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9.3

THE COVALENT BONDING MODEL

Look through the Handbook of Chemistry and Physics, and you’ll find that the number of covalent compounds dwarfs the number of ionic compounds. Covalent substances range from diatomic hydrogen to biological and synthetic macromolecules with many thousands of atoms and even to some minerals that have covalent bonds throughout the sample. And covalent bonds occur in all polyatomic ions, too. Without doubt, sharing electrons is the main way that atoms interact.

The Formation of a Covalent Bond Why does hydrogen gas consist of H2 molecules and not separate H atoms? Figure 9.12 plots the potential energy of a system of two isolated H atoms versus the distance between their nuclei (see also Figure 2.14). Let’s start at the right end of the curve and move along it to the left, as the atoms get closer: ∙ At point 1, the atoms are far apart, and each acts as though the other were not present. ∙ At point 2, the distance between the atoms has decreased enough for each nucleus to start attracting the other atom’s electron, which lowers the potential energy. As the atoms get closer, these attractions increase, but so do repulsions between the nuclei and between the electrons. ∙ At point 3 (bottom of the energy “well”), the maximum attraction is achieved in the face of the increasing repulsion, and the system has its minimum energy. ∙ At point 4, if it were reached, the atoms would be too close, and the rise in potential energy from increasing repulsions between the nuclei and between the electrons would push them apart toward point 3 again. Thus, a covalent bond arises from the balance between the nuclei attracting the electrons and electrons and nuclei repelling each other, as shown in the blow-up of the structure at point 3. (We’ll return to Figure 9.12 shortly.) Formation of a covalent bond always results in greater electron density between the nuclei. Figure 9.13 (on the next page) depicts this fact with an electron density contour map (A), and an electron density relief map (B). 4

2

3

1

Potential energy (kJ/mol)

0

–100

1

This energy is absorbed when the bond breaks (+Bond Energy).

This energy is released when the bond forms (−Bond Energy).

2

–200

Electron Nucleus –300

–

4

Attraction Repulsion +

+

–400 –432

–500

Energy released when H2 bond forms 74

–

3 H2 bond length 100 Internuclear distance (pm)

Bond length 200

Figure 9.12 Covalent bond formation in H2 . The energy difference between points 1 and 3 is the H2 bond energy (432kJ/mol). The internuclear distance atpoint 3 is the H2 bond length (74 pm).

Figure 9.13 Distribution of electron density in H 2. A, Electron density (blue shading) is high around and between the nuclei. Electron density doubles with each concentric curve. B, The highest regions of electron density are shown as peaks. H nuclei B

A

Bonding Pairs and Lone Pairs Unlike ionic compounds in which atoms gain or lose enough electrons to obtain an octet of electrons, atoms in covalent compounds share electrons. To achieve a full outer (valence) level of electrons, each atom in a covalent bond “counts” the shared electrons as belonging entirely to itself. Thus, the two shared electrons in H2 simultaneously fill the outer level of both H atoms, as clarified by the blue circles added below. The shared pair, or bonding pair, is represented by a pair of dots or a line: bonding pair

H H

or

H

H

An outer-level electron pair that is not involved in bonding is called a lone pair, or unshared pair. The bonding pair in HF fills the outer level of the H atom and, together with three lone pairs, fills the outer level of the F atom as well: bonding pair

H F

lone pairs

or

H

F

In F2, the bonding pair and three lone pairs fill the outer level of each F atom, so that each has an octet of electrons: F F

or

F

F

(This text generally shows bonding pairs as lines and lone pairs as dots.)

Properties of a Covalent Bond: Order, Energy, and Length A covalent bond has three important properties that are closely related to one another and to the compound’s reactivity—bond order, bond energy, and bond length. 1. Bond order. The bond order is the number of electron pairs being shared by a given pair of atoms: ∙ A single bond, as shown above in H2, HF, or F2, is the most common bond and consists of one bonding pair of electrons: a single bond has a bond order of 1. ∙ Many molecules (and ions) contain multiple bonds, in which more than one pair is shared between two atoms. Multiple bonds usually involve C, O, and/or N atoms. A double bond consists of two bonding electron pairs, four electrons shared between two atoms, so the bond order is 2. Ethylene (C2H4) contains a carboncarbon double bond and four carbon-hydrogen single bonds: H

