Average Bond Energies

Heats of Atomization

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As a prelude to this topic, you should be familiar with Hess's Law, Heats of Formation, Heats of Combustion and Bond Dissociation Energies (BDE's).

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Index: C-H Bonds C-C Single Bonds C=C Double Bonds CC Triple Bonds C-O Bonds O-H Bonds C=O Bonds: Aldehydes and Ketones C=O Bonds: Carboxylic Acids C=O Bonds: Esters and Carbonates C-X Bonds: Chlorides and Bromides

Some Relevant Atoms and Radicals ΔHfo (kcal/mol) H +52 (1/2 BDE) Cl +29 (1/2 BDE) Br +23 (1/2 BDE) I +18 (1/2 BDE) C +171 CH3 (see below) +34 C2H5 (see below) +26 O +59.6

C-H Bonds: Average Bond Energies (ABE's) provide a means of estimating the strength of bonds such as C-H, C-O, carbonyls, double bonds and triple bonds. The method employs heats of atomization and heats of formation. The ABE's are calculated averages and not directly measurable quantities like bond dissociaton energies (BDE's). The table above lists the heats of formation of atoms and radicals that have been imported from the BDE Tables. The diagram on the upper right, which is not to scale, describes the heat of atomization of methane. The section in blue describes the type of diagram employed in illustrating bond dissociation energy (BDE) of methane. Rather than stop at the formation of a methyl radical and a hydrogen atom, what if C-H bonds were successively cleaved from the methyl radical to afford CH2, CH and C along with three atoms of hydrogen (in green). The sum total of the blue and green areas equals what is in red. The calculated heat of atomization of 1 mole of graphite and the formation of four moles of hydrogen atoms is 379 kcal/mol. From this total is subtracted the negative heat of formation of methane to give a value of 397 kcal/mol for the heat of atomization of methane. Of course, methane has four C-H bonds. If the heat of atomization of methane is divided by four, the average bond energy (ABE) for a C-H bond is 99 kcal/mol. Just as a class average grade may be 85 (we certainly hope so) no single grade need be 85. Likewise, no C-H bond need be 99 kcal/mol. Indeed, with an average of 99 kcal/mol and an initial bond dissociation energy of 104 kcal/mol, at least one of the successive processes (in green) must be less than 99 kcal/mol. The energy for each of these steps is known. Using a more up-to-date BDE (105 kcal/mol) for methane, Ellison has reported the following values (Table 1) for the stepwise conversion CH4 -----> C + 4H. Notice that three of the BDE's are greater than the ABE while one is smaller. The same ABE can be obtained using the heat of formation of methane in conjunction with the heats of formation of carbon and hydrogen atoms (Table 2).

Table 1 BDE (kcal/mol) ABE (C-H) CH4 -------> CH3 H 105 CH3 -------> CH2 H 110 CH2 -------> CH H 101 CH -------> C H 81 SUM: CH4 -------> C 4H 397 99 Table 2 ΔHo/rxn.---> CH4 ------> C 4H ΔHfo -17.9 ------> +171 4 (+52) ΔHrxno +397 ΔHABEo/ C-H bond +99

C-C Single Bonds: What is an ABE for a C-C single bond? This value is readily obtained by analyzing alkanes such as ethane, which has only C-H bonds and a single C-C single bond (Table 3). Ethane upon "atomization" yields two carbon atoms and six hydrogens for a total of 654 kcal/mol. Subtracting -20 kcal/mol for the ΔHfo of ethane leaves 674 kcal/mol for this hypothetical reaction. Subtraction of 594 kcal/mol for the six hydrogen atoms leaves 80 kcal/mol for the ABE of a C-C single bond. Higher homologs of ethane, ---namely -- propane, n-butane, isobutane and cyclohexane give values of 81, 81, 82 and 82 kcal/mol, respectively. In each of these examples, one must divide the "final" total by the number of C-C bonds. Clearly, a strained ring system would not be able to provide an accurate ABE for the C-C bond. For cyclopropane the ABE is 72.5 kcal/mol. Because ethane is less representative of alkanes than alkanes with methylene and methine hydrogens, ethane is atypical. For unstrained systems, 82 kcal/mol is the ABE for a C-C single bond.

