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The bond-dissociation energy (BDE, ''D''0, or ''DH°'') is one measure of the
strength Strength may refer to: Physical strength *Physical strength, as in people or animals * Hysterical strength, extreme strength occurring when people are in life-and-death situations *Superhuman strength, great physical strength far above human c ...
of a
chemical bond A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
. It can be defined as the standard
enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
change when is cleaved by homolysis to give fragments A and B, which are usually radical species. 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 Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibration ...
), although the enthalpy change at 298 K (
standard conditions Standard temperature and pressure (STP) are standard sets of conditions for experimental measurements to be established to allow comparisons to be made between different sets of data. The most used standards are those of the International Union ...
) is also a frequently encountered parameter. As a typical example, the bond-dissociation energy for one of the C−H bonds in
ethane Ethane ( , ) is an organic chemical compound with chemical formula . At standard temperature and pressure, ethane is a colorless, odorless gas. Like many hydrocarbons, ethane is isolated on an industrial scale from natural gas and as a petroc ...
() is defined as the standard enthalpy change of the process : , : ''DH''°298() = Δ''H°'' = 101.1(4) kcal/mol = 423.0 ± 1.7 kJ/mol = 4.40(2)  eV (per bond). 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 The pyrolysis (or devolatilization) process is the thermal decomposition of materials at elevated temperatures, often in an inert atmosphere. It involves a change of chemical composition. The word is coined from the Greek-derived elements ''py ...
or
photolysis Photodissociation, photolysis, photodecomposition, or photofragmentation is a chemical reaction in which molecules of a chemical compound are broken down by photons. It is defined as the interaction of one or more photons with one target molecule. ...
, measurements of
chemical kinetics Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in wh ...
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 (4–10 kJ/mol). Moreover, values measured in the past, especially before the 1970s, can be especially unreliable and 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 modern 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. 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.


Definitions and related parameters

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 (''D''0) 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 ''D''0(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 Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple re ...
of the bond, ''D''e, known as the ''electronic energy''. This is due to the existence of a
zero-point energy Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty pri ...
ε0 for the vibrational ground state, which reduces the amount of energy needed to reach the dissociation limit. Thus, ''D''0 is slightly less than ''D''e, and the relationship ''D''0 = ''D''e − ε0 holds. The bond dissociation energy is an enthalpy change of a particular chemical process, namely homolytic bond cleavage, and "bond strength" as measured by the BDE should not be regarded as an intrinsic property of a particular bond type but rather as an energy change that depends on the chemical context. For instance, Blanksby and Ellison cites the example of ketene (H2C=CO), which has a C=C bond dissociation energy of 79 kcal/mol, while ethylene (H2C=CH2) has a bond dissociation energy of 174 kcal/mol. This vast difference is accounted for by the thermodynamic stability of carbon monoxide (CO), formed upon the C=C bond cleavage of ketene. The difference in availability of spin states upon fragmentation further complicates the use of BDE as a measure of bond strength for head-to-head comparisons, and force constants have been suggested as an alternative. 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 (Δ''G''°) 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''). 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 (p''K''a) and standard redox potentials (ε°) that are measured in solution.


Bond energy

Except for
diatomic molecules Diatomic molecules () are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen () or oxygen (), then it is said to be homonuclear. Ot ...
, the bond-dissociation energy differs from the ''
bond energy In chemistry, bond energy (''BE''), also called the mean bond enthalpy or average bond enthalpy is the measure of bond strength in a chemical bond. IUPAC defines bond energy as the average value of the gas-phase bond-dissociation energy (usually ...
''. 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. For a homoleptic compound EX''n'', the E–X bond energy is (1/''n'') multiplied by the enthalpy change of the reaction EX''n'' → E + ''n''X. 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 HOH bond of a water molecule (H2O) requires 118.8 kcal/mol (497.1 kJ/mol). The dissociation of the remaining
hydroxyl radical The hydroxyl radical is the diatomic molecule . The hydroxyl radical is very stable as a dilute gas, but it decays very rapidly in the condensed phase. It is pervasive in some situations. Most notably the hydroxyl radicals are produced from the ...
requires 101.8 kcal/mol (425.9 kJ/mol). The bond energy of the covalent OH bonds in water is said to be 110.3 kcal/mol (461.5 kJ/mol), the average of these values. 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.


Strongest bonds and weakest bonds

According to 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). The BDE for F3Si−F is even larger, at 166 kcal/mol. One consequence to these data are that many reactions generate silicon fluorides, such as glass etching,
deprotection A protecting group or protective group is introduced into a molecule by chemical modification of a functional group to obtain chemoselectivity in a subsequent chemical reaction. It plays an important role in multistep organic synthesis. In man ...
in organic synthesis, and volcanic emissions. The strength of the bond is attributed to the substantial electronegativity difference between silicon and fluorine, which leads to a substantial contribution from both ionic and covalent bonding to the overall strength of the bond. The C−C single bond of diacetylene (HC≡C−C≡CH) linking two sp-hybridized carbon atoms is also among the strongest, at 160 kcal/mol. The strongest bond for a neutral compound, including multiple bonds, is found in carbon monoxide at 257 kcal/mol. The protonated forms of CO, HCN and N2 are said to have even stronger bonds, although another study argues that the use of BDE as a measure of bond strength in these cases is misleading. On the other end of the scale, there is no clear boundary between a very weak covalent bond and an intermolecular interaction. Lewis acid–base complexes between transition metal fragments and noble gases are among the weakest of bonds with substantial covalent character, with (CO)5W:Ar having a W–Ar bond dissociation energy of less than 3.0 kcal/mol. Held together entirely by the
van der Waals force In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and th ...
,
helium dimer The helium dimer is a van der Waals molecule with formula He2 consisting of two helium atoms. This chemical is the largest diatomic molecule—a molecule consisting of two atoms bonded together. The bond that holds this dimer together is so weak ...
, He2, has the lowest measured bond dissociation energy of only 0.021 kcal/mol.


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: : 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 a solvent.


Representative bond energies

The data tabulated below shows how bond strengths vary over the periodic table. There is great interest, especially in
organic chemistry Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J.; ...
, concerning relative strengths of bonds within a given group of compounds, and representative bond dissociation energies for common organic compounds are shown below.


See also

*
Bond energy In chemistry, bond energy (''BE''), also called the mean bond enthalpy or average bond enthalpy is the measure of bond strength in a chemical bond. IUPAC defines bond energy as the average value of the gas-phase bond-dissociation energy (usually ...
*
Electronegativity Electronegativity, symbolized as , is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the d ...
*
Ionization energy Ionization, or Ionisation is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule i ...
*
Electron affinity The electron affinity (''E''ea) of an atom or molecule is defined as the amount of energy released when an electron attaches to a neutral atom or molecule in the gaseous state to form an anion. ::X(g) + e− → X−(g) + energy Note that this is ...
*
Lattice energy In chemistry, the lattice energy is the energy change upon formation of one mole of a crystalline ionic compound from its constituent ions, which are assumed to initially be in the gaseous state. It is a measure of the cohesive forces that bind ...


References

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Dissociation energy The bond-dissociation energy (BDE, ''D''0, or ''DH°'') is one measure of the strength of a chemical bond . It can be defined as the standard enthalpy change when is cleaved by homolysis to give fragments A and B, which are usually radical s ...
Binding energy