# How can enthalpy changes for a reaction be estimated from bond energies?

I have a problem on a worksheet that reads as:

Estimate the enthalpy change for the reaction 2CO + O2 2 CO2 given the following bond energies: BE(CO) = 1074 kJ, BE(O=O) = 499 kJ, BE(C=O) = 802 kJ.

I have done change in enthalpy but i do not understand the format on this one. If you can help I would sincerely appreciate it.
Will Aycock 7/10/99

 Vocabulary bond energy enthalpy of reaction heat capacity Hess's law thermochemical equation work
Enthalpies of reaction are determined in large part by three things:

1. Energy is absorbed when bonds break. Imagine stretching a rubber band until it breaks. You must do work to stretch the band because the tension in the band opposes your efforts. You lose energy; the band gains it. Something similar happens when bonds break in a chemical reaction. The energy required to break the bonds is absorbed from the surroundings. (See a previous question about how energy transforms for more.)

2. Energy is released when bonds form. If breaking a bond absorbs energy from the surroundings, forming a bond must release energy. If that weren't so, it would be possible to destroy energy by repeatedly breaking and reforming a bond.

3. Energy is absorbed or released when the heat capacities of the products and reactants differ. Molecules can store energy in a variety of different ways. The products can absorb some of the energy produced by the reaction. (This is an important consideration in choosing rocket fuels, because energy absorbed by exhaust gases isn't available as thrust).

The heat capacity contribution is often small enough to be neglected, and most of the heat absorbed or released in a reaction comes from making and breaking of bonds during the reaction.

If there was some way to figure out how much energy a single bond absorbed when broken, the enthalpy of reaction could be estimated by subtracting the bond energies for bonds formed from the total bond energies for bonds broken. For example, if we know that

 O2(g) 2 O(g) H°0 = 490.4 kJ H2(g) 2 H(g) H°0 = 431.2 kJ H2O(g) 2 H(g) + O(g) H°0 = 915.6 kJ
we can estimate the bond enthalpies of O=O, H-H, and O-H as 490.4 kJ/mol, 431.2 kJ/mol, and 457.7 kJ/mol, respectively. Now suppose we need to know estimate how much heat is liberated by burning hydrogen gas in pure oxygen by the following reaction:
2 H2(g) + O2(g) 2 H2O(g)   0 = ?

 moles ofbonds broken Energyabsorbed (kJ) moles of bonds formed Energyreleased (kJ) 2 H-H @ 431.2 kJ each 862.4 4 O-H @ 457.7 kJ each 1830.9 kJ 1 O=O @ 490.4 kJ each 490.4 1352.7 1830.9
so the enthalpy for the reaction as written is 1352.7 - 1830.9 kJ, or 0 = -478.2 kJ. (Remember that the minus sign means "energy released", so you add the bond energies for broken bonds and subtract energies for bonds formed to get the total energy.)

A calculation based on enthalpies of formation give 298 = -483.7 kJ for the same reaction. Why don't the two results agree? Part of the discrepancy is due to differences in heat capacity between the reactants and products, which were ignored completely in the calculation based on bond energies. But most of the error is due to the fact that bonds in a molecule influence each other, which means that bond energies aren't really additive. An O-H bond in a water molecule has a slightly different energy than an O-H bond in H2O2, because it's in a slightly different environment.

Reaction enthalpies calculated from bond energies are very rough approximations!

Bond energies aren't appropriate for directly predicting enthalpies of reactions that occur in liquids, solutions, or solids, because they account only for bond breaking and making within molecules, and neglect attractions that are broken and formed between molecules. If you want to predict condensed phase reaction enthalpies, you'll have to build steps for vaporizing and recondensing all the reactants and products into your calculation.

Author: Fred Senese senese@antoine.frostburg.edu

General Chemistry Online! How can enthalpy changes for a reaction be estimated from bond energies?