H

H C

C H

H

H

or

C

C H

H

Each carbon “counts” the four electrons in the double bond and the four in its two single bonds to hydrogen atoms to attain an octet. ∙ A triple bond consists of three shared pairs: two atoms share six electrons, so the bond order is 3. The N2 molecule has a triple bond, and each N atom also has a lone pair. Six shared and two unshared electrons give each N atom an octet: N

N

or

N

N

2. Bond energy. The strength of a covalent bond depends on the magnitude of the attraction between the nuclei and shared electrons. The bond energy (BE) (also called bond enthalpy or bond strength) is the energy needed to overcome this attraction and

is defined as the standard enthalpy change for breaking the bond in 1 mol of gaseous molecules. Bond breakage is an endothermic process, so bond energy is always positive: AB( g) ⟶ A(g) + B(g)

Internuclear distance (bond length)

Covalent radius

143 pm

72 pm

ΔH°bond breaking = BEA—B ( always > 0)

The bond energy is the difference in energy between separated and bonded atoms (the potential energy difference between points 1 and 3—the energy “well”—in Figure 9.12). The same quantity of energy absorbed to break the bond is released when the bond forms. Bond formation is an exothermic process, so the sign of its enthalpy change is always negative: A( g) + B(g) ⟶ AB(g)

F2 199 pm

100 pm

ΔHbond ° forming = −BEA—B (always < 0)

Table 9.2 lists the energies of some common bonds. By definition, ∙ Stronger bonds have a larger BE because they are lower in energy (have a deeper energy well). ∙ Weaker bonds have a smaller BE because they are higher in energy (have a shallower energy well).

Cl 2 228 pm

The energy of a given bond varies slightly from molecule to molecule and even within the same molecule, so each value is an average bond energy. In other words, the CH bond energy value of 413 kJ/mol is the average of the CH bond energy values in all molecules containing this bond. 3. Bond length. A covalent bond has a bond length, the distance between the nuclei of the two bonded atoms. In Figure 9.12, bond length is the distance between the nuclei at the point of minimum energy (bottom of the well), and Table 9.2 shows the lengths of some covalent bonds. Like bond energies, these values are average bond lengths for a bond in different substances. Bond length is related to the sum of the radii of the bonded atoms. In fact, most atomic radii are calculated from measured bond lengths (see Figure 8.12C). Bond lengths for a series of similar bonds, as in the halogens, increase with atomic size (Figure 9.14).

Br2 133 pm

266 pm

I2

Figure 9.14 Bond length and covalent radius.

Average Bond Energies (kJ/mol) and Bond Lengths (pm)

Table 9.2

Bond

114 pm

Length

Bond

Energy

Length

Single Bonds HH 432 HF 565 HCl 427 HBr 363 HI 295

Energy

74 92 127 141 161

CH CC CSi CN CO CP CS CF CCl CBr CI

109 154 186 147 143 187 181 133 177 194 213

NH NN NP NO NF NCl NBr NI

391 160 209 201 272 200 243 159

101 146 177 144 139 191 214 222

SiH SiSi SiO SiS SiF SiCl SiBr SiI

323 226 368 226 565 381 310 234

148 234 161 210 156 204 216 240

OH OP OO OS OF OCl OBr OI

467 351 204 265 190 203 234 234

96 160 148 151 142 164 172 194

PH PSi PP PF PCl PBr PI

320 213 200 490 331 272 184

142 227 221 156 204 222 246

NN NO O2

418 607 498

122 120 121

CC CN CO

839 891 1070

121 115 113

413 347 301 305 358 264 259 453 339 276 216

Multiple Bonds CC 614 CN 615 CO 745 (799 in CO2)

134 127 123

Bond

Energy Length

Bond SH SS SF SCl SBr SI FF FCl FBr FI ClCl ClBr ClI Br Br Br I II NN NO

Energy Length 347 266 327 271 218 ∼170

134 204 158 201 225 234

159 193 212 263 243 215 208 193 175 151

143 166 178 187 199 214 243 228 248 266

945 1020

110 106

Table 9.3

The Relation of Bond Order, Bond Length, and Bond Energy

Bond

Bond Order

Average Bond Length (pm)

