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11.1: The Covalent Bond

Difficulty Level: At Grade Created by: CK-12

Lesson Objectives

The student will:

• explain what covalent bonds are.
• explain why covalent bonds are formed.
• compare covalent bonds with ionic bonds in terms of how their definitions and how they are formed.
• draw Lewis structures for simple covalent molecules.
• use Lewis structures to show the formation of single, double, and triple covalent bonds.
• identify pairs of atoms that will form covalent bonds.
• define coordinate covalent bond.
• explain the equivalent bond strengths in resonance structures.

Vocabulary

• bond energy
• bond length
• coordinate covalent bond
• covalent bond
• double bond
• pi bond
• resonance
• sigma bond
• triple bond

Introduction

As we saw in the chapter “Ionic Bonds and Formulas,” metallic atoms can transfer one or more electrons to nonmetallic atoms, producing positively charged cations and negatively charged anions. The attractive force between these oppositely charged ions is called an ionic bond. However, chemical bonding does not require the complete transfer of electrons from one atom to another. When a bond forms between two nonmetallic atoms, neither has a low enough electronegativity to completely give up an electron to its partner. Instead, the atoms overlap their orbitals, and the electrons residing in these shared orbitals can be considered to be in the valence shells of both atoms at the same time. These atoms are now in a covalent bond, held together by the attraction of both nuclei to the shared electrons.

Ionic versus Covalent Bonding

The way that atoms bind together is due to a combination of factors: the electrical attraction and repulsion between atoms, the arrangement of electrons in atoms, and the natural tendency for matter to achieve the lowest potential energy possible. In most cases, these factors favor atoms that have obtained a complete octet of valence electrons. In ionic bonding, the atoms acquired this octet by gaining or losing electrons, while in covalent bonding, the atoms acquire the noble gas electron configuration by sharing electrons.

As you may recall from the discussion of ionic bonds in the chapter “Ionic Bonds and Formulas,” ionic bonds form between metals and nonmetals. Nonmetals, which have high electronegativity, are able to take electrons away from metals. The oppositely charged metal and nonmetal ions will then be attracted to each other. In covalent bonds, electrons are shared, meaning that metals will form few, if any, covalent bonds. Metals do not hold on to electrons with enough strength to participate in covalent bonding. For a covalent bond to form, we need two atoms that both attract electrons strongly, or two atoms with high electronegativity. Hence, the great majority of covalent bonds will form between two nonmetals. When both atoms in a bond are from the right side of the periodic table, the bond is most likely to be covalent.

An animation showing ionic and covalent bonding (2a) is available at http://www.youtube.com/watch?v=QqjcCvzWwww (1:57).

Single Bond

In covalent bonding, the atoms acquire a stable octet of electrons by sharing electrons. The covalent bonding process produces molecular substances, as opposed to the lattice structures produced by ionic bonding. The covalent bond, in general, is much stronger than the ionic bond, and there are far more covalently bonded substances than ionically bonded ones.

The simplest covalent bond is made between two atoms of hydrogen. Each hydrogen atom has one electron in its 1s\begin{align*}1s\end{align*} orbital. When two hydrogen atoms approach one another and their orbitals overlap, it creates a common volume between the two nuclei that both electrons occupy (as seen in the figure below). Since these electrons are shared, both hydrogen atoms now have a full valence shell.

Since electrons are constantly in motion, they will not always be directly in the center of a covalent bond. However, the simulated probability pattern below shows that they do spend the majority of their time in the area directly between the two nuclei. The extra time spent between the two nuclei is the source of the attraction that holds the atoms together in a covalent bond.

Another example of a covalent bond is found in the diatomic F2\begin{align*}\text{F}_2\end{align*} molecule (seen below). Recall that fluorine atoms have 7 valence electrons. Two are placed in the 2s\begin{align*}2s\end{align*} orbital, and five are placed in the three 2p\begin{align*}2p\end{align*} orbitals. Since each orbital can hold two electrons, this means that one of the 2p\begin{align*}2p\end{align*} orbitals is only half full, so it is available for bonding. When two fluorine atoms interact, their half-filled orbitals overlap, creating a covalent bond that gives both atoms a complete octet of valence electrons.

Some Compounds Have Both Covalent and Ionic Bonds

If you recall the introduction to polyatomic ions, you will remember that the bonds that hold the polyatomic ions together are covalent bonds. Once the polyatomic ion is constructed with covalent bonds, it reacts with other substances as an ion. The bond between a polyatomic ion and another ion will be ionic. An example of this type of situation is in the compound sodium nitrate. Sodium nitrate is composed of a sodium ion and a nitrate ion. The nitrate ion is held together by covalent bonds, and the nitrate ion is attached to the sodium ion by an ionic bond (see sketch below).

Bond Strength

When atoms that attract each other move closer together, the potential energy of the system (the two atoms) decreases. When a covalent bond is formed, the atoms move so close together that their electron clouds overlap. As the atoms continue to move closer yet, the potential energy of the system continues to decrease – to a point. If you continue to move atoms closer and closer together, eventually the two nuclei will begin to repel each other. If you push the nuclei closer together beyond this point, the repulsion causes the potential energy to increase. Each pair of covalently bonding atoms will have a distance between their nuclei that is the lowest potential energy distance. This position has the atoms close enough for the attraction between the nucleus of one atom and the electrons of the other is maximum, but not too close that the nuclei have not begun to repel each other strongly. This distance is called the bond length. The more potential energy released as this bond formed, the stronger the bond will be. In order to break this bond, you must input an equivalent amount of energy.

The strength of a diatomic covalent bond can be expressed by the amount of energy necessary to break the bond and produce separate atoms. The energy needed to break a covalent bond is called bond energy and is measured in kilojoules per mole. Bond energy is used as a measure of bond strength. The bond strength of HBr\begin{align*}\text{HBr}\end{align*} is 365 kilojoules\begin{align*}365 \ \mathrm{kilojoules}\end{align*} per mole, meaning that it would take 365 kilojoules\begin{align*}365 \ \mathrm{kilojoules}\end{align*} to break all the chemical bonds in 1 mole, or 6.02×1023 molecules\begin{align*}6.02 \times 10^{23} \ \mathrm{molecules}\end{align*}, of HBr\begin{align*}\text{HBr}\end{align*} and produce separate hydrogen and bromine atoms. In comparison, the bond strength of HCl\begin{align*}\text{HCl}\end{align*} is 431 kilojoules\begin{align*}431 \ \mathrm{kilojoules}\end{align*} per mole. Consequently, the bond in HCl\begin{align*}\text{HCl}\end{align*} is stronger than the bond in HBr\begin{align*}\text{HBr}\end{align*}.

Molecular Stability

The bond energy can be used to indicate molecular stability. When stable compounds are formed, large amounts of energy are given off. In order to break the molecule apart, all the energy that was given off must be put back in. The more energy needed to break a bond, the more stable the compound will be. Therefore, compounds with higher bond strengths tend to be more stable.

The molecule of glucose, shown below, can react with six molecules of oxygen to produce six molecules of carbon dioxide and six molecules of water. During the reaction, the atoms of the glucose molecule are rearranged into the structures of carbon dioxide and water. The bonds in glucose are broken, and new bonds are formed. As this occurs, potential energy is released because the new bonds have lower potential energy than the original bonds. Since the bonds in the products are lower energy bonds, the product molecules are more stable than the reactants.

Double and Triple Bonds

In the previous examples, only one pair of electrons was shared between the two bonded atoms. This type of bond is called a single bond. However, it is possible for atoms to share more than one pair of electrons. When two or three pairs of electrons are shared by two bonded atoms, they are referred to as double bonds or triple bonds, respectively.

A double bond is formed when two pairs of orbitals overlap with each other at the same time. The O2\begin{align*}\text{O}_2\end{align*} molecule provides an example of a double bond. Oxygen has six valence electrons. Two electrons are placed in the 2s orbital, while the remaining four are distributed among the three 2p orbitals. Hund’s rule tells us that each p orbital will receive one electron before a second electron is added, so the oxygen atom will have two half-filled orbitals available for bonding (a filled orbital will not participate in bonding).

