0.13 Reaction energy and bond energy  (Page 6/7)

The energy required to perform this reaction is measured to be 926.9 kJ/mol. Therefore, the energy of [link] must be the energy required to break two H ₂ bonds and one O ₂ bond minus twice the energy of [link] . We calculate that ΔHº = 2(436 kJ/mol) + (498.3 kJ/mol) – 2(926.9 kJ/mol) = –483.5 kJ/mol, which agrees with the measured enthalpy of formation. What we learn from this calculation is that the combustion of hydrogen gas in [link] is strongly exothermic because of the very large amount of energy released when two hydrogen atoms and one oxygen atom form a water molecule.

Let’s look a little more closely at [link] . It is tempting to use the energy of [link] to calculate the energy of an O-H bond, since we break two O-H bonds in the reaction and breaking the two O-H bonds in water requires 926.9 kJ/mol. It must be true that both O-H bonds are identical, so it seems that breaking a single O-H bond requires (926.9 kJ/mol)/2 = 463.5 kJ/mol.

We can check this by looking at the energy of the reaction

in which only one O-H bond is broken. Data tell us that the energy of this reaction is 492 kJ/mol. This is quite a bit higher than what we just predicted. Where did we go wrong with our prediction?

If we compare [link] and [link] and use Hess’ Law, we can calculate the energy of breaking the bond in an OH(g) molecule:

Therefore, the energy required to break an O-H bond in H ₂ O is quite a bit different than 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. Does this mean that the two bonds in H ₂ O are not the same? Of course, the two bonds in H ₂ O are identical so they have the same bond strength. However, after the first O-H bond is broken, the O-H bond which remains no longer has the same bond strength. Once the first H atom has departed, along with its electron, the bonding of the atoms left behind has changed. It’s pretty clear that the remaining O-H bond is weakened when the first O-H bond is broken.

Our observation that different O-H bonds have different bond energies is general when we look at more data. For example, we find that the energy required to break the O-H bond in methanol (CH ₃ OH) is 437 kJ/mol, which differs substantially from the energy of [link] and differs somewhat from the energy in [link] .

This makes sense, but it does greatly complicate our measurements and calculations. To be able to use bond energies to calculate reaction energies, we would need to know the energy of each successive bond breaking in a molecule with more than one bond. This would be an overwhelming amount of data to collect and store. Rather than become discouraged, we need to develop a model and this requires more observations.

Let’s consider C-H bonds. The energy required to break a single C-H bond in methane (CH ₄ ) 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. This means that breaking each C-H bond in succession gives different energies each time. As another such comparison, the energy required to break a C-H bond is 400 kJ/mol in trichloromethane (HCCl ₃ ), 414 kJ/mol in dichloromethane (H ₂ CCl ₂ ), and 422 kJ/mol in chloromethane (H ₃ CCl).