Average Bond Energy (kJ/mol)

CO

1

143

358

CO

2

123

745

CO

3

113

1070

CC

1

154

347

CC

2

134

614

CC

3

121

839

NN

1

146

160

NN

2

122

418

NN

3

110

945

The order, energy, and length of a covalent bond are interrelated. Two nuclei are more strongly attracted to two shared electron pairs than to one, so double-bonded atoms are drawn closer together and are more difficult to pull apart than single-bonded atoms. Therefore, for a given pair of atoms: ∙ a higher bond order results in a smaller bond length. As bond order increases, bond length decreases. ∙ a higher bond order results in a higher bond energy. As bond order increases, bond energy also increases. Thus, as Table 9.3 shows, for a given pair of atoms, a shorter bond is a stronger bond. In some cases, we can see a relation among atomic size, bond length, and bond energy by varying one of the atoms involved in a single bond while holding the other constant:

Student Hot Spot Student data indicate that you may struggle with comparing bond length and strength. Access the SmartBook to view additional Learning Resources on this topic.

∙ Variation within a group. The trend in carbon-halogen single bond lengths, CI > CBr > CCl > CF, parallels the trend in atomic size, I > Br > Cl > F, and is opposite to the trend in bond energy, CF > CCl > CBr > CI. ∙ Variation within a period. Looking again at single bonds involving carbon, the trend in bond lengths, CN > CO > CF, parallels the trend in atomic size, N > O > F, and is opposite to the trend in bond energy, CF > CO > CN. In general, bond length increases (and bond energy decreases) with increasing atomic radii of the atoms in the bond.

SAMPLE PROBLEM 9.3

Comparing Bond Length and Bond Strength

Problem Without referring to Table 9.2, rank the bonds in each set in order of decreasing bond length and decreasing bond strength: (a) SF, SBr, SCl (b) CO, CO, CO Plan (a) S is singly bonded to three different halogen atoms, so the bond order is the same. Bond length increases and bond strength decreases as the halogen’s atomic radius increases. (b) The same two atoms are bonded, but the bond orders differ. In this case, bond strength increases and bond length decreases as bond order increases. Solution (a) Atomic size increases down a group, so F < Cl < Br.

(b) By ranking the bond orders, CO > CO > CO, we obtain

Check From Table 9.2, we see that the rankings are correct.

Comment Remember that for bonds involving pairs of different atoms, as in part (a), the relationship between length and strength holds only for single bonds and not in every case, so apply it carefully. FOLLOW-UP PROBLEMS 9.3A Rank the bonds in each set in order of decreasing bond length and decreasing bond strength: (a) CN, CO, CC (b) PI, PF, PBr 9.3B Rank the bonds in each set in order of increasing bond length and increasing bond strength: (a) SiF, SiC, SiO (b) NN, NN, NN SOME SIMILAR PROBLEMS 9.39 and 9.40

How the Model Explains the Properties of Covalent Substances The covalent bonding model proposes that electron sharing between pairs of atoms leads to strong, localized bonds. Most, but not all, covalent substances consist of individual molecules. These molecular covalent substances have very different physical properties than network covalent solids do because different types of forces give rise to the two kinds of substances. 1. Physical properties of molecular covalent substances. At first glance, the model seems inconsistent with physical properties of covalent substances. Most are gases (such as methane and ammonia), liquids (such as benzene and water), or low-melting solids (such as sulfur and paraffin wax). If covalent bonds are so strong (~200 to 500 kJ/mol), why do covalent substances melt and boil at such low temperatures? To answer this, we’ll focus on two different forces: (1) strong bonding forces hold the atoms together within the molecule, and (2) weak intermolecular forces act between separate molecules in the sample.

Strong covalent bonds within molecules Gaseous phase do not break. Liquid phase

Weak forces between molecules are overcome.

Figure 9.15 Strong forces within molecules and weak forces between them. Source: © McGraw-Hill Education/Stephen Frisch, photographer

It is the weak forces between one molecule and the other molecules around it that account for the physical properties of molecular covalent substances. For example, look what happens when pentane (C5H12) boils (Figure 9.15): weak forces between pentane molecules are overcome during this process; the strong CC and CH covalent bonds within each pentane molecule are not broken. 2. Physical properties of network covalent solids. Some covalent substances do not consist of separate molecules. Rather, these network covalent solids are held together by covalent bonds between atoms throughout the sample, and their properties do reflect the strength of covalent bonds. Two examples are quartz and diamond (Figure 9.16). Quartz (SiO2; top) has silicon-oxygen covalent bonds in three dimensions; no separate SiO2 molecules exist. It is very hard and melts at 1550°C. Diamond (bottom) has covalent bonds connecting each carbon atom to four others. It is the hardest natural substance known and melts at around 3550°C. Thus, covalent bonds are strong, but most covalent substances consist of separate molecules with weak forces between them. (We discuss intermolecular forces in detail in Chapter 12.) 3. Electrical conductivity. An electric current is carried by either mobile electrons or mobile ions. Most covalent substances are poor electrical conductors, whether melted or dissolved, because their electrons are localized as either shared or unshared pairs and are not mobile, and no ions are present. The Tools of the Laboratory essay describes a technique used widely for studying the types of bonds in covalent substances.

Quartz

Diamond

Silicon

Oxygen

Carbon

Figure 9.16 Covalent bonds of network covalent solids: quartz and diamond.

TOOLS OF THE LABORATORY

Infrared Spectroscopy

I

nfrared (IR) spectroscopy is an instrumental technique most often used to study covalently bonded molecules. The key components of an IR spectrometer are the same as those of other types of spectrometers (see Figure B7.3). The source emits radiation of many wavelengths, but only those in the IR region are selected. The sample is typically a pure liquid or solid that absorbs varying amounts of different IR wavelengths. An IR spectrum consists of peaks that indicate these various absorptions.

DIATOMIC MOLECULE Stretch

Molecular Vibrations and IR Absorption

LINEAR TRIATOMIC MOLECULE

An IR spectrum indicates the types of bonds in a molecule based on their vibrations. All molecules undergo motion through space, rotation around several axes, and vibrations between bonded atoms. Consider a sample of ethane gas. The H3CCH3 molecules zoom throughout the container, the whole molecule rotates, and its two CH3 groups rotate about the CC bond. But let’s disregard motion through space and rotation and focus on the motion most important to IR spectroscopy: each pair of atoms is vibrating as though the bonds were springs that stretch and bend. Figure B9.1 depicts the vibrations of diatomic and triatomic molecules; larger molecules vibrate in many more ways. The energies of IR photons are in the range of these vibrational energies. Each vibration has a frequency based on the type of motion, masses of the atoms, and strength of the bond. The frequencies correspond to IR wavelengths between 2.5 and 25 μm. The energy of these vibrations is quantized. Just as an atom can absorb a photon whose energy equals the difference between electron energy levels, a molecule can absorb an IR photon whose energy equals the difference between vibrational energy levels.

IR Radiation and Global Warming Carbon dioxide, OCO, is a linear molecule that bends and stretches symmetrically and asymmetrically when it absorbs IR radiation (Problem B9.2). Sunlight is absorbed by Earth’s surface and re-emitted as heat, much of which is IR radiation. Atmospheric CO2 absorbs this radiation and re-emits it, thus warming the atmosphere (see the Chemical Connections at the end of Section 6.6).

Compound Identification An IR spectrum can be used to identify a compound for three related reasons: 1. Each kind of bond absorbs a specific range of wavelengths. That is, a CC bond absorbs a different range than does a CC bond, a CH bond, a CO bond, and so forth. 2. Different types of organic compounds have characteristic spectra. The different groupings of atoms that define an alcohol, a carboxylic acid, an ether, and so forth (see Chapter 15) absorb differently. 3. Each compound has a unique spectrum. The IR spectrum acts like a fingerprint to identify the compound, because the quantity of each wavelength absorbed depends on the detailed molecular structure. For example, no other compound has the IR spectrum of acrylonitrile, a compound used to make plastics (Figure B9.2). 384

Stretch symmetrical

Stretch asymmetrical

Bend

NONLINEAR TRIATOMIC MOLECULE

Stretch symmetrical

Stretch asymmetrical Bend

Figure B9.1 Vibrational motions in general diatomic and triatomic molecules.

Recall from Chapter 3 that constitutional (structural)...