data for estimating the enthalpy of a reaction. 

Essentially, the analytical approach outlined above for the open circuit gas turbine plants is that used in modem computer codes. However, gas properties, taken from tables such as those of Keenan and Kaye [6], may be stored as data and then used directly in a cycle calculation. Enthalpy changes are then determined directly, rather than by mean specific heats over temperature ranges (and the estimation of n and n ), as outlined above. 

In a chemical reaction, old bonds are broken and new ones formed. We can estimate reaction enthalpies if we know the enthalpy changes that accompany the breaking and making of bonds. The strength of a chemical bond is measured by the bond enthalpy, AHR, the difference between the standard molar enthalpies of a molecule, X-Y (for instance, H3C—OH), and its fragments X and Y (such as CH3 and OH) in the gas phase ... 

Estimate the enthalpy change of the reaction between gaseous iodoethane and water vapor ... 

STRATEGY Decide which bonds are broken and which bonds are formed. Use the mean bond enthalpies in Table 6.8 to estimate the change in enthalpy when the reactant bonds break and the change in enthalpy when the new product bonds form. For diatomic molecules, use the information in Table 6.7 for the specific molecule. Finally, add the enthalpy change required to break the reactant bonds (a positive value) to the enthalpy change that occurs when the product bonds form (a negative value). 

The standard enthalpy of formation AH°f of a compound is defined as the enthalpy change when one mol of the compound is formed from its constituent elements in the standard state. The enthalpy of formation of the elements is taken as zero. The standard heat of any reaction can be calculated from the heats of formation —AH of the products and reactants if these are available or can be estimated. 

Van Vorst, W.D. Make Your Own Diagram to Estimate Enthalpy Changes of Real Gases, Chemical Engineering, June 19, 1967, p. 229. 

Thus, the enthalpy change is about half that for the dissolution of ammonium nitrate in water. An estimate of the temperature achieved by the ice pack can be calculated knowing the amounts of water and salt present and assuming that the salt dissolves completely. 

The enthalpy changes associated with proton transfer in the various 4, -substituted benzophenone contact radical ion pairs as a function of solvent have been estimated by employing a variety of thermochemical data [20]. The effect of substituents upon the stability of the radical IP were derived from the study of Arnold and co-workers [55] of the reduction potentials for a variety of 4,4 -substituted benzophenones. The effect of substituents upon the stability of the ketyl radical were estimated from the kinetic data obtained by Creary for the thermal rearrangement of 2-aryl-3,3-dimethylmethylenecyclopropanes, where the mechanism for the isomerization assumes a biradical intermediate [56]. The solvent dependence for the energetics of proton transfer were based upon the studies of Gould et al. [38]. The details of the analysis can be found in the original literature [20] and only the results are herein given in Table 2.2. 

The van t Hoff plots for thermal denaturation of proteins are linear in the transition region, thus allowing the enthalpy change (AHm) of unfolding at the transition temperature (Tm) to be estimated. Because of the change in free energy in (AG) = 0 at Tm (reversible process), the entropy of unfolding (ASm) at the transition midpoint can be calculated from ... 

However, to estimate the standard enthalpy of formation, it is necessary to add two reactions to Equation (4.46), because, by definition, the standard enthalpy of formation refers to the formation of the compound in its standard state from the elements in their standard states. Therefore we introduce the following enthalpy changes to convert the elements from their standard states to the gaseous atoms at 298 K ... 

Further use of tabulated data (such as those in Table 2.3) enables an estimate to be made of the temperature of the reaction of black powder. Using equation (2.18), the standard enthalpy change may be calculated from the standard heats of formation of the reactants and products as in equation (2.20). 

The area of a DSC peak can be used to estimate the enthalpy of transition, AH, provided the thermal history of the sample is considered [29]. Calibration with respect to enthalpy requires an area that corresponds to a well-defined enthalpy change—a heat of fusion AH(Tm) is commonly used, especially that of indium [3]. 

The enthalpies of formation of aqueous ions may be estimated in the manner described, but they are all dependent on the assumption of the reference zero that the enthalpy of formation of the hydrated proton is zero. In order to study the effects of the interactions between water and ions, it is helpful to estimate values for the enthalpies of hydration of individual ions, and to compare the results with ionic radii and ionic charges. The standard molar enthalpy of hydration of an ion is defined as the enthalpy change occurring when one mole of the gaseous ion at 100 kPa (1 bar) pressure is hydrated and forms a standard 1 mol dm-3 aqueous solution, i.e. the enthalpy changes for the reactions Mr + (g) — M + (aq) for cations, X (g) — Xr-(aq) for monatomic anions, and XOj (g) —< XO (aq) for oxoanions. M represents an atom of an electropositive element, e.g. Cs or Ca, and X represents an atom of an electronegative element, e.g. Cl or S. 

The cycle allows the overall enthalpy of formation of the aqueous solution of cations and anions to be sub-divided into stages whose enthalpy changes are known except for the two enthalpies of hydration, allowing their sum to be estimated. The equation to be solved is ... 

The standard enthalpy change for the reduction of M + (aq) to M(s) may be estimated from the above data by carrying out a calculation using the thermochemical cycle shown in Figure 6.1 for the overall reaction ... 

The most stable state of nitrogen in acidic solution is the ammonium ion, NH4(aq), which is isoelectronic with CH4 and H30+. It is a tetrahedral ion with strong N-H bonds. The mean N-H bond enthalpy in NH4(aq) is 506 kJ mol 1 (that of the O-H bonds in H30 + is 539 kJ mol" ). The enthalpy of hydration of the ammonium ion is — 345 kJ mol V This value placed into the Born equation (3.32) gives an estimate of the radius of the ammonium ion of 135 pm, a value insignificantly different from its thermochemical radius of 136 pm. The value is comparable to that estimated for the smaller H30+ ion (99 pm) from its more negative enthalpy of hydration (— 420 kJ mol -see Section 2.6.1). The proton affinity of the ammonia molecule is of interest in a comparison of its properties with those of the water molecule. The proton affinity is defined as the standard enthalpy change for the reaction ... 

Compare the estimated enthalpy change for the reaction of acetylene with hydrogen to give ethane... 

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