Of the two p orbitals available for bonding, the first pair will have a head-to-head overlap, placing the shared electrons directly in between the two nuclei. This type of a bond, shown in the figure below, is called a sigma (σ\begin{align*}\sigma\end{align*}) bond.

The second pair of half-filled orbitals is orientated perpendicularly to the first pair, so a similar head-to-head overlap is not possible. However, a bond can still be made by overlapping the two p orbitals side-by-side, as shown in the figure below. This type of bond is called a pi (π\begin{align*}\pi\end{align*}) bond.

Whenever possible, the first bond will form directly between the two atomic nuclei involved in bonding. This allows for maximum overlap between the two orbitals, helping to minimize the electrostatic repulsion between the two positively charged nuclei. Thus, single bonds consist of one sigma bond, double bonds consist of one sigma and one pi bond, and triple bonds consist of one sigma and two pi bonds.

Note that double bonds are less than twice as strong as a single bond between the same two atoms. Since sigma bonds are “better” (stronger) than pi bonds, a combination of one sigma and one pi is slightly weaker than adding two sigma bonds together.

Lewis Dot Structures

It would not be very efficient if we had to draw an orbital picture every time we wanted to describe a molecule. Lewis dot structures, first developed by G.N. Lewis, are a shorthand way of drawing the arrangement of atoms, bonds, and valence electrons in a molecule. In the earlier chapter “The Electron Configuration of Atoms,” we introduced Lewis dot diagrams for drawing individual atoms. When we draw molecules, the diagrams are known as Lewis dot formulas, Lewis structures, or Lewis formulas. The Lewis structures of a molecule show how the valence electrons are arranged among the atoms of the molecule.

In a Lewis structure, each valence electron is represented by a dot, and bonds are shown by placing electrons in between the symbols for the two bonded atoms. Often, a pair of bonding electrons is further abbreviated by a dash. For example, we can represent the covalent bond in the F2\begin{align*}\text{F}_2\end{align*} molecule by either of the Lewis structures shown below.

Double bonds (4 electrons shared between two atoms) can be represented either with 4 dots or 2 dashes. The Lewis structure for an oxygen molecule (O2\begin{align*}\text{O}_2\end{align*}) is shown below.

Similarly, triple bonds can be written as 6 dots or 3 dashes. An example of a molecule with triple bonds is the nitrogen molecule, N2\begin{align*}\text{N}_2\end{align*}. The Lewis structure for a nitrogen molecule can be represented by either of the two ways shown below. It is important to keep in mind that a dash always represents a pair of electrons. .

Several other examples of representing covalent bonds are shown in the figure below.

Drawing Lewis Structures

The rules outlined below for writing Lewis structures are based on observations of thousands of molecules (note that there will be some exceptions to the rules). We learned earlier that atoms are generally most stable with 8 valence electrons (the octet rule). The major exception is hydrogen, which requires only 2 valence electrons to have a complete valence shell (sometimes called the duet rule). Lewis structures allow one to quickly assess whether each atom has a complete octet (or duet) of electrons.

Rules for Writing Lewis Structures:

1. Decide which atoms are bounded.
2. Count all the valence electrons of all the atoms.
3. Place two electrons between each pair of bounded atoms.
4. Complete all the octets (or duets) of the atoms attached to the central atom.
5. Place any remaining electrons on the central atom.
6. If the central atom does not have an octet, look for places to form double or triple bonds.

Example:

Write the Lewis structure for water, H2O\begin{align*}\text{H}_2\text{O}\end{align*}.

Step 1: Decide which atoms are bounded.

Begin by assuming the hydrogen atoms are bounded to the oxygen atom. In other words, assume the oxygen atom is the central atom.

HOH\begin{align*}\text{H} - \text{O} - \text{H}\end{align*}

Step 2: Count all the valence electrons of all the atoms.

The oxygen atom has 6\begin{align*}6\end{align*} valence electrons, and each hydrogen has 1\begin{align*}1\end{align*}. The total number of valence electrons is 8\begin{align*}8\end{align*}.

Step 3: Place two electrons between each pair of bounded atoms.

