Enthalpy of the reaction

Equations 20.176 and 20.179 emphasise the essentially thermodynamic nature of the standard equilibrium e.m.f. of a cell or the standard equilibrium potential of a half-reaction E, which may be evaluated directly from e.m.f. meeisurements of a reversible cell or indirectly from AG , which in turn must be evaluated from the enthalpy of the reaction and the entropies of the species involved (see equation 20.147). Thus for the equilibrium Cu -)-2e Cu, the standard electrode potential u2+/cu> hence can be determined by an e.m.f. method by harnessing the reaction... 

Of course, even in the case of acyclic alkenes reaction enthalpy is not exactly zero, and therefore the product distribution is never completely statistically determined. Table V gives equilibrium data for the metathesis of some lower alkenes, where deviations of the reaction enthalpy from zero are relatively large. In this table the ratio of the contributions of the reaction enthalpy and the reaction entropy to the free enthalpy of the reaction, expressed as AHr/TASr, is given together with the equilibrium distribution. It can be seen that for the metathesis of the lower linear alkenes the equilibrium distribution is determined predominantly by the reaction entropy, whereas in the case of the lower branched alkenes the reaction enthalpy dominates. If the reaction enthalpy deviates substantially from zero, the influence of the temperature on the equilibrium distribution will be considerable, since the high temperature limit will always be a 2 1 1 distribution. Typical examples of the influence of the temperature are given in Tables VI and VII. 

Basu and Searcy [736] have applied the torsion—effusion and torsion— Langmuir techniques, referred to above for calcite decomposition [121], to the comparable reaction of BaC03, which had not been studied previously. The reaction rate at the (001) faces of single crystals was constant up to a product layer thickness of 1 mm. The magnitude of E (225.9 kJ mole-1) was appreciably less than the enthalpy of the reaction (252.1 kJ mole-1). This observation, unique for carbonates, led to the conclusion that the slowest step in BaC03 vacuum decomposition at 1160—1210 K is diffusion of one of the reaction components in a condensed phase or a surface reaction of C02 prior to desorption. 

We can therefore report that AH = —208 kj because the enthalpy of the reaction mixture decreases by 208 kj in this reaction (Fig. 6.18). An endothermic process absorbs heat, and so when ammonium nitrate dissolves in water the enthalpy of the system increases (Fig. 6.19). Note that AH < 0 for exothermic reactions, whereas AH > 0 for endothermic reactions. 

Now let s see how to combine standard enthalpies of formation to calculate a standard reaction enthalpy. To do so, we imagine carrying out the reaction in two steps we reverse the formation of the reactants from the elements, then combine the elements to form the products. The first step is usually to calculate the reaction enthalpy for the formation of all the products from their elements. For this step, we use the enthalpies of formation of the products. Then, we calculate the reaction enthalpy for the formation of all the reactants from their elements. The difference between these two totals is the standard enthalpy of the reaction (Fig. 6.31) ... 

Sele-Tfst 6.18A Estimate the standard enthalpy of the reaction CCl3CHCl2(g) +... 

Calculate an overall reaction enthalpy from the enthalpies of the reactions in a reaction sequence by using Hess s law (Toolbox 6.1 and Example 6.9). 

An important reaction that takes place in the atmosphere is N02(g) -+ NO(g) + O(g), which is brought about by sunlight. How much energy must be supplied by the Sun to cause it Calculate the standard enthalpy of the reaction from the following information... 

Table 3 shows that the small activation enthalpies of the reactions (3) and (4) are clearly affected by the zero point energy corrections. But the relative order of the activation enthalpies remains the same with or without the corrections. The activation entropies have great negative values, which is of mechanistic interest (see part 4.3.1). However, because of their similarity, when comparing the three reactions to one another they have only small importance, e.g. for estimation of copolymerization parameters (see part 4.3.2). 

The addition of an ion to butadiene is clearly an exothermic process in the gas phase due to the formation of aa-bond substituting a rc-bond. The agreement of the reaction enthalpies of the reactions (11) and (12) with equal R (except R = H) is surprising (Table 11). 

Heats of atomization belong to the most important characteristics of ground states. Unfortunately, the number of conjugated radicals for which experimental data are available is very limited. A heat of atomization is defined as the enthalpy of the reaction... 

Hence, we find a relation between K and the enthalpy of the reaction, instead of the free energy, and the expression for the equilibrium is in conflict with equilibrium thermodynamics, in particular with Eq. (32) of Chapter 2, since the prefactor can not be related to the change of entropy of the system. Hence, collision theory is not in accordance with thermodynamics. 

The free energy change in a chemical reaction is expressed in the same way as the enthalpy of the reaction is expressed. For example, the free energy change in the reaction... 

J. E. Huheey n) has proposed another explanation following the reasoning of R. S. Drago 12). If the enthalpies of the reaction... 

Enthalpies are often used to describe the energetics of bond formations. For example, when an amide forms through the condensation reaction between an ester and an amine, the new C-N bond, has an enthalpy of formation of -293 kj/mole. The higher the negative value for the bond enthalpy of formation, the stronger the bond. An even more useful concept is the enthalpy of a reaction. For any reaction, we can use the fact that enthalpy is a state function. A state function is one whose value is independent of the path traveled. So, no matter how we approach a chemical reaction, the enthalpy of the reaction is always the same. The enthalpy of... 

The reaction favours the formation of ozone with a significant equilibrium constant. Appendix C also lists the enthalpies of formation and the standard enthalpy of the reaction ArH° can be calculated. The answer for the enthalpy calculation is ArH° = —106.47 kJ mol, showing this to be an exothermic reaction, liberating heat. The entropy change at 298 K can also be calculated because ArG° = ArH° — T ArS°, so ArS° = 25.4 Jmol-1 K-1, indicating an increase in the entropy of the reaction as it proceeds by creating one molecule from two. 

The values of the formation enthalpies of aldehydes, ketones, and parent hydrocarbons are presented in Table 1.6. The last column contains the values of enthalpies of the reactions... 

The formation enthalpies of a few acids and parent hydrocarbons are given in Table 1.6. The oxidation of the methyl group of hydrocarbon to carboxyl group is a highly exothermic reaction. The enthalpy of the reaction... 

The activation energies for highly endothermic reactions are known to be virtually equal to the enthalpy of the reaction. According to IPM, each group of reactions is characterized by the critical value of the enthalpy of the reaction A//cm ix. When the reaction enthalpy AHe > AWemax, the activation energy E=AH+0.5RT, whereas A//emax depends on parameters a and bre [115]. 

The activation energy for these reactions is close to the enthalpy of the reaction ... 

A clear-cut dependence of the activation energy on the heat (enthalpy) of the reaction, which is equal, in turn, to the difference between the dissociation energies of the ruptured (Z> ) and the formed (D j bonds, was established for a great variety of radical abstraction reactions [1,2,16]. In parabolic model, the values of Dei and Def, incorporating the zero-point energy of the bond vibrations, are examined. The enthalpy of reaction AHe, therefore, also includes the difference between these energies (see Equation [6.7]). 

The important role of reaction enthalpy in the free radical abstraction reactions is well known and was discussed in Chapters 6 and 7. The BDE of the O—H bonds of alkyl hydroperoxides depends slightly on the structure of the alkyl radical D0 H = 365.5 kJ mol 1 for all primary and secondary hydroperoxides and P0—h = 358.6 kJ mol 1 for tertiary hydroperoxides (see Chapter 2). Therefore, the enthalpy of the reaction RjOO + RjH depends on the BDE of the attacked C—H bond of the hydrocarbon. But a different situation is encountered during oxidation and co-oxidation of aldehydes. As proved earlier, the BDE of peracids formed from acylperoxyl radicals is much higher than the BDE of the O—H bond of alkyl hydroperoxides and depends on the structure of the acyl substituent. Therefore, the BDEs of both the attacked C—H and O—H of the formed peracid are important factors that influence the chain propagation reaction. This is demonstrated in Table 8.9 where the calculated values of the enthalpy of the reaction RjCV + RjH for different RjHs including aldehydes and different peroxyl radicals are presented. One can see that the value A//( R02 + RH) is much lower in the reactions of the same compound with acylperoxyl radicals. 

Like for aldehydes, two factors are important for the reactivity of ketones in reactions with peroxyl radicals reaction enthalpy and polar interaction. The enthalpy of the reaction of the peroxyl radical with ketone is AH = DC—a A> H- The BDE of the a-C—H bonds of ketones are lower than those of the C—H bonds of the hydrocarbons (see Table 8.11) and the BDEs of the O—H bonds in a-ketohydroperoxides are marginally higher than those of alkylhydroperoxides. Therefore, the enthalpies of R02 + RH reactions are lower than those of parent hydrocarbons (Table 8.15). 

Measurements based on the law of conservation of energy are of two main types. In phase change calorimetry the enthalpy of the reaction is exactly balanced by the enthalpy of a phase change of a contained compound surrounded by a larger reservoir of the same compound used to maintain isothermal conditions in the calorimeter. The latter enthalpy, the measurand, is often displayed indirectly through the change in the volumetric properties of the heat reservoir compound, e.g. ice/water. 

Enthalpy changes of processes depend only on the end states. Normally the enthalpy change of reaction is known at some standard temperature, Tb = 298 K for instance. The simplest formulation of the heat balance, accordingly, is to consider the reaction to occur at this temperature, to transfer whatever heat is required and to raise the enthalpy of the reaction products to their final values. 

The enthalpy of the reaction, AH, is the difference between the enthalpies of the products and the enthalpies of the reactants. 

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