1.4 The Covalent Bond: Bond Energy and Bond Length

In a compound, nuclei are held together by chemical bonds. Two types of fundamental bonds in chemistry are the covalent bond and the ionic bond (see Section 1.8). A covalent bond is characterized by the sharing of valence electrons between two or more atoms, as shown for two H atoms in a molecule of H2 (hydrogen gas) in Figure 1-9.

Lewis structures show the formation of a hydrogen molecule from covalent bonding between two isolated hydrogen atoms. Each hydrogen atom has an electron, and a covalent bond between these two electrons bring the two isolated atoms together to form a hydrogen molecule. The caption reads, �A covalent bond: A covalent bond is the sharing of two electrons between nuclei.�
FIGURE 1-9 A covalent bond A covalent bond is the sharing of two electrons between nuclei.

In Section 1.5, we will explore how various molecules can be constructed from atoms through the formation of covalent bonds, but first let’s examine the nature of covalent bonds more closely. Why do they form at all?

Connections Molecular hydrogen (Fig. 1-9) is a very light gas and was used for buoyancy in the Hindenburg, a commercial passenger airship in the 1930s. Unfortunately, hydrogen gas is also very highly flammable, and the airship caught fire and was destroyed over New Jersey on May 6, 1937, killing 36 people.

A black-and-white photo shows Hindenburg, a commercial passenger airship, going up in flames mid-air.

We can begin to answer this question by examining Figure 1-10a, which illustrates how the energy of two H atoms changes as a function of the distance between their nuclei. In particular, when two H atoms separated by a large distance are brought together, their total energy begins to decrease.

A line graph and an analogous image of the energy levels at different internuclear distances for two hydrogen atoms. The graph shows the distance between two hydrogen atoms along the horizontal axis and the energy in kilojoules per mole, from 0 to 600, along the vertical axis. The energy of the atoms is at its highest, above 600 kilojoules per mole, when they are extremely close. As the internuclear distance increases, the energy dips steeply and reaches a minimum level at the most stable distance. As the distance between the atoms increases further to infinity, the energy levels rise up slightly and remain at a stable level thereafter, around 400 kilojoules per mole. The point on the horizontal axis that corresponds to the lowest energy level is labeled as the bond length, and the distance on the vertical axis that represents the difference between the lowest energy levels and the energy at infinite internuclear distance is labeled as bond energy. The analogous representation shows a grassy surface in the shape of the graphical curve. A ball located on the gently sloping surface rolls down to the hollow that represents the most stable point. This hollow corresponds to the point of the lowest energy on the graph. The caption reads, Formation of a chemical bond: A: Plot of energy as a function of the internuclear distance for two hydrogen atoms. The hydrogen atoms are most stable at the distance at which energy is a minimum. B: A ball at the top of a hill becomes more stable at the bottom of the hill, and therefore tends to roll downhill.
FIGURE 1-10 Formation of a chemical bond (a) Plot of energy as a function of the internuclear distance for two H atoms. The H atoms are most stable at the distance at which energy is a minimum. (b) A ball at the top of a hill becomes more stable at the bottom of the hill, and therefore tends to roll downhill.

Lower energy corresponds to greater stability.

At one particular internuclear distance, the energy of the molecule is at a minimum, while at shorter distances the energy rises dramatically.

The internuclear distance at which energy is the lowest is called the bond length of the H—H bond. The energy that is required to remove the H atoms from that internuclear distance to infinity (toward the right in the figure) is the bond strength, or bond energy, of the H—H bond.

This idea is analogous to a ball rolling down a hill (Fig. 1-10b). A ball at the top of a hill has more potential energy than a ball at the bottom, so the ball at the top tends to roll downhill, coming to rest at the bottom. By the same token, it takes energy to roll the ball from the bottom of the hill back to the top.

YOUR TURN 1.3
SHOW ANSWERS

Estimate the bond energy of the bond represented by Figure 1-10a.

Bond energy of H2≈ 450 kJ/mol – 0 kJ/mol = 450 kJ/mol.

Connections The behavior of covalent bonds as springs (Fig. 1-11) is what enables greenhouse gases like carbon dioxide (CO2) and methane (CH4) to absorb infrared radiation and warm the atmosphere.

It is often convenient to think of a covalent bond as a spring that connects two atoms. Just as it takes energy to lengthen or shorten a covalent bond from its bond length, it takes energy to stretch or compress a spring from its rest position, as shown in Figure 1-11.

A line graph shows the varying energy levels when a spring connecting two masses is stretched and compressed. The graph shows the internuclear bond distance along the horizontal axis and the energy along the vertical axis. The graphical curve begins at a high point that represents the rise in energy when a spring is compressed. As the spring is stretched out and brought to the rest position, the energy dips steeply and reaches a minimum level. And as the spring is stretched further, the energy rises once again. The caption reads, �The spring model of a covalent bond: The energy curve of a spring connecting two masses resembles that of the covalent bond shown in Figure 1-10a. Both stretching and compressing the spring from its rest position increase the energy in the spring.�
FIGURE 1-11 The spring model of a covalent bond The energy curve of a spring connecting two masses resembles that of the covalent bond shown in Figure 1-10a. Both stretching and compressing the spring from its rest position increase the energy in the spring.

Solved Problem 1.5

In the diagram shown here, which curve represents a stronger covalent bond?

A line graph of energy versus internuclear bond distances for two bond breaking processes. The graph shows the internuclear bond distance along the horizontal axis and the energy along the vertical axis for two bonding breaking processes. Two curves are shown with both the curves beginning at a high point on the graph�s energy scale. The first curve begins at a point slightly higher than the second. Then, the two curves dip steeply to reach the points of minimum energy. This point is higher for the first curve than for the second. Thereafter, the two curves rise gently and become nearly parallel to the horizontal axis, with the first curve rising more gently than the second.

Think
SHOW SECTION

How can bond breaking be represented for each curve? Which of those processes requires more energy?

Solve
SHOW SECTION

Bond breaking is represented by climbing from the bottom of the curve toward the right (i.e., the internuclear bond distance increases toward the right). For this process, more energy is required for the red curve, so the red curve represents a stronger bond.

problem 1.6 Which of the two curves in Solved Problem 1.5 represents a longer bond?

An illustration shows the formation of a covalent bond between two separate hydrogen atoms. Each of the two isolated hydrogen nuclei is bonded to one electron. This state signifies lower stability and higher energy. A covalent bond between the two atoms results in each electron being attracted to both the hydrogen nuclei. This state signifies higher stability and lower energy, and is represented by a quadrilateral with the two electrons and the two hydrogen nuclei at opposite corners. The caption reads, Stabilization of electrons in a covalent bond: In an isolated hydrogen atom, the electron is attracted to a single nucleus. In a covalent bond, electrons are attracted simultaneously to two hydrogen nuclei, thus lowering the energy of each electron.
FIGURE 1-12 Stabilization of electrons in a covalent bond In an isolated H atom (left), the electron is attracted to a single nucleus. In a covalent bond (right), electrons are attracted simultaneously to two H nuclei, thus lowering the energy of each electron.

Why are two hydrogen atoms connected by a covalent bond lower in energy than two isolated hydrogen atoms? Largely it is because of the additional electrostatic attraction experienced by electrons when they are shared between nuclei. In each isolated hydrogen atom, the negatively charged electron is attracted to just one positively charged nucleus (Fig. 1-12, left), but when the two hydrogen atoms are close together, each of the two electrons is attracted simultaneously to both nuclei (Fig. 1-12, right). This additional attraction lowers each electron’s energy, making the species more stable. When the atoms are too close together, however, the energy rises dramatically due to the repulsion between their positively charged nuclei.

Although single bonds are the most common type of bond found in organic molecules, we frequently encounter double bonds and triple bonds as well. The main difference among single, double, and triple bonds is the number of electrons involved. In a single bond, two electrons are shared between two nuclei; in a double bond, four electrons are shared; and in a triple bond, six electrons are shared.

