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Bond Energy

Definition

            When a bond is formed between two atoms, energy is released. The same amount of energy is absorbed when the bond is broken to form neutral atoms. So, ‘’the bond energy is the average amount of energy required to break all bonds of a particular type in one mole of the substance’’.

Explanation

It is determined experimentally, by measuring the heat involved in a chemical reaction. It is also called bond enthalpy as it is a measure of enthalpy change at 298 K.

The enthalpy change in splitting a molecule into its component atoms is called enthalpy of atomization.

IUPAC defines the average value of bond disassociation energies in the gas phase for all same chemical species of the same type of bond. For example carbon-hydrogen bond energy in methane H(C-H), their enthalpy change involved with breaking up the molecule of methane into carbon atom and four hydrogen radicals divided by 4 [1].

The bond energy is given in kJ/mol which is the energy required to break an Avogadro’s number (6.02 x 1022) of bonds. It is also released when an Avogadro’s number of the bonds are formed. It may be noted that energies of multiple bonds are greater than those of single bonds. But a double bond is not twice as strong as a single bond or a triple bond is not as strong as a single bond.it means that σ- bond is stronger than a π- bond. Similarly a polar covalent bond stronger than a non- polar covalent bond.

Factors Affecting Bond Energy

Bond energy is the measure of the strength of a bond. The strength of the bond depends upon the following factors [2].

  1. Electronegativity difference of bonded atom
  2. Sizes of the atom
  3. Bond length

Electronegativity difference of bonded atom

The bond energies of H-X type of compounds, where X= F, Cl, Br, I. electrons are nor equally shared between the bonded atoms i.e. HX. As halogen atom is more electronegative, the bonded pair is more attracted towards X atom and thereby polarity develop. This give rise to additional attractive force for binding.

For example: calculate the increase in the strength of H-Cl bond due to ionic character present in it.

The H-H bond energy is 436 kJ/mol

                                       H + H → H2                                ΔH = -436 kJ/mol

It means 436 kJ/mol of heat is required to break the Avogadro’s number of H2 molecules into individual atoms. Thus, bond energy per bond is 72.42 x 1023 kJ/mol. This is obtained by dividing 436 by 6.02 x 10 23. As the bonding electron pair is equally shared between the two H-atoms, we assume that each bonded H-atom contributes half of the bond energy i.e., 36.21 x1023Kj/mol.

Similarly, the bond energy for Cl2 is 240 kJ/mol. Therefore each Cl-atom should contribute 19.93 x 1023 kJ to any bond where sharing of an electron pair is equal. This bond is polar so bond energy of H-Cl is 56.14 x 1023 kJ per molecule which is the sum of 36.21 x1023 and 19.93 x 1023 kJ. For Avogadro’s number of HCl molecule, the calculated bond energy is 337.96 kJ/mol, which is obtained by multiplying 56.14 x 10 23 with 6.02 x 1023.

The bonds with higher bond energy values have shorter bond lengths. The bond energies of C to C bonds being in the order C=C ˃ C=C ˃ C-C. Their bond length are in the reverse order i.e., C-C ˃ C=C ˃ C=C

Size of the Atom

There is a direct relationship between the size of atom and bond dissociation. Larger the atomic size of atom lesser the energy will be required to break the bond. For example HI. Iodine is larger as compared to other elements in the halogens group so the attraction from the nucleus and outermost orbit is low. So a small amount of energy is required to break the bond.

Bond length

The distance between the nuclei of two atoms forming a covalent bond is called the bond length. The bond lengths are experimentally determined by physical techniques [3]. The techniques may be electron diffraction, X-ray diffraction or spectral studies. The covalent bond length between two atoms is often but not always independent of the nature of the molecules. For example, the bond length of C-C is 154 pm, it is also found to be same in the diamond.

The covalent radii for different elements are almost addictive in nature. The single bond covalent radius of carbon is 77 pm which is half of the C-C bond length (154 pm). Similarly, the covalent radius of Cl is 99 pm i.e. one half of the Cl-Cl bond length (198). So the bond length of C-Cl will be 77 + 99 =176 pm.

With the increase in electronegativity difference between the bonded atoms, the bond becomes shortened. The ionic character results in shortening of the bond length due to the force of attraction between polar ends. Moreover, the hybridization scheme involved, also explains the shortening of bonds due to the predominant participation of s- orbitals. Since, the 2s- orbital of carbon has a smaller mean radius than the 2p-orbitals, greater the s character in the hybrid orbital shorter will be the bond distance. Thus C-C bond lengths are 154, 133 and 120pm for ethane, ethane and ethyne. The π bonding also reduces bond distance. The bond length increases as we move from top to bottom in IV-A group of the periodic table. Thus Si-Si bond length is greater than C-C in group IV-A and P-P bond length is greater than N-N. As the atomic radii increases in the group, the effect of the effective nuclear charge decreases on electron.

            In the periodic table shortening of bond, length occurs from left to right in a periodic table. Therefore C-C bond length is greater than N-N bond length.

Enthalpy changes of reaction from bond enthalpies

In Gaseous Phase

In gas-phase we can easily use bond enthalpies [4]. For example in the reaction of carbon monoxide and steam hydrogen is produced.

             CO (g) + H2O (g) → CO2 (g) + H2 (g)

 The bond enthalpies are:

  Bond enthalpy (kJ/mol)
C-O in carbon monoxide +1077
C-O in carbon dioxide +805
O-H +464
H-H +436

Now solve the equation to find the enthalpy change in the reaction.

ΔH + 2(805) +436 = 1077 + 2(464)

ΔH= 1077 + 2(464) – 2(805) – 436

ΔH= -41 kJ/mol

Shortcut method for simple cases

In some cases where there is small changes occur in the molecule like chlorine reacts with ethane and produce chloroethane and hydrogen chloride.

                                       C2H6 + Cl2 → C2H5Cl + HCl

The changed is that actually C-H bond and Cl-Cl bond broken and made a new C-Cl bond and H-Cl bond.

  Bond enthalpy (kJ/mol)
C-H +413
Cl-Cl +243
C-Cl +346
H-Cl +432

Energy required to break C-H and C-Cl

+413 + 243 = +656 kJ/mol

Energy released when make C-Cl and H-Cl

-346 – 432 =-778 kJ/mol

So net change is +656-778= -122 kJ/mol

Liquid phase

Bond energy is working directly in the gas phase but in liquid extra energy is required to convert liquid into gas that is called enthalpy change of vaporization. It is represented by the symbol ΔHvap or ΔHv.

This enthalpy change is defined as when 1 mole of the liquid convert into gas at its boiling point with a pressure of 1 bar.

For water: ΔHvap is +41 kJ/mol, it means that it take 41 kJ to change 1 mol of water into steam, changing liquid into gas required heat and reverse back reaction of changing gas to liquid also required same amount of heat,

For example, combustion of methane       

                 CH4 + 2O2 → CO2 + 2 H2O

     The bond enthalpies are

  Bond enthalpy (kJ/mol)
C-H +413
O=O +498
C=O in carbon dioxide +805
O-H +464

Now calculations

ΔH +2(805) + 2(41) + 4(464) = 4(413) + 2(498)

ΔH = 4(413) + 2(498) – 2(805) – 2(41) – 4(464)

ΔH= -900 kJ/mol

References

  1.  IUPACCompendium of Chemical Terminology, 2nd ed. (the “Gold Book”) (1997). Online corrected version:  (2006–) “Bond energy (mean bond energy)“. doi:10.1351/goldbook.B00701
  2. https://en.wikipedia.org/wiki/Bond_energy
  3. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Chemical_Bonding/Fundamentals_of_Chemical_Bonding/Chemical_Bonds/Bond_Lengths_and_Energies
  4. https://www.chemguide.co.uk/physical/energetics/bondenthalpies.html
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