Table 3 CH3CH3 ------> 2C 6H ΔHfo -20 ------> 2(+171) 6(+52) ΔHrxno +674 ΔHABEo C-H 6(+99) = 594 ΔHABEo /C-C 674-594 = 80

C=C Double Bonds: Now consider the strength of a C=C double bond. Ethylene serves as a useful example. The computation in Table 4 reveals an ABE for the C=C double bond of 142 kcal/mol. But ethylene is not typical of most double bonds since it is one of a kind. Compare some of the constitutional isomers of the hexenes: (1-hexene, 144 kcal/mol; (E)-3-hexene, 144 kcal/mol; (E)-3-methyl-2-pentene, 149 kcal/mol; 2,3-dimethyl-2-butene, 151 kcal/mol. As the double bond becomes more substituted with carbon atoms, the double bond becomes more stable. This ordering of energies is also reflected in the heats of formation. An ABE for a C=C double bond is ~146 kcal/mol. Since the double bond has, in addition to a σ-bond, it also has a π-bond. Not surprisingly, double bonds are stronger than C-C single bonds. How much stronger? Take the difference to find the contribution of a π-bond. Thus, 146 - 82 = 64 kcal/mol for a π-bond.

Table 4 CH2=CH2 ------> 2C 4H ΔHfo +12.5 ------> 2(+171) 4(+52) ΔHrxno +538 ΔHABEo/C-H 4(+99) = 396 ΔHABEo/C=C 538-396 = 142

CC Triple Bonds: The CC triple bond is stronger than the C=C double bond. See acetylene in (Table 5). As with the case of the double bond, increased carbon substitution increases the stability of the triple bond. Accordingly, 1-butyne and 1-hexyne have a triple bond ABE of 199 kcal/mol while the internal alkynes 2-butyne, 2- and 3-hexyne have ABE's of 203 kcal/mol. Employing an average ABE of 201 kcal/mol for a triple bond, the incremental π-bond is calculated to be worth 55 kcal/mol (201 - 146 kcal/mol). The second π-bond in an alkyne is ~9 kcal/mol less stable than the π-bond in an alkene.

Table 5 HCCH ------> 2C 2H ΔHfo +54.5 ------> 2(+171) 2(+52) ΔHrxno +392 ΔHABEo C-H 2(+99) = 198 ΔHABEo /CC 392-198 = 194

C-O Bonds: The C-O single bond ABE can be determined as shown in Tables 6 and 7 using dimethyl ether and diethyl ether as models. As was the case with using ethane as a model, dimethyl ether gives a value for the C-O ABE of 82 kcal/mol. On the other hand, diethyl ether affords an ABE of 85 kcal/mol. Based upon several calculations. an "average" ABE for the C-O bond is 84 kcal/mol.

Table 6 CH3OCH3 ------> 2C 6H O ΔHfo -44.0 ------> 2(+171) 6(+52) +59.6 ΔHrxno +758 +342 +312 +59.6 ΔHABEo C-H 6(+99) = 594 ΔHABEo/C-O (758-594)/2 = 82 Table 7 CH3CH2OCH2CH3 ------> 4C 10H O ΔHfo -60.4 ------> 4(+171) 10(+52) +59.6 ΔHrxno +1324 684 +520 +59.6 ΔHABEo C-H 10(+99) = 990 ΔHABEo C-C 2(+82) = 164 ΔHABEo /C-O (1324-990-164)/2 = 85

O-H Bonds: The heat of formation of an oxygen atom is ~60 kcal/mol. At 25oC water is a liquid. The O-H bond in water has an ABE of 116 kcal/mol (Table 8). Its heat of formation is -68.3 kcal/mol. As a gas at this temperature, the heat of vaporization drops the heat of formation to -57.8 kcal/mol and, accordingly, the bond strength is 111 kcal/mol for water in the gas phase. Primary alcohols [ethanol (Table 9), 1-propanol] have ABE's of 109 kcal/mol; secondary alcohols (2-propanol, 2-butanol) have values of 113 kcal/mol; and tertiary alcohols (t-butanol) an ABE of 117 kcal/mol. Ethylene glycol, which has two primary hydroxyls, has an O-H bond ABE of 111 kcal/mol. An ABE of 111 kcal/mol is a convenient estimate for the ABE of the O-H bond.

Table 8 H2O (l) H2O (g) ------> 2H O ΔHfo -68.3 -57.8 ------> 2(+52) +59.6 ΔHrxno +232 +222 +104 +59.6 ΔHABEo /O-H bond +116 +111 Table 9 CH3CH2OH ------> 2C 10H O ΔHfo -56.2 ------> 2(+171) 6(+52) +59.6 ΔHrxno +770 +342 +312 +59.6 ΔHABEo C-H 5(+99) = 495 ΔHABEo C-C +82 ΔHABEo /C-O +84 770-495-82-84 = 109

C=O Bonds: Aldehydes and Ketones The calculation of the ABE of a carbonyl group (C=O) follows the same method that was employed in computing the ABE of a C=C double bond. As was the case with C=C double bonds, there is a variation of the ABE that depends upon what atoms are attached to the carbon of the carbonyl. Like ethylene, formaldehyde (Table 10) gives a lower value than typical aldehydes (Table 12). For ketones the ABE is typically in the range 176 - 179 kcal/mol (Table 11). Cyclopentanone and cyclopentanone both have ABE's of 176 kcal/mol. Table 11 (CH3)2C=O ------> 3C 6H O ΔHfo -52.2 ------> 3(+171) 6(+52) +59.6 ΔHrxno +937 ΔHABEo C-H 6(+99) = 594 ΔHABEo C-C 2(+82) = 160 ΔHABEo /C=O 937-594-164 = 179

