# Bond Energies

The bond energy is a measure of the amount of energy needed to break apart one mole of covalently bonded gases. The SI units used to describe bond energy is kiloJoules per mole of bonds (kJ/mol).

### Introduction

Atoms bond together to form compounds because in doing so they attain lower energies than they possess as individual atoms. A quantity of energy, equal to the difference between the energies of the bonded atoms and the energies of the separated atoms, is released, usually as heat. That is, the bonded atoms have a lower energy than the individual atoms do. When atoms combine to make a compound, energy is always given off, and the compound has a lower overall energy.

When a chemical reaction occurs, molecular bonds are broken and other bonds are formed to make different molecules. For example, the bonds of two water molecules are broken to form hydrogen and oxygen.

$2H_2O \rightarrow 2H_2 + O_2$

Bonds do not break and form spontaneously-an energy change is required. The energy input required to break a bond is known as bond energy. While the concept may seem simple, bond energy serves a very important purpose in describing the structure and characteristics of a molecule. It can be used to determine which Lewis Dot Structure is most suitable when there are multiple Lewis Dot Structures.

When a bond is strong, there is a higher bond energy because it takes more energy to break a strong bond. This correlates with Bond Order and Bond Length. When the Bond Order is higher, bond length is shorter, and the shorter the bond length means a greater the Bond Energy because of increased electric attraction. In general, the shorter the bond length, the greater the bond energy.

Think about it this way: it is easy to snap a pencil, but if you keep snapping the pencil it gets harder each time since the length of the pencil decreases. A higher bond energy (or a higher bond order or shorter bond length) means that a bond is less likely to break apart. In other words, it is more stable than a molecule with a lower bond energy. With Lewis Structures then, the structure with the higher bond energy is  more likely to occur.

### Average Bond Energy

Although each molecule has its own characteristic bond energy, some generalizations are possible. For example, although the exact value of a C–H bond energy depends on the particular molecule, all C–H bonds have a bond energy of roughly the same value because they are all C–H bonds. It takes roughly 100 kcal of energy to break 1 mol of C–H bonds, so we speak of the bond energy of a C–H bond as being about 100 kcal/mol. A C–C bond has an approximate bond energy of 80 kcal/mol, while a C=C has a bond energy of about 145 kcal/mol. We can calculate a more general bond energy by finding the average of the bond energies of a specific bond in different molecules to get the average bond energy.

 Average Bond Energies (kJ/mol) Single Bonds Multiple Bonds H—H 432 N—H 391 I—I 149 C = C 614 H—F 565 N—N 160 I—Cl 208 C ≡ C 839 H—Cl 427 N—F 272 I—Br 175 O = O 495 H—Br 363 N—Cl 200 C = O* 745 H—I 295 N—Br 243 S—H 347 C ≡ O 1072 N—O 201 S—F 327 N = O 607 C—H 413 O—H 467 S—Cl 253 N = N 418 C—C 347 O—O 146 S—Br 218 N ≡ N 941 C—N 305 O—F 190 S—S 266 C ≡ N 891 C—O 358 O—Cl 203 C = N 615 C—F 485 O—I 234 Si—Si 340 C—Cl 339 Si—H 393 C—Br 276 F—F 154 Si—C 360 C—I 240 F—Cl 253 Si—O 452 C—S 259 F—Br 237 Cl—Cl 239 Cl—Br 218 Br—Br 193 *C == O(CO2) = 799

Average bond energies are the averages of bond dissociation energies (see Table T3 for more complete list). For example the average bond energy of O-H in H2O is 464 kJ/mol. This is due to the fact that the H-OH bond requires 498.7 kJ/mol to dissociate, while the O-H bond needs 428 kJ/mol.
$\dfrac{498.7\; kJ/mol + 428\; kJ/mol}{2}=464\; kJ/mol$

When more bond energies of the bond in different molecules that are taken into consideration, the average will be more accurate. Keep in mind that:

• Average bonds values are not as accurate as a molecule specific bond-dissociation energies.
• Double bonds are higher energy bonds in comparison to a single bond (but not necessarily 2-fold higher).
• Triple bonds are even higher energy bonds than double and single bonds (but not necessarily 3-fold higher).

### Bond Breakage and Formation

When a chemical reaction occurs, the atoms in the reactants rearrange their chemical bonds to make products. The new arrangement of bonds does not have the same total energy as the bonds in the reactants. Therefore, when chemical reactions occur, there will always be an accompanying energy change.

In some reactions, the energy of the products is lower than the energy of the reactants. Thus, in the course of the reaction, the substances lose energy to the surrounding environment. Such reactions are exothermic and can be represented by an energy-level diagram like the one shown below. In most cases, the energy is given off as heat (although a few reactions give off energy as light).

Figure: Exothermic Reactions. For an exothermic chemical reaction, energy is given off as reactants are converted to products.

In chemical reactions where the products have a higher energy than the reactants, the reactants must absorb energy from their environment to react. These reactions are endothermic and can be represented by an energy-level diagram like the one shown below.

Figure: Endothermic Reactions. For an endothermic chemical reaction, energy is absorbed as reactants are converted to products.

Note: Temperature is Neither a Reactant nor Product

It is not uncommon that textbooks and instructors to consider heat as a independent "species" in a reaction. While this is rigorously incorrect because one cannot "add or remove heat" to a reaction as with species, it serves as a convenient mechanism to predict the shift of reactions with changing temperature. For example, if heat is a "reactant" ($$\Delta{H} > 0$$), then the reaction favors the formation of products at elevated temperature. Similarly, if heat is a "product" ($$\Delta{H} < 0$$), then the reaction favors the formation of reactants. A more accurate, and hence preferred, description is discussed below.

Exothermic and endothermic reactions can be thought of as having energy as either a product of the reaction or a reactant. Exothermic reactions give off energy, so energy is a product. Endothermic reactions require energy, so energy is a reactant.

Example 1

Is each chemical reaction exothermic or endothermic?

1. $$2H_{2(g)} + O_{2(g)} \rightarrow 2H_2O_{(ℓ)} + \text{135 kcal}$$
2. $$N_{2(g)} + O_{2(g)} + \text{45 kcal} \rightarrow 2NO_{(g)}$$

SOLUTION

1. Because energy is a product, energy is given off by the reaction. Therefore, this reaction is exothermic.
2. Because energy is a reactant, energy is absorbed by the reaction. Therefore, this reaction is endothermic.

Example 2

What is the enthalpy change for this reaction and is it endothermic or exothermic?
$H_2(g)+I_2(g) \rightarrow 2HI(g)$
SOLUTION

First look at the equation and determine what bonds exist.

• one H-H bond,
• one I-I bond, and
• two H-I bonds

Then examine the bond breakage which is located in the reactant side:

• 1 mol H-H bonds: 436 kJ/mol
• 1 mol I-I bonds: 151 kJ/mol

The sum of enthalpies on the reaction side is: 436 kJ/mole + 151 kJ/mole = 587 kJ/mol. This is how much energy is needed to break the bonds on the reactant side.

Then we look at the bond formation which is on the product side:

• 2 mol H-I bonds: 297 kJ/mol

The sum of enthalpies on the product side is 2 x 297 kJ/mol= 594 kJ/mol. This is how much energy is needed to break the bonds on the product side.

• The net change of the reaction is therefore 594-587= +7 kJ/mol. Since this is positive ($$\Delta{H}>0$$, the reaction is exothermic.

Hess's Law relates to this equation as it depicts how the energy of the overall reaction is equal to the sum of the individual steps involving energy change.

### Summary

The breakage and formation of bonds is similar to a relationship: you can either get married or divorced and it is more favorable to be married.

• Energy is released to make bonds, which is why the enthalpy change for breaking bonds is positive.
• Energy is required to break bonds. Atoms are much happier when they are "married" and release energy because it is easier and more stable to be in a relationship (e.g., to generate octet electronic configurations). The enthalpy change is negative because the system is releasing energy when forming bond.

### Problems

1. What is the definition of bond energy? When is energy released and absorbed?
2. If the bond energy for H-Cl is 431 kJ/mol. What is the overall bond energy of 2 moles of HCl?
3. Using the bond energies given in the chart above, find the enthalpy change for: the decomposition of water $2H_2O (g) \rightarrow 2H_2 + O_2 (g)$
4. Is the reaction written above exothermic or endothermic? Explain.
5. Which bond in this list has the highest bond energy? The lowest? H-H, H-O, H-I, H-F.

#### Solutions

1. Bond energy is the energy required to break a bond that exists between two atoms. Energy is given off when the bond is broken, but is absorbed when a new bond is created.
2. Simply multiply the average bond energy of H-Cl by 2. This leaves you with 862 kJ/mol (see Table T3).
3. The enthalpy change deals with breaking two mole of O-H bonds and the formation of 1 mole of O-O bonds and two moles of H-H bonds (see Table T3).
• The sum of the energies required to break the bonds on the reactants side is 4 x 460 kJ/mol = 1840 kJ/mol.
• The sum of the energies released to form the bonds on the products side is
• 2 moles of H-H bonds = 2 x 436.4 kJ/mol = 872.8 kJ/mol
• 1 moles of O=O bond = 1 x 498.7 kJ/mil = 498.7 kJ/mol

which is an output (released) energy = 872.8 kJ/mol + 498.7 kJ/mol = 1371.5 kJ/mol.

Total energy difference is 1840 kJ/mol – 1371.5 kJ/mol = 469 kJ/mol, which indicates that the reaction is endothermic and that 469 kJ of heat is needed to be supplied to carry out this reaction.

1. For this question simply look at the number you calculated as your enthalpy of reaction. Is it positive or negative? It is positive so this means that it is in fact endothermic. It requires energy in order to create bonds.
2. H-F has the highest bond energy since the difference in electronegativity is the greatest. However, the H-I bond is the lowest bond (not due to the electronegativity difference, but due to the greater size of the I atom).

### References

1. Petrucci, Ralph H., Harwood, William S., Herring, F. G., and Madura Jeffrey D. General Chemistry: Principles and Modern Applications. 9th ed. Upper Saddle River: Pearson Education, Inc., 2007.
2. Carruth, Gorton, Ehrlich, Eugene. "Bond Energies." Volume Library. Ed. Carruth, Gorton. Vol 1. Tennessee: Southwestern, 2002.
3. "Bond Lengths and Energies." UWaterloo, n.d. Web. 21 Nov 2010. <http://www.science.uwaterloo.ca/~cch...20/bondel.html>
4. "Bond Energy." N.p., n.d. Web. 21 Nov 2010. <http://users.rcn.com/jkimball.ma.ult...ndEnergy.htmll>.
5. For more practice problems:  http://www.chalkbored.com/lessons/chemistry-11/bond-energies-worksheet.pdf

### Contributors

• Kim Song (UCD), Donald Le (UCD)

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