H : O : H\begin{align*}\text{H} \ : \ \text{O} \ : \ \text{H}\end{align*}

Step 4: Complete all the octets or duets of the atoms attached to the central atom.

The hydrogen atoms are attached to the central atom and require a duet of electrons. Those duets are already present.

Step 5: Place any remaining electrons on the central atom.

The total number of valence electrons is 8\begin{align*}8\end{align*}, and we have already used 4\begin{align*}4\end{align*} of them. The other 4\begin{align*}4\end{align*} will fit around the central oxygen atom.

Is this structure correct?

• Are the total number of valence electrons correct? Yes
• Does each atom have the appropriate duet or octet of electrons? Yes

The structure, then, is correct.

Example:

Write the Lewis structure for carbon dioxide, CO2\begin{align*}\text{CO}_2\end{align*}.

Step 1: Decide which atoms are bounded.

Begin by assuming the carbon is the central atom and that both oxygen atoms are attached to the carbon.

Step 2: Count all the valence electrons of all the atoms.

The oxygen atoms each have 6\begin{align*}6\end{align*} valence electrons and the carbon atom has 4\begin{align*}4\end{align*}. The total number of valence electrons is 16.

Step 3: Place two electrons between each pair of bounded atoms.

O : C : O\begin{align*}\text{O} \ : \ \text{C} \ : \ \text{O}\end{align*}

Step 4: Complete all the octets or duets of the atoms attached to the central atom.

Step 5: Place any remaining electrons on the central atom.

We have used all 16\begin{align*}16\end{align*} of the valence electrons so there are no more to place around the central carbon atom.

Is this structure correct?

• Is the total number of valence electrons correct? Yes
• Does each atom have the appropriate duet or octet of electrons? NO

Each oxygen has the proper octet of electrons, but the carbon atom only has 4\begin{align*}4\end{align*} electrons. Therefore, this structure is not correct.

Step 6: If the central atom does not have an octet, look for places to form double or triple bonds.

Double bonds can be formed between carbon and each oxygen atom.

Notice this time that each atom is surrounded by 8\begin{align*}8\end{align*} electrons.

Example:

Write the Lewis structure for ammonia, NH3\begin{align*}\text{NH}_3\end{align*}.

Step 1: Decide which atoms are bounded.

The most likely bonding for this molecule is to have nitrogen as the central atom and each hydrogen bounded to the nitrogen. Therefore, we can start by putting nitrogen in the center and placing the three hydrogen atoms around it.

Step 2: Count all the valence electrons of all the atoms.

The nitrogen atom has five valence electrons, and each hydrogen atom has one. The total number of valence electrons is 8\begin{align*}8\end{align*}.

Step 3: Place two electrons between each pair of bounded atoms, as seen in the middle drawing of the figure below.

Step 4: Complete all the octets or duets of the atoms attached to the central atom.

In this case, all the non-central atoms are hydrogen, and they already have a duet of electrons.

Step 5: Place any remaining electrons on the central atom.

There are still two electrons left, so they would complete the octet for nitrogen. If the central atom, at this point, does not have an octet of electrons, we would look for places to create a double or triple bond, but that is not the case here. The final drawing on the right in the figure above is the Lewis structure for ammonia.

Example:

Write the Lewis structure for nitric acid, HNO3\begin{align*}\text{HNO}_3\end{align*}.

Solution:

The skeleton for nitric acid has the three oxygen atoms bounded to the nitrogen and the hydrogen bounded to one of the oxygen atoms, as seen in diagram 1 shown below. The total number of valence electrons is 5+6+6+6+1=24\begin{align*}5 + 6 + 6 + 6 + 1 = 24\end{align*}.

The next step, shown in diagram 2, is to put in a pair of electrons between each bonded pair. So far, we have accounted for 8\begin{align*}8\end{align*} of the 24\begin{align*}24\end{align*} valence electrons. The next step is to complete the octet or duet for each of the non-central atoms, as seen in diagram 3. At that point, we have used all of the valence electrons, but the central atom does not have an octet of electrons. The rules tell us to find a place to put a double or triple bond. Based on what we have learned up to this point, any of the three oxygen atoms is just as good as the others for participating in a double bond. For this example, we moved two of the electrons from the oxygen atom on the far left between the oxygen and nitrogen. Now every atom in the molecule has the appropriate octet or duet of electrons. We have a satisfactory Lewis structure for the nitric acid molecule.

For an introduction to drawing Lewis electron dot symbols (2e), see http://www.youtube.com/watch?v=y6QZRBIO0-o (4:19).

Coordinate Covalent Bond

A variation of covalent bonding is coordinate covalent bonding. Coordinate covalent bonds form when the two shared electrons of a covalent bond are both donated by the same atom. So far, we have looked at covalent bonds formed by the overlap of two half-filled orbitals. A coordinate covalent bond is different in that it involves the overlap of one full orbital and one empty one. Once formed, a coordinate covalent bond is no different from an ordinary covalent bond. The difference is simply in the source of the electrons forming the bond. You should note that the bond still involves only one pair of electrons and one pair of orbitals, but only one atom provides both of the shared electrons. Many polyatomic ions include coordinate covalent bonds. The ammonium ion is an example of this type of bonding. When hydrogen chloride gas and ammonia gas are brought into contact with each other, they form ammonium chloride, NH4Cl\begin{align*}\text{NH}_4\text{Cl}\end{align*}. When ammonium chloride is dissolved in water, ammonium ions and chloride ions are produced.

HCl+NH3NH4Cl+H2ONH+4 (aq)+Cl(aq)\begin{align*}\text{HCl} + \text{NH}_3 \rightarrow \text{NH}_4\text{Cl} + \text{H}_2\text{O} \rightarrow \text{NH}^+_{4 \ (aq)} + \text{Cl}^-_{(aq)}\end{align*}

In one of the nitrogen-hydrogen bonds, both electrons came from the nitrogen atom. However, once the ammonium ion has been formed, all four nitrogen-hydrogen bonds are identical, regardless of where the electrons in the bonds came from.

Resonance

Sometimes, more than one valid Lewis structure is possible for the same molecule. Consider the Lewis structure for the nitrite ion, NO2\begin{align*}\text{NO}_2^-\end{align*}. The charge on the ion indicates an electron has been gained from an external source. In other words, the ion contains an electron that did not originally belong to the nitrogen or the oxygen atoms in the ion. In this case, the 1\begin{align*}-1\end{align*} charge indicates that the valence electron count will have one additional electron added in order to account for the electron that came from outside the ion. The total number of valence electrons for this ion is 5+6+6+1=18\begin{align*}5 + 6 + 6 + 1 = 18\end{align*}. We can then draw the Lewis structure for this ion following the normal rules. Before applying the last rule of creating double or triple bonds, the incomplete Lewis structure will look like that in the figure below.

All 18\begin{align*}18\end{align*} of the available valence electrons have been used. The final rule for writing Lewis structures states that if the central atom does not have an octet of electrons, double or triple bonds need to be created. In this case, either one of the nitrogen-oxygen bonds can be made into a double bond, as demonstrated in the figure below.

The two structures in the image above suggest that one of the nitrogen-oxygen bonds should be shorter and stronger than the other one. It has been experimentally shown, however, that the two nitrogen-oxygen bonds are identical. In fact, the nitrogen-oxygen bond lengths are about halfway between the expected values for a single bond and a double bond. Neither of the Lewis structures above matches the experimental evidence, and there is no good way to write one that does. The solution to this problem is the use of a concept called resonance. Resonance is the condition where there is more than one valid Lewis structure can be written for the molecule or ion. The actual structure of the molecule or ion is actually a composite, or average, of all the valid Lewis structures. In the case of the nitrite ion above, the second pair of electrons in the double bond is actually shared between all the atoms, giving each bond the strength of about 1.5\begin{align*}1.5\end{align*} bonds. Each of the Lewis structures that is drawn is called a resonance structure, with the actual structure being a resonance hybrid of all the contributing structures.

Resonance is also present in the Lewis structures for nitrate ion, NO3\begin{align*}\text{NO}_3^-\end{align*}.

All of these are valid Lewis structures, but none of them accurately portray the structure of the ion. Just like in the case of nitrite, the actual nitrate ion is an average of all three structures. All three nitrogen-oxygen bonds are identical, and they are all slightly shorter and stronger than a normal nitrogen-oxygen single bond. We saw earlier that the second bond in a double bond is a pi bond, created by two p orbitals lining up side by side. It is those pi electrons that cannot be described well by a single Lewis structure. Rather than creating a true pi bond between just two atoms, the extra electrons are shared among all four atoms.

When the concept of resonance was first introduced, it was thought that the molecule was rapidly switching, or resonating, between the various resonance forms. Although later evidence showed that this is not the case, the term has survived. Note the double headed arrows (\begin{align*}\longleftrightarrow\end{align*}) between each structure. Using this type of arrow indicates that the structures shown are resonance structures, implying that the entire figure attempts to describe a single molecule or ion.

Lesson Summary

• Covalent bonds are formed by electrons being shared between two atoms.
• Covalent bonds are formed between atoms with relatively high electronegativity.
• Bond energy is the amount of energy necessary to break the covalent bond and is an indication of the strength and stability of the bond.
• Some atoms are capable of forming double or triple bonds.
• Multiple bonds between atoms require multiple half-filled orbitals.
• End-to-end orbital overlaps are called sigma bonds.
• Side-to-side orbital overlaps are called pi bonds.
• Lewis structures are commonly used to show the valence electron arrangement in covalently bonded molecules.
• Resonance is a condition occurring when more than one valid Lewis structure can be written for a particular molecule. The actual electronic structure is not represented by any one of the Lewis structures but by the average of all of the valid structures.

The learner.org website allows users to view the Annenberg series of chemistry videos. You are required to register before you can watch the videos, but there is no charge to register. The video called “Chemical Bonds” explains the differences between ionic and covalent bonds using models and examples from nature.

This animation explores the differences between ionic and covalent bonding.

The website below provides a guide to drawing Lewis structures.

Review Questions

1. Describe the characteristics of two atoms that would be expected to form an ionic bond.
2. Describe the characteristics of two atoms that would be expected to form a covalent bond.
3. If a molecule had a very high bond energy, would you expect it to be stable or unstable?
4. When gaseous potassium ions and gaseous fluoride ions join together to form a crystal lattice, the amount of energy released is \begin{align*}821 \ \mathrm{kJ/mol}\end{align*}. When gaseous potassium ions and gaseous chloride ions join together to form a crystal lattice, the amount of energy released is \begin{align*}715 \ \mathrm{kJ/mol}\end{align*}. Which bond is stronger, \begin{align*}\text{KF}\end{align*} or \begin{align*}\text{KCl}\end{align*}? If these two compounds were increasingly heated, which compound would break apart at the lower temperature?
5. Of the following compounds listed in Table below, which would you expect to be ionically bonded and which would you expect to be covalently bonded?
Table for Review Question 5
Compound Ionic or Covalent
\begin{align*}\text{CS}_2\end{align*}
\begin{align*}\text{K}_2\text{S}\end{align*}
\begin{align*}\text{FeF}_3\end{align*}
\begin{align*}\text{PF}_3\end{align*}
\begin{align*}\text{BF}_3\end{align*}
\begin{align*}\text{AlF}_3\end{align*}
\begin{align*}\text{BaS}\end{align*}
1. How many sigma bonds and how many pi bonds are present in a triple bond?
2. Which of the following molecules will have a triple bond?
1. \begin{align*}\text{C}_2\text{H}_2\end{align*}
2. \begin{align*}\text{CH}_2\text{Cl}_2\end{align*}
3. \begin{align*}\text{BF}_3\end{align*}
4. \begin{align*}\text{CH}_3\text{CH}_2\text{OH}\end{align*}
5. \begin{align*}\text{HF}\end{align*}
3. Draw the Lewis structure for \begin{align*}\text{CCl}_4\end{align*}.
4. Draw the Lewis structure for \begin{align*}\text{SO}_2\end{align*}.
5. Draw a Lewis structure for \begin{align*}\text{CO}_3^{2-}\end{align*}. Explain why all three carbon-oxygen bonds have the same length.

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