Bond-dissociation energy

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 fragments A and B, which are usually radical species.[1][2] 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.[3] 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

CH3CH2–H → CH3CH2• + H•,
DH°298 (CH3CH2–H) = ΔH° = 101.1(4) kcal/mol = 423.0 ± 1.7 kJ/mol = 4.40(2) eV (per bond).[4]

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.[5] 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(5) kcal/mol). Even in recent times (between 1990 and 2004), the O-H bond of phenol has been reported to be anywhere from 85.8 to 91.0 kcal/mol.[6] 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(1) kcal/mol.[5]

The term bond-dissociation energy is similar to the related notion of 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.[7] Some textbooks ignore the temperature dependence,[8] while others have defined the bond-dissociation energy to be the reaction enthalpy of homolysis at 298 K.[9][10][11]

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.[7]

Historically, the vast majority of tabulated bond energy values are bond enthalpies. More recently, however, the free energy analogue of bond-dissociation enthalpy, known as the bond-dissociation free energy (BDFE), has become more prevalent in the chemical literature. The BDFE of a bond A–B can be defined in the same way as the BDE as the standard free energy change (ΔG°) accompanying homolytic dissociation of AB into A and B. However, it is often thought of and computed stepwise as the sum of the free energy changes of heterolytic bond dissociation (A–B → A+ + :B–), followed by one-electron reduction of A (A+ + e– → A•) and one-electron oxidation of B (:B– → •B + e–).[12] In contrast to the BDE, which is usually defined and measured in the gas phase, the BDFE is often determined in the solution phase with respect to a solvent like DMSO, since the free energy changes for the aforementioned thermochemical steps can be determined from parameters like acid dissociation constants (pKa) and standard redox potentials (ℇ°) that are measured in solution.[13]

Bond energy

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, the bond energy is the average of all the bond-dissociation energies of the bonds of the same type for a given molecule.[14] For a homoleptic compound EXn, the E–X bond energy is (1/n) multiplied by the enthalpy change of the reaction EXn → E + nX. Average bond energies given in tables are the average values of the bond energies of a collection of species containing 'typical' examples of the bond in question.

For example, dissociation of HO–H bond of a water molecule (H2O) requires 118.8 kcal/mol (497.1 kJ/mol). The dissociation of the remaining hydroxyl radical requires 101.8 kcal/mol (425.9 kJ/mol). The bond energy of the covalent O–H bonds in water is said to be 110.3 kcal/mol (461.5 kJ/mol), the average of these values.[15]

In the same way, for removing successive hydrogen atoms from methane the bond-dissociation energies are 105 kcal/mol (439 kJ/mol) for D(CH3–H), 110 kcal/mol (460 kJ/mol) for D(CH2–H), 101 kcal/mol (423 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.[16][7]

Strongest bonds

According BDE data, the strongest single bonds are Si-F bonds. The BDE for H3Si-F is 152 kcal/mol, almost 50% stronger than the H3C-F bond (110 kcal/mol). One onsequence to these data are that many reactions generate silicon fluorides, such as glass etching, deprotection in organic synthesis, and volcanic emissions.[17]

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 = 400.4 kcal/mol (gas phase)[18]
H2 → H+ + H−           ΔH = 66 kcal/mol (in water)

Note that in the gas phase, the enthalpy of heterolysis is larger than that of homolysis, due to the need to separate unlike charges. However, this value is lowered substantially in the presence of solvent.

