Using mean bond enthalpies

Although accurate calculations must use bond enthalpies for the molecule in question and its successive fragments, when such data are not available, there is no choice but to make estimates by using mean bond enthalpies, AHp, which are the averages of bond enthalpies over a related series of compounds (Table 1.4). For example, the mean HO bond enthalpy, AHb(H-O) = 463 kj mol , is the mean of the 0-H bond enthalpies in HjO and several other similar compounds, including methanol, CH3OH. 

Use information from the Resource section and bond enthalpy data from Tables 1.3 and 1.4 to estimate the standard enthalpy change for the reaction 

Strategy In calculations of this kind, the procedure is to break the overall process down into a sequence of steps such that their sum is the chemical equation required. 

Always ensure, when using bond enthalpies, that all the species are in the gas phase. That may mean including the appropriate enthalpies of vaporization or sublimation. One approach is to atomize all the reactants and then to build the products from the atoms so produced. When explicit bond enthalpies are available (that is, data are given in the tables available), use them otherwise, use mean bond enthalpies to obtain estimates. 

We have used the mean bond enthalpy value from Table 1.4 for the O-H bond and the exact bond enthalpy value for the 0-0 bond in HO-OH from Table 1.3. In the second step, four O-H bonds and one 0=0 bond are formed. The standard enthalpy change for bond formation (the reverse of dissociation) is the negative of the bond enthalpy. We can use exact values for the enthalpy of the O-H bond in H20(g) and for the 0=0 bond in Oj(g)  

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Reaction enthalpies can be estimated by using mean bond enthalpies to determine the total energy required to break the reactant bonds and form the product bonds. In practice, only the bonds that change are treated. Because bond enthalpies refer to gaseous substances, to use the tabulated values, all substances must be gases or converted into the gas phase. 

EXAMPLE 6.14 Using mean bond enthalpies to estimate the enthalpy of a reaction... 

We know that heat is given out during this reaction. But where exactly does the heat energy come from We will now calculate the enthalpy change for this reaction using mean bond enthalpies. To do this we carry out the following operations ... 

Table 1.4 is useful for many calculations, but its data caimot be used to estimate the differences between the standard enthalpies of formation of conformational isomers. For example, we would obtain the same enthalpy of formation for the equatorial and axial conformers of methylcyclohexane (3 and 4, respectively) if we were to use mean bond enthalpies. However, it has been observed experimentally that these conformers have different standard enthalpies of formation due to the steric repulsions in the axial conformer, which raise its energy relative to that of the equatorial conformer. 

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). 

A note on good practice. The use of mean bond enthalpies is hazardous because actual bond enthalpies often differ considerably from mean values. The modem procedure for estimating a reaction enthalpy is to use commercial software to calculate the enthalpies of formation of the reactants and products and then to take the difference, as in Section 6.18. 

The bond enthalpy in NO is 632 kj-mol 1 and that of each N—O bond in N02 is 469 kj-mol. Using Lewis structures and the mean bond enthalpies given in Table 6.8, explain (a) the difference in bond enthalpies between the two molecules (b) the fact that the bond enthalpies of the two bonds in N02 are the same. 

Benzene is more stable and less reactive than would be predicted from its Kekule structures. Use the mean bond enthalpies in Table 6.8 to calculate the lowering in molar energy when resonance is allowed between the Kekule structures of benzene. 

The standard enthalpies of formation of BH3(g) and diborane are +100 kj-mol 1 and +36 kj-mol, respectively, and the enthalpies of formation of B(g) and H(g) are +563 kj-mol-1 and +218 kj-mol"1, respectively, (a) Use these values to calculate the mean bond enthalpies of the B—H bonds in each case (b) Assume that terminal B—H bonds have the same strengths in each compound and estimate the bond enthalpy of the three-center B—H—B bonds in diborane. (c) Which bonds would you expect to be longer, the terminal B—H bonds or the three-center bonds Explain your answer. 

Mean bond enthalpies are defined as the enthalpy changes involved in breaking bonds in molecules. They may be determined from thermochemical cycles using Hess Law, although assumptions of transferability are sometimes required. 

The bond dissociation enthalpies of bonds such as C-H, C-Cl, C=0, N=N and O-H are approximately the same in different molecules. If the values of bond dissociation enthalpy for a bond between two atoms (A and B) in several different molecules are averaged, the resulting value is called the mean bond enthalpy (Table 13.4). Mean bond enthalpies are useful in estimating enthalpy changes for reactions for which standard enthalpies of formation are unavailable, but the fact that such values may have been obtained by averaging bond dissociation enthalpies from different types of molecule may lead to substantial errors in the calculated value of AH. ... 

Self-test 1.4 J Estimate the enthalpy change for the reaction between 1 mol C2H5OH as liquid ethanol, a fuel made by fermenting corn, and 02(g) to yield C02(g) and H20(l) under standard conditions by using the bond enthalpies, mean bond enthalpies, and the appropriate standard enthalpies of vaporization. 

Use bond enthalpies and mean bond enthalpies to estimate (a) the enthalpy of the anaerobic breakdown of glucose to lactic acid in cells that are starved of Oj, QH Ojlaq) —> 2 CHjCHlOH) COOH(aq), and (b) the enthalpy of combustion of glucose. Ignore the contributions of enthalpies of fusion and vaporization. 

Strictly, these values are bond enthalpies, but the term energies is commonly used. Other descriptions are average standard bond energies, mean bond energies . 

Using data from Table 9.2 and standard graphing software, determine the enthalpy and entropy of the equilibrium N204(g) — 2 N02(g) and estimate the N—N bond enthalpy in N204. How does this value compare with the mean N—N bond enthalpy in Table 6.8 ... 

In the previous exercise (whose outcome was not very successful), we used a new concept to assess the thermodynamic stability of chemical bonds the mean bond dissociation enthalpy (also known as mean bond disruption enthalpy). It is represented by DH° or by (DH°) (the symbol we adopt). As indicated, for... 

Mortimer and co-workers extended these studies to many other CoL2X2 compounds and, using estimated or measured enthalpies of sublimation and heat capacities of the complexes and the ligands, were able to derive the corresponding Co-L mean bond dissociation enthalpies [238]. 

Clearly, one should not use tabulated bond energy data for polyatomic molecules without knowing whether they are mean bond energies or bond dissociation energies. In any event, the relationship with the heat of formation of CH4 can be illustrated by an enthalpy cycle ... 

Mean standard bond enthalpies can be used to gne an aj estimate of the standard enthalpy diange which occurs in. ... 

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