The bond-dissociation energy (BDE, D0, or DH°) is one measure of the strength of a chemical bond A–B. It can be defined as the standard enthalpy change when A–B is cleaved by homolysis to give radicals A• and •B. The enthalpy change is temperature dependent, and the bond-dissociation energy is often defined to be the enthalpy change of the homolysis at 0 K (absolute zero), although the enthalpy change at 298 K (standard conditions) is also a frequently encountered parameter. As a typical example, the bond-dissociation energy for one of the C–H bonds in ethane (C2H6) is defined as the standard enthalpy change of the process
To convert a molar BDE to the energy needed to dissociate the bond per molecule, the conversion factor 23.060 kcal/mol (96.485 kJ/mol) for each eV can be used.
A variety of experimental techniques, including spectrometric determination of energy levels, generation of radicals by pyrolysis or photolysis, measurements of chemical kinetics and equilibrium, and various calorimetric and electrochemical methods have been used to measure bond dissociation energy values. Nevertheless, bond dissociation energy measurements are challenging and are subject to considerable error. The majority of currently known values are accurate to within ± 1 or 2 kcal/mol. Moreover, values measured in the past, especially before the 1970s, can be especially unreliable have been subject to revisions on the order of 10 kcal/mol (e.g., benzene C-H bonds, from 103 kcal/mol in 1965 to the modern accepted value of 112.9 kcal/mol). Even recently (between 1990 and 2004), the O-H bond of phenol has been reported to be anywhere from 85.8 to 91.0 kcal/mol. On the other hand, the bond dissociation energy of H2 at 298 K has been measured to high precision and accuracy: DH°298 (H–H) = 104.1539 ± 0.0001 kcal/mol.
The bond-dissociation energy is similar to the bond-dissociation enthalpy (or bond enthalpy), which is sometimes used interchangeably. However, some authors make the distinction that the bond-dissociation energy (D0) refers to the enthalpy change at 0 K, while the term bond-dissociation enthalpy is used for the enthalpy change at 298 K (unambiguously denoted DH°298). The former parameter tends to be favored in theoretical and computational work, while the latter is more convenient for thermochemical studies. For typical chemical systems, the numerical difference between the quantities is small and the distinction can often be ignored. For a hydrocarbon RH where R is significantly larger than H, for instance, the relationship D0(R—H) ≈ DH°298(R—H) – 1.5 kcal/mol is a good approximation. Some textbooks ignore the temperature dependence, while others have defined the bond-dissociation energy to be the reaction enthalpy of homolysis at 298 K.
The bond dissociation energy is related to but slightly different from the depth of the associated potential energy well of the bond, De, known as the electronic energy. This is due to the existence of a zero-point energy ε0 for the vibrational ground state, which reduces the amount of energy needed to reach the dissociation limit. Thus, D0 is slightly less than De, and the relationship D0 = De – ε0 holds.
Except for diatomic molecules, the bond-dissociation energy differs from the (average) bond energy. While the bond-dissociation energy is the energy of a single chemical bond, bond energy is the average of all the bond-dissociation energies of the bonds in a molecule between the two elements in question.
For example, dissociation of HO–H bond of a water molecule (H2O) requires 117.9 kcal/mol (493.4 kJ/mol). The dissociation of the remaining hydroxyl radical requires 101.4 kcal/mol (424.4 kJ/mol). The bond energy of the covalent O–H bonds in water is said to be 109.7 kcal/mol (458.9 kJ/mol), the average of these values.
In the same way, for removing successive hydrogen atoms from methane the bond-dissociation energies are 104 kcal/mol (435 kJ/mol) for D(CH3–H), 106 kcal/mol (444 kJ/mol) for D(CH2–H), 106 kcal/mol (444 kJ/mol) for D(CH–H) and finally 81 kcal/mol (339 kJ/mol) for D(C–H). The bond energy is, thus, 99 kcal/mol or 414 kJ/mol (the average of the bond-dissociation energies). None of the individual bond-dissociation energies equals the bond energy of 99 kcal/mol.
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Following dissociation, if new bonds of greater bond-dissociation energy are formed, these products are at lower enthalpy, there is a net loss of energy, and thus the process overall is exothermic. In particular, the conversion of the weak double bonds in O2 to the stronger bonds in CO2 and H2O makes combustion exothermic.
As illustration, first, normal combustion in open air be considered. Such reactions usually take place under standard atmospheric pressure, without constraints in the volumes of the reactants and products.
The case of the combustion of butane in open air is one such case employed for efficient cooking using LPG. A combination of n-butane and isopropane (2, methyl propane), its melting-point varies up to 6 units and boiling-point varies up to two units. There are four carbon-carbon bonds and 10 carbon-hydrogen bonds. At a very crude level, looking at the table of bond-dissociation energy, the four C-C bonds have a total ~ 4 × 3.65 (average) eV/Bond ≈ 14.6 eV for the four bonds and the ten C-H bonds have a total ~ 10 × 4.37 (an average of methyl-, ethyl- and tertiary-bonds) ≈ 43.7 eV, a total of 58.3 eV for one molecule of n-Butane.
BDE of O-O bond is 5.15 eV, whereas for the products, CO2 and H2O, the BDEs are [11.16(C-O bond) + 5.51(CO-O bond)] 16.17 eV and [4.77 eV (O-H Bond) + 2.78 eV (OH-H bond)] 7.55 eV, respectively. A balanced chemical equation is as follows:
- 2C4H10 + 13O2 + Initial Energy ⇌ 8CO2 + 10H2O
- ⇒ (2 × 58.3 eV) + (13 × 5.15 eV) + Initial Energy yields (8 × 16.17 eV) + (10 × 7.55 eV)
- ⇒ 116.6 eV + 66.95 eV + Initial Energy → 129.36 eV + 75.5 eV
- ⇒ 183.55 + Initial Energy → 204.86 eV
It is clearly apparent that the final BDE is higher than those of the reactants, and this energy is released when the products are formed. Since for all the reactants the BDE is positive, energy is to be provided externally to break up the bonds between C-C, C-H and O-O bonds to initiate the reaction. However, since the BDEs of the products are much higher than those of the reactants, the energy released during the initiation is utilised to break up the bonds of next set of reactants. But how?
Though the reaction takes place in open air, the burner hob, the cooking utensil surface exposed to the heat and the surrounding air keeps the local energy just about adequate to keep the bonds of the continually-added reactants breaking in a cascade and sustain the exothermic reaction. Hence, the final chemical equation could be re-written as:
- 2C4H10 + 13O2 + Initial Energy ⇌ 8CO2 + 10H2O + Energy Released
This is a reasonably logical analysis based on the axiomatic fact that an initial match-stick or a spark-lighter is enough to keep the burner running as long as required.
Next, for an Internal Combustion Engine using methane and air mixture as reactants and running adiabatically, a similar balanced equation and logical analysis could be attempted, but in this case the enthalpy of the system would be conserved, slightly modifying the operational set-up to account for heat dissipation and cooling of the engine. However, such methodical set-ups are routine in the laboratories of engine manufacturers and research institutes to increase the efficiency of the engine, which is essentially and perpetually a work in progress.
Homolytic versus heterolytic dissociation
Bonds can be broken symmetrically or asymmetrically. The former is called homolysis and is the basis of the usual BDEs. Asymmetric scission of a bond is called heterolysis. For molecular hydrogen, the alternatives are:
- H2 → 2 H• ΔH = 104 kcal/mol (see table below)
- H2 → H+ + H− ΔH = 66 kcal/mol (in water)
|Bond||Bond||Bond-dissociation energy at 298 K||Comment|
|C–C||Carbon||83–85||347–356||3.60–3.69||Strong, but weaker than C–H bonds|
|Cl–Cl||Chlorine||58||242||2.51||Indicated by the yellowish colour of this gas|
|Br–Br||Bromine||46||192||1.99||Indicated by the brownish colour of Br2|
Source of the Br• radical
|I–I||Iodine||36||151||1.57||Indicated by the purplish colour of I2|
Source of the I• radical
|H–H||Hydrogen||104||436||4.52||Strong, nonpolarizable bond|
Cleaved only by metals and by strong oxidants
|O–H||Hydroxide||110||460||4.77||Slightly stronger than C–H bonds|
|OH–H||Hydroxide-Hydron||64||268||2.78||Far weaker than C–H bonds|
|C–O||Monoxide||257||1077||11.16||Far stronger than C–H bonds|
|O–CO||Dioxide||127||532||5.51||Slightly stronger than C–H bonds|
|O=O||Oxygen||119||498||5.15||Stronger than single bonds|
Weaker than many other double bonds
|N≡N||Nitrogen||226||945||9.79||One of the strongest bonds|
Large activation energy in production of ammonia
The data tabulated above shows how bond strengths vary over the periodic table. There is great interest, especially in organic chemistry, concerning relative strengths of bonds within a given group of compounds.
|Bond||Bond||Bond-dissociation energy at 298 K||Comment|
|H3C–H||Methyl C–H bond||105||439||4.550||One of the strongest aliphatic C–H bonds|
|C2H5–H||Ethyl C–H bond||101||423||4.384||Slightly weaker than H3C–H|
|(CH3)3C–H||Tertiary C–H bond||96.5||404||4.187||Tertiary radicals are stabilized|
|(CH3)2NCH2–H||C–H bond α to amine||380.7||lone-pair bearing heteroatoms weaken C-H bonds|
|(CH2)3OCH–H||C–H bond α to ether||385.3||lone-pair bearing heteroatoms weaken C-H bonds|
THF tends to form hydroperoxides
|CH2CH–H||Vinyl C–H bond||111||464||4.809||Vinyl radicals are rare|
|HC2–H||acetylenic C–H bond||133||556||5.763||Acetylenic radicals are very rare|
|C6H5–H||Phenyl C–H bond||113||473||4.902||Comparable to vinyl radical, rare|
|CH2CHCH2–H||Allylic C–H bond||89||372||3.856||Such bonds show enhanced reactivity|
see drying oil
|C6H5CH2–H||Benzylic C–H bond||90||377||3.907||Akin to allylic C–H bonds|
Such bonds show enhanced reactivity
|H3C–CH3||Alkane C–C bond||83–85||347–356||3.596-3.690||Much weaker than a C–H bond|
|H2C=CH2||Alkene C=C bond||146–151||611–632||6.333-6.550||About 2× stronger than a C–C single bond|
|HC≡CH||Alkyne C≡C triple bond||200||837||8.675||About 2.5× stronger than a C–C single bond|
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