Bond Bond Bond-dissociation energy at 298 K Comment
(kcal/mol) (kJ/mol) (eV/Bond)
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 in methanol 440 Slightly stronger than C–H bonds
O–H in alpha-tocopherol (an antioxidant) 323 O-H bond strength depends strongly on substituent on O
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.[7]

Bond Bond Bond-dissociation energy at 298 K Comment
(kcal/mol) (kJ/mol) (eV/Bond)
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

See also

References

  1. ↑ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Bond-dissociation energy".
  2. ↑ The value reported as the bond-dissociation energy (BDE) is generally the enthalpy of the homolytic dissociation of a gas-phase species. For instance, the BDE of diiodine is calculated as twice the heat of formation of iodine radical (25.5 kcal/mol) minus the heat of formation of diiodine gas (14.9 kcal/mol). This gives the accepted BDE of diiodine of 36.1 kcal/mol. (By definition, diiodine in the solid state has a heat of formation of 0.)
  3. ↑ The IUPAC Gold Book does not stipulate a temperature for its definition of bond-dissociation energy (ref. 1).
  4. ↑ The corresponding BDE at 0 K (D0) is 99.5(5) kcal/mol.
  5. 1 2 Luo YR (2007). Comprehensive handbook of chemical bond energies. Boca Raton: CRC Press. ISBN 978-0-8493-7366-4. OCLC 76961295.
  6. ↑ Mulder P, Korth HG, Pratt DA, DiLabio GA, Valgimigli L, Pedulli GF, Ingold KU (March 2005). "Critical re-evaluation of the O-H bond dissociation enthalpy in phenol". The Journal of Physical Chemistry A. 109 (11): 2647–55. doi:10.1021/jp047148f. PMID 16833571.
  7. 1 2 3 4 Blanksby SJ, Ellison GB (April 2003). "Bond dissociation energies of organic molecules". Accounts of Chemical Research. 36 (4): 255–63. CiteSeerX 10.1.1.616.3043. doi:10.1021/ar020230d. PMID 12693923.
  8. ↑ Anslyn EV, Dougherty DA (2006). Modern physical organic chemistry. Sausalito, CA: University Science. ISBN 978-1-891389-31-3. OCLC 55600610.
  9. ↑ Darwent Bd (January 1970). Bond Dissociation Energies in Simple Molecules (PDF). NSRDS-NBS 31. Washington, DC: U.S. National Bureau of Standards. LCCN 70602101.
  10. ↑ Streitwieser A, Heathcock CH, Kosower EM (2017). Introduction to Organic Chemistry. New Delhi: Medtech (Scientific International, reprint of 4th revised edition, 1998, Macmillan). p. 101. ISBN 9789385998898.
  11. ↑ Carroll FA (2010). Perspectives on structure and mechanism in organic chemistry (2nd ed.). Hoboken, N.J.: John Wiley. ISBN 978-0-470-27610-5. OCLC 286483846.
  12. ↑ Miller DC, Tarantino KT, Knowles RR (June 2016). "Proton-Coupled Electron Transfer in Organic Synthesis: Fundamentals, Applications, and Opportunities". Topics in Current Chemistry. 374 (3): 30. doi:10.1007/s41061-016-0030-6. PMC 5107260. PMID 27573270.
  13. ↑ Bordwell FG, Cheng JP, Harrelson JA (February 1988). "Homolytic bond dissociation energies in solution from equilibrium acidity and electrochemical data". Journal of the American Chemical Society. 110 (4): 1229–1231. doi:10.1021/ja00212a035.
  14. ↑ Norman RO, Coxon JM (2001). Principles of organic synthesis (3rd ed.). London: Nelson Thornes. p. 7. ISBN 978-0-7487-6162-3. OCLC 48595804.
  15. ↑ Lehninger AL, Nelson DL, Cox MM (2005). Lehninger Principles of Biochemistry (4th ed.). W. H. Freeman. p. 48. ISBN 978-0-7167-4339-2. Retrieved May 20, 2016.
  16. ↑ "Table of Bond Dissociation Energies" (PDF). 19 September 2018.
  17. ↑ Lide, David R., ed. (2006). CRC Handbook of Chemistry and Physics (87th ed.). Boca Raton, FL: CRC Press. ISBN 0-8493-0487-3.
  18. ↑ Bartmess JE, Scott JA, McIver RT (September 1979). "Scale of acidities in the gas phase from methanol to phenol". Journal of the American Chemical Society. 101 (20): 6046–6056. doi:10.1021/ja00514a030.
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