Bond-dissociation energy (BDE or D0) is one measure of the strength of a chemical bond. It can be defined as the standard enthalpy change when a bond is cleaved by homolysis, with reactants and products of the homolysis reaction at 0 K (absolute zero). For instance, the bond-dissociation energy for one of the C–H bonds in ethane (C2H6) is defined by the process:
- CH3CH2–H → CH3CH2• + H•
The bond-dissociation energy is sometimes called the bond-dissociation enthalpy (or bond enthalpy), but these terms may not be strictly equivalent. Bond-dissociation enthalpy usually refers to the above reaction enthalpy at 298 K (standard conditions) rather than at 0 K, and differs from D0 by about 1.5 kcal/mol (6 kJ/mol) in the case of a bond to hydrogen in a large organic molecule. Nevertheless, the term bond-dissociation energy and the symbol D0 have been used for the reaction enthalpy at 298 K as well.[page needed]
Except for diatomic molecules, the bond-dissociation energy differs from the 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.[page needed]
For example, dissociation of HO–H bond of a water molecule (H2O) requires 493.4 kJ/mol. The dissociation of the remaining hydroxyl radical requires 424.4 kJ/mol. The bond energy of the covalent O–H bonds in water is said to be 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.
For computing the Bond Dissociation Energy for splitting up a bond, what is needed is the energy E of an electron to remove it from a positively charged plate of 1 Volt Potential Energy to free space without any field, namely E = 0.160218 attojoules, and the fact that a mole of anything (free atoms, molecules, etc.,) is the Avogadro's number NA of them. The two quantities, when multiplied together, yield 96.485 kJ/mole as the energy density corresponding to 1 ev per bond, in the case of one broken bond per molecule.
For example, the energy needed to convert a mole of ethane to a mole of ethyl radicals, 423.0 kJ/mol, is, for each bond in that mole, 423.0/96.485 = 4.38 ev/bond ≈ 4.40 ev/bond. Likewise, 460 kJ/mol becomes 460/96.485 = 4.77 ev/bond.
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 X 3.65 (average) eV/Bond ≈ 14.6 eV for the four bonds and the ten C-H bonds have a total ~ 10 X 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 X 58.3 eV) + (13 X 5.15 eV) + Initial Energy yields (8 X 16.17 eV) + (10 X 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|
- IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Bond-dissociation energy".
- Blanksby, S. J.; Ellison, G. B. (2003). "Bond Dissociation Energies of Organic Molecules". Acc. Chem. Res. 36 (4): 255–263. doi:10.1021/ar020230d. PMID 12693923.
- Darwent, B. deB. (January 1970). Bond Dissociation Energies in Simple Molecules (PDF). NSRDS-NBS 31. Washington, DC: U.S. National Bureau of Standards. LCCN 70602101.
- Morrison, Robert Thornton; Boyd, Robert Neilson (1983). Organic Chemistry (4th ed.). Boston: Allyn & Bacon. ISBN 0-205-05838-8.
- Lehninger, Albert L.; Nelson, David L.; Cox, Michael M. (2005). Lehninger Principles of Biochemistry (4th ed.). W. H. Freeman. p. 48. ISBN 978-0-7167-4339-2. Retrieved May 20, 2016.
- Schmidt-Rohr, K. (2015). "Why Combustions Are Always Exothermic, Yielding About 418 kJ per Mole of O2". J. Chem. Educ. 92: 2094–2099. Bibcode:2015JChEd..92.2094S. doi:10.1021/acs.jchemed.5b00333.