Table 10 CH2=O ------> C 2H O ΔHfo -27.7 ------> (+171) 2(+52) +59.6 ΔHrxno +362 ΔHABEo C-H 2(+99) = 198 ΔHABEo C=O 362-198 = 164 Table 12 CH3CHO ------> 2C 4H O ΔHfo -40.8 ------> 2(+171) 4(+52) +59.6 ΔHrxno +650 +342 +208 +59.6 ΔHABEo C-H 4(+99) = 396 ΔHABEo C-C +82 ΔHABEo/C=O 650-396-82 = 172

C=O Bonds: Carboxylic Acids The carbonyl group of carboxylic acids has an ABE of 199 kcal/mol. Acetic acid (Table 14) is typical. Formic acid, like formaldehyde (Table 13) compared to other aldehydes, has a lower carbonyl ABE (181 kcal/mol).

Table 13 HCO2H ------> 1C 2H 2O ΔHfo -80.5 ------> +171 2(+52) 2(+59.6) ΔHrxno +475 +171 +104 +119.2 ΔHABEo C-H +99 ΔHABEo C-O +84 ΔHABEo O-H +111 ΔHABEo /C=O 475-99-84-111 = 181 Table 14 CH3CO2H ------> 2C 4H 2O ΔHfo -103.5 ------> 2(+171) 4(+52) 2(+59.6) ΔHrxno +773 +342 +208 +119.2 ΔHABEo C-H 3(+99) = 297 ΔHABEo C-C +82 ΔHABEo C-O +84 ΔHABEo O-H +111 ΔHABEo /C=O 773-297-82--84-111 = 199

C=O Bonds: Esters and Carbonates The ABE of the carbonyl group of esters are comparable to the values determined for carboxylic acids. Formates (Table 16) are typically lower valued than esters of other carboxylic acids. The 202 kcal/mol for the carbonyl ABE of ethyl acetate (Table 17) is what is seen with most aliphatic esters. Note the progression of carbonyl bond strength in the series: formaldehyde, aldehyde, ketone, ester and carbonate (Table 16, 216 kcal/mol). Successive interpolation of carbon and oxygen increases the ABE of the carbonyl group. Table 16 (C2H5O)2CO ------> 5C 10H 3O ΔHfo -152.5 ------> 5(+171) 10(+52) 3(+59.6) ΔHrxno +1031 +855 +520 +178.8 ΔHABEo C-H 10(+99) = 990 ΔHABEo C-C 2(+82) = 164 ΔHABEo C-O 2(+84) = 168 ΔHABEo /C=O 1031-990-164-168 = 216

Table 15 HCO2CH2CH3 ------> 3C 6H 2O ΔHfo -86.5 ------> 3(+171) 6(+52) 2(+59.6) ΔHrxno +1031 +513 +312 +119.2 ΔHABEo C-H 6(+99) = 594 ΔHABEo C-C +82 ΔHABEo C-O 2(+84) = 168 ΔHABEo /C=O 1031-594-82-168 = 187 Table 17 CH3CO2CH2CH3 ------> 4C 8H 2O ΔHfo -106.5 ------> 4(+171) 8(+52) 2(+59.6) ΔHrxno +1326 +684 +416 +119.2 ΔHABEo C-H 8(+99) = 792 ΔHABEo C-C 2(+82) = 164 ΔHABEo C-O 2(+84) = 168 ΔHABEo /C=O 1326-792-164-168 = 202

C-X Bonds: Halides The calculation of ABE's for C-X bonds of halides are in the range of BDE's but there is a fairly wide range of values. The variance in BDE's for C-Cl bonds (Table 18) is small and it is a value of 81 kcal/mol that is often employed in computations. The same situation applies to alkyl bromides. A bond dissociation energy of 68 kcal/mol is utilized for the ABE. This makes sense since the BDE is an experimental value with a small range of values for the BDE. Table 18 RCl (kcal/mol) ABE BDE chloromethane 79 84 chloroethane 81 81 1-chloropropane 81 81 1-chlorobutane 81 81 2-chloropropane 84 80 2-chlorobutane 84 80 2-chloro-2-methylpropane 87 79

Table 19 RBr (kcal/mol) ABE BDE bromomethane 61 70 bromoethane 63 68 1-bromopropane 64 68 1-bromobutane 64 68 2-bromopropane 67 68 2-bromobutane 67 68 2-bromo-2-methylpropane 70 65

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