Tables 1-2 and 1-3 list average bond energies for a variety of common bonding partners found in organic species. Table 1-2 contains only single bonds, whereas Table 1-3 compares bond energies and lengths for some common single, double, and triple bonds.

Table 1-2 shows the average bond energies of common single bonds between different elements. There are nineteen columns and eleven rows, with column headers from left to right and row starters from top to bottom being hydrogen, carbon, nitrogen, oxygen, fluorine, chlorine, bromine, iodine, and silicon. The elements are represented by their symbols. Data are included in the accompanying table.
Table 1-3, with ten columns and eight rows, shows the average bond energies and lengths of single and multiple bonds between different elements. Data are included in the accompanying table.

Notice in Table 1-3 that as the number of bonds increases between a pair of atoms, the bond energy increases and the bond length decreases. Thus, double and triple bonds can be viewed as shorter, stronger springs than single bonds (Fig. 1-13).

An illustration shows the variation in bond strength and bond length across single, double, and triple bonds. An arrow pointing to the right depicts increasing bond strength and decreasing bond length. On the left end of the arrow is a pair of atoms, X and Y, connected by a single bond. Toward the middle of the arrow is the same pair of atoms connected by a double bond. At the right end is a molecule where atoms X and Y are connected by a triple bond. The caption reads, Bond strength and bond length: For a particular pair of atoms that are covalently bonded, like atoms X and Y here, a triple bond is shorter and stronger than a double bond, which is shorter and stronger than a single bond.
FIGURE 1-13 Bond strength and bond length For a particular pair of atoms that are covalently bonded (X and Y), a triple bond is shorter and stronger than a double bond, which is shorter and stronger than a single bond.

YOUR TURN 1.4
SHOW ANSWERS

Refer to Tables 1-2 and 1-3 to answer the following questions, which are designed to acquaint you with the range of strengths of common bonds.

 (a) What is the value of the strongest single bond listed? _________________

 (b) What bond does that correspond to? _______________________________

 (c) What is the value of the weakest single bond? _______________________

 (d) What bond does that correspond to? _______________________________

 (e) What is the value of the strongest bond of any type? __________________

 (f) What bond does that correspond to? _______________________________

(a) 586 kJ/mol (140 kcal/mol). (b) The Si—F bond. (c) 138 kJ/mol (33 kcal/mol). (d) The O—O bond. (e) 1072 kJ/mol (256 kcal/mol). (f) The C≡O triple bond.

Turning an Inorganic Surface into an Organic Surface

Gold (Au) is a relatively unreactive metal, which is one reason it is widely used in jewelry and high-end electronic components. Gold, however, has a relatively high affinity for sulfur (S); the Au—S bond energy is roughly 120–150 kJ/mol (~30–40 kcal/mol), or nearly half the strength of a typical C—C bond. Sulfur also forms a relatively strong bond to carbon, about 290 kJ/mol (70 kcal/mol). This dual affinity of sulfur has enabled chemists to use sulfur to anchor organic groups to the surface of gold. The reaction is extremely easy to carry out: A sample of gold metal is simply immersed in a solution of an alkanethiol [CH3(CH2)n—SH] and the Au—S bond forms spontaneously, yielding a self-assembled monolayer (shown below) in which the alkyl chains extend away from the gold surface. Effectively, then, the inorganic gold surface is converted into an organic one.

These self-assembled monolayers have a wide variety of applications, such as protecting the gold surface from substances that would otherwise cause corrosion. More interestingly, by changing the organic portion to which the thiol group (—SH) is attached, the gold surface can be programmed to have specific affinity for other molecules. Gold nanoparticles (GNP), for example, have been capped with thiol-terminated molecules that enable the GNP to form bonds to epidermal growth-factor receptor antibodies. The resulting antibody–GNP conjugates have been used to image cancer cells.

A space-filling model shows layers of alkyl chains above a single layer of sulfur atoms, which lies above a layer of gold.