chemistry owl book chapter 8

8 Covalent Bonding and Molecular Structure

Chapter Outline8.1 AnIntroductiontoCovalentBonding

8.2 LewisStructures

8.3 BondProperties

8.4 ElectronDistributioninMolecules

8.5 Valence-ShellElectron-PairRepulsionTheoryandMolecularShape

8.6 MolecularPolarity

In This Chapter…We will examine chemical bonding in detail in this chapter and the next. Here we will apply what you have learned in Chapters 6 and 7 (atomic structure, electron configurations, and periodic trends) to the chemical bonds formed between atoms and ions and the shapes of molecules and ions that contain covalent bonds. This chapter and the next primarily ad-dress covalent bonding; we examined ionic bonding briefly in Chapter 2, and we will do so in more detail in Chapter 12. We will also examine the forces that exist between individual particles, called intermolecular forces, in Chapter 11.

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Important: These pages have not yet been proofread or checked for accuracy and may contain errors. We are providing them as advance materials for your class testing project.

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230Chapter8 Covalent Bonding and Molecular Structure

8.1 AnIntroductiontoCovalentBondingMatter is made up of atoms and ions that experience both attractive and repulsive forces. It is the balance of these forces that result in chemical bonding within molecules, in metals, and in ionic compounds. In this section, we describe the forces between particles and how these forces result in the formation of covalent bonds within molecules.

8.1a Coulomb’sLaw

Matter is made up of atoms and ions that experience both attractive and repulsive forces. The strength of the force between two charged particles together in any material is described by Coulomb’s law (Equation 8.1). According to this law, the force of attraction or repulsion between two charged species is directly proportional to the magnitude of the charge on the particles (qA and qB in Equation 8.1) and inversely proportional to the square of the distance between the two particles (r in Equation 8.1).

Force ~ 1qA2 1qB2

r2 (8.1)

For electrons, q = −e, and for nuclei, q = +Ze

where

e = magnitude of electron charge (1.6022 3 10−19 C)Z = nuclear charge (number of protons)r = distance between particles A and B

Both attractive and repulsive forces exist in matter, and it is the balance of these forces (and the resulting overall decrease in energy) that results in the formation of chemical bonds, interactions that hold two or more atoms together. Chemical attractive forces involve opposite charges, such as those between protons in a nucleus and the electrons surrounding that nucleus, and between positive and negative ions. Repulsive forces occur between species with like charges, such as the positively charged nuclei of two bonded atoms.

Chemical bonding can be categorized by the types of attractive forces that exist between particles. For example, in ionic bonding, found in ionic solids such as NaCl and CaCO3, there are strong attractive forