Using Bond Energies to Calculate AH

We can think of a reaction as a two-step process in which heat is absorbed (AH° is positive) to break reactant bonds and form separate atoms and then is released (AH° is negative) when the atoms rearrange to form product bonds. The sum (symbolized by Z) of these enthalpy changes is the heat of reaction, AHnn- 

An equivalent form of Equation 9.2 uses bond energies  

The minus sign is needed because all bond energies are positive values (see Table 9.2). 

We use bond energies to calculate A// by assuming that aU the reactant bonds break to give individual atoms, from which all the product bonds form. Even though the actual reaction may not occur this way—typically, only certain bonds break and form—Hess s law (see Section 6.5) allows us to sum the bond energies (with their appropriate signs) to arrive at the overall heat of reaction. (This method assumes that all reactants and products are in the same physical state. When phase changes occur, additional heat must be taken into account. We address this topic in Chapter 12.) 

It is interesting to compare this value with the value obtained by calorimetry 

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Figure 9.16 Using bond energies to calculate AH xn- Any chemical reaction can be divided conceptually into two hypothetical steps (1) reactant bonds break to yield separate atoms in a step that absorbs heat (+ sum of BE), and (2) the atoms combine to form product bonds in a step that releases heat (- sum of BE). When the total bond energy of the products is greater than that of the reactants, more energy is released than is absorbed, and the reaction is exothermic (as shown) AH xn is negative. When the total bond energy of the products is less than that of the reactants, the reaction is endothermic AH°xn is positive.

Figure 9.17 Using bond energies to calculate AH°,n of methane.

SAMPLE PROBLEM 9.3 Using Bond Energies to Calculate AH°xn Problem Calculate A//° n for the chlorination of methane to form chloroform ... 

Exercise 12-16 Use the data of Table 12-3 and any needed bond energies to calculate AH° for the following reaction in the vapor state at 25° with n — 3, 4, and 5 ... 

Exercise 12-17 Use the heats of combustion to liquid water given in Table 12-3 and appropriate bond energies to calculate AH° (vapor) for ring-opening of the cycloalkanes with bromine in the range n = 2 to n = 6 ... 

Use your cyclopropane bond energies to calculate AH° values for the following... 

Thus the use of bond energies to calculate AH works quite well in this case. 

A reaction involves breaking reactant bonds and forming product bonds. Applying Hess s law, we use tabulated bond energies to calculate AH . 

Exercise 26-2 Use bond and stabilization energies to calculate AH°(g) for the reaction of Equation 26-1 on the assumption that the extra stabilization energy of 2-naphthalenol relative to naphthalene is 5 kcal mole-1 (see Tables 4-3 and 21-1). Compare your answer to A/-/0 calculated for the corresponding reactions of benzenol (Section 26-1 A). 

Calculate Ktq and AG° of reactions, and use bond dissociation energies to calculate AH° of reactions. 

To calculate AH° for the combustion of one mole of methane, first we break bonds as follows, using 98.7 kcal mole-"1 for the energy of each of the... 

Exercise 4-5 Use the bond-energy table (4-3) to calculate AH° for the following reactions in the vapor phase at 25° ... 

Use 83 kcal mole-1 for the bond-dissociation energy of a normal C-C bond and 68 kcal mole-1 for the bond-dissociation energy of a C-Br bond. (An easy way to solve a problem of this type is first to calculate AH of each step for cyclohexane, for which there is no strain, then to make suitable corrections for the strain that is present for smaller values of n)... 

Exercise 18-9 Use bond energies and the stabilization energy of ethanoic acid (18 kcal mole-1, Section 18-2A) to calculate AH° for the addition of water to ethanoic acid to give 1,1,1-trihydroxyethane. Compare the value you obtain with a calculated AH° for the hydration of ethanal in the vapor phase. Would you expect the rate, the equilibrium constant, or both, for hydration of ethanoic acid in water solution to be increased in the presence of a strong acid such as sulfuric acid Explain. 

Examine the equations to ascertain which bonds are made and which are broken. Then use the bond dissociation energies in Table 4.3 to calculate AH° for each reaction. 

Tables of AH° for compounds are the most important data source for thermochemistry. From them it is easy to calculate AH° for reactions of the compounds, and thereby systematically compare the energy changes due to bond rearrangements in different reactions. Appendix D gives a short table of standard enthalpies of formation at 25°C. The following example shows how they can be used to determine enthalpy changes for reactions performed at 25°C and 1 atm pressure.

Use the bond dissociation energies in Table 5.3 to calculate AH° for the reaction of ethylene with HCl, HBr, and HI. Which reaction is most favorable ... 

Bond dissociation energies have, as we shall see, a variety of uses. They can be used, for example, to calculate the enthalpy change (AH°) for a reaction. To make such a calcula-... 

Bond energies. The net reaction CD + RH = RC1 + HC1 proceeds by a chain mechanism in which the propagators are Cl and R (but not H ), and chain-breaking occurs by dimerization of Cl. Write a scheme consistent with this and derive its rate law. Show how one can use E and AH for the bond dissociation of CP to calculate an activation energy for an elementary reaction. 

Bond dissociation energies can be used to calculate the enthylpy change (AH°) for a reaction. 

Previous attempts to calculate bond energies in tin compounds employed levels of theory that were inadequate to provide accurate results. As discussed above, accurate bond energies require the use of either composite ah initio methods or methods employing a high level of electron correlation coupled with isogyric reactions to minimize basis set truncation and other systematic errors. Consequently, the results reported by Basch [46,96], which use a number of imcorrected ah initio methods or with very simple corrections (i.e., across-the-board energy corrections by finite amounts), are unhkely to be particularly accurate. 

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