Bond-dissociation energy

In chemistry, bond-dissociation energy (BDE) or D0, is one measure of the strength in a chemical bond. It can be defined as the standard enthalpy change when a bond is cleaved by homolysis,[1] 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·

D0 = ΔH = 101.1 kcal/mol = 423.0 kJ/mol = 4.40 eV (per bond)

Definitions of BDE and related parameters

The bond-dissociation energy is sometimes also called the bond-dissociation enthalpy (or bond enthalpy), but these terms may not be strictly equivalent, as the latter 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.[2] Nevertheless, the term bond-dissociation energy and the symbol Do has often been used for the reaction enthalpy at 298 K as well.[3]

BDE versus bond energy

Except in the case of diatomic molecules, the bond-dissociation energy is different from the bond energy, which is an average calculated from the sum of the bond-dissociation energies of all bonds in a molecule.[4]

For example, an HO–H bond of a water molecule (H–O–H) has 493.4 kJ/mol of bond-dissociation energy, and 424.4 kJ/mol is needed to cleave the remaining O–H bond. The bond energy of the covalent O–H bonds in water is 458.9 kJ/mol, which is the average of the values. Hydrogen bond-dissociation energy in water is about 23 kJ/mol.[5]

In the same way for removing successive hydrogen atoms from methane the bond-dissociating 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). Notice that none of the C-H BDEs is 99 kcal/mol.

Following dissociation, if new bonds of larger 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.[6]

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)

Bromocarbons are often labile and are useful fire retardants.

Bond Bond Bond-dissociation energy (298 K) Comment
(kcal/mol) (kJ/mol) (eV)
C–C C–C bond 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 hydroxyl 110 460 4.77 comparable to strength of O=O and C–H bonds
O=O oxygen 119 498 5.15 strong bond, but O–H bonds are of comparable strength
N≡N nitrogen 226 945 9.79 one of the strongest bonds
production of ammonia consumes significant energy

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.[2]

Bond Bond Bond-dissoc. energy (298 K) Comment
(kcal/mol) (kJ/mol)
H3C–H Methyl C–H bond 105 439 One of the strongest aliphatic C–H bonds
C2H5-H Ethyl C–H bond 101 423 slightly weaker than H3C–H
(CH3)3C–H tertiary C–H bond 96.5 404 tertiary radicals are stabilized
CH2CH–H vinyl C–H bond 111 464 vinyl radicals are rare
HC2-H acetylenic C–H bond 133 556 acetylenic radicals are very rare
C6H5-H phenyl C–H bond 113 473 comparable to vinyl radical, rare
CH2CHCH2-H allylic C–H bond 89 372 such bonds show enhanced reactivity
C6H5CH2-H benzylic C–H bond 90 377 akin to allylic C–H bonds
such bonds show enhanced reactivity
H3C–CH3 Alkane C–C bond 83–85 347–356 much weaker than a C–H bond
H2C=CH2 Alkene C=C bond 146–151 611–632 about 2x stronger than a C–C single bond
HC≡CH alkyne C≡C triple bond 200 837 about 2.5x stronger than a C–C single bond

See also

References

  1. ↑ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (1994) "Bond dissociation energy".
  2. 1 2 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.
  3. ↑ Darwent, B. deB. (1970). "Bond Dissociation Energies in Simple Molecules" Nat. Stand. Ref. Data Ser., Nat. Bur. Stand. (U.S.) 31, 52 pages.
  4. ↑ Morrison & Boyd Organic Chemistry 4th Ed. ISBN 0-205-05838-8
  5. ↑ Principles of biochemistry by Albert L. Lehninger, David Lee Nelson, Michael M. Cox; edition 4, page 48
  6. ↑ Schmidt-Rohr, K. (2015). "Why Combustions Are Always Exothermic, Yielding About 418 kJ per Mole of O2" J. Chem. Educ. 92: 2094-2099. http://dx.doi.org/10.1021/acs.jchemed.5b00333
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