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# Bond Energies in Polyatomic Molecules

Author: John Hutchinson

The bond energy for a molecule is the energy required to separate the two bonded atoms to great distance. We recall that the total energy of the bonding electrons is lower when the two atoms are separated by the bond distance than when they are separated by a great distance. As such, the energy input required to separate the atoms elevates the energy of the electrons when the bond is broken.

We can use diatomic bond energies to calculate the heat of reaction ΔH for any reaction involving only diatomic molecules. We consider two simple examples. First, the reaction

 H2(g)+Br(g) H(g)+HBr(g) [7]

is observed to be endothermic with heat of reaction 70 kJ/mol. Note that this reaction can be viewed as consisting entirely of the breaking of the H2 bond followed by the formation of the HBr bond. Consequently, we must input energy equal to the bond energy of H2 (436 kJ/mol), but in forming the HBr bond we recover output energy equal to the bond energy of HBr (366 kJ/mol). Therefore the heat of equation 7 at constant pressure must be equal to difference in these bond energies, 70 kJ/mol.

Now we can answer the question, at least for this reaction, of where the energy "goes" during the reaction. The reason this reaction absorbs energy is that the bond which must be broken, H2, is stronger than the bond which is formed, HBr. Note that energy is released when the HBr bond is formed, but the amount of energy released is less than the amount of energy required to break the H2 bond in the first place.

The second example is similar:

 H2(g)+Br2(g) 2 HBr(g) [8]

This reaction is exothermic with ΔH°=-103 kJ/mol. In this case, we must break an H2 bond, with energy 436 kJ/mol, and a Br2 bond, with energy 193 kJ/mol. Since two HBr molecules are formed, we must form two HBr bonds, each with bond energy 366 kJ/mol. In total, then, breaking the bonds in the reactants requires 629 kJ/mol, and forming the new bonds releases 732 kJ/mol, for a net release of 103 kJ/mol. This calculation reveals that the reaction is exothermic because, although we must break one very strong bond and one weaker bond, we form two strong bonds.

There are two items worth reflection in these examples. First, energy is released in a chemical reaction due to the formation of strong bonds. Breaking a bond, on the other hand, always requires the input of energy. Second, equation 8 does not actually proceed by the two-step process of breaking both reactant bonds, thus forming four free atoms, followed by making two new bonds. The actual process of the reaction is significantly more complicated. The details of this process are irrelevant to the energetics of the reaction, however, since, as we have shown, the heat of reaction ΔH does not depend on the path of the reaction. This is another example of the utility of Hess' law. We now proceed to apply this bond energy analysis to the energetics of reactions involving polyatomic molecules. A simple example is the combustion of hydrogen gas discussed previously here. This is an explosive reaction, producing 483.6 kJ per mole of oxygen. Calculating the heat of reaction from bond energies requires us to know the bond energies in H2O. In this case, we must break not one but two bonds:

 H2O(g) 2H(g)+O(g) [9]

The energy required to perform this reaction is measured to be 926.9 kJ/mol. equation 4 can proceed by a path in which we first break two H2 bonds and one O2 bond, then we follow the reverse of equation 9 twice:

 2 H2(g)+O2(g) 4H(g)+2 O(g) [10]

4 H(g)+2 O(g) 2 H2O(g)
2 H2(g)+O2(g) 2 H2O(g)

Therefore, the energy of equation 4 must be the energy required to break two H2 bonds and one O2 bond minus twice the energy of equation 9. We calculate that ΔH° = 2*(436 kJ/mol) + 498.3 kJ/mol - 2*(926.9 kJ/mol) = -483.5 kJ/mol. It is clear from this calculation that equation 4 is strongly exothermic because of the very large amount of energy released when two hydrogen atoms and one oxygen atom form a water molecule.

It is tempting to use the heat of equation 9 to calculate the energy of an O-H bond. Since breaking the two O-H bonds in water requires 926.9 kJ/mol, then we might infer that breaking a single O-H bond requires 926.9 kJ/mol/2 = 463.5 kJ/mol. However, the reaction

 H2O(g) OH(g)+H(g) [11]

has ΔH°=492 kJ/mol. Therefore, the energy required to break an O-H bond in H2O is not the same as the energy required to break the O-H bond in the OH diatomic molecule. Stated differently, it requires more energy to break the first O-H bond in water than is required to break the second O-H bond.

In general, we find that the energy required to break a bond between any two particular atoms depends upon the molecule those two atoms are in. Considering yet again oxygen and hydrogen, we find that the energy required to break the O-H bond in methanol (CH3OH) is 437 kJ/mol, which differs substantially from the energy of equation 11. Similarly, the energy required to break a single C-H bond in methane (CH4) is 435 kJ/mol, but the energy required to break all four C-H bonds in methane is 1663 kJ/mol, which is not equal to four times the energy of one bond. As another such comparison, the energy required to break a C-H bond is 400 kJ/mol in trichloromethane (HCCl3), 414 kJ/mol in dichloromethane (H2CCl2), and 422 kJ/mol in chloromethane (H3CCl).

These observations are somewhat discouraging, since they reveal that, to use bond energies to calculate the heat of a reaction, we must first measure the bond energies for all bonds for all molecules involved in that reaction. This is almost certainly more difficult than it is desirable. On the other hand, we can note that the bond energies for similar bonds in similar molecules are close to one another. The C-H bond energies in the three chloromethanes above illustrate this quite well. We can estimate the C-H bond energy in any one of these chloromethanes by the average C-H bond energy in the three chloromethanes molecule, which is 412 kJ/mol. Likewise, the average of the C-H bond energies in methane is 1663 kJ/mol / 4 = 416 kJ/mol and is thus a reasonable approximation to the energy required to break a single C-H bond in methane.

By analyzing many bond energies in many molecules, we find that, in general, we can approximate the bond energy in any particular molecule by the average of the energies of similar bonds. These average bond energies can then be used to estimate the heat of a reaction without measuring all of the required bond energies. Consider for example the combustion of methane to form water and carbon dioxide:

 CH4(g)+2 O2(g) CO2(g)+2 H2O(g) [12]

We can estimate the heat of this reaction by using average bond energies. We must break four C-H bonds at an energy cost of approximately 4×412 kJ/mol and two O2 bonds at an energy cost of approximately 2×496 kJ/mol. Forming the bonds in the products releases approximately 2×743 kJ/mol for the two C=O double bonds and 4×463 kJ/mol for the O-H bonds. Net, the heat of reaction is thus approximately ΔH°=1648+992-1486-1852 = -698 kJ/mol. This is a rather rough approximation to the actual heat of combustion of methane, -890 kJ/mol. Therefore, we cannot use average bond energies to predict accurately the heat of a reaction. We can get an estimate, which may be sufficiently useful. Moreover, we can use these calculations to gain insight into the energetics of the reaction. For example, equation 12 is strongly exothermic, which is why methane gas (the primary component in natural gas) is an excellent fuel. From our calculation, we can see that the reaction involved breaking six bonds and forming six new bonds. The bonds formed are substantially stronger than those broken, thus accounting for the net release of energy during the reaction.

Last Update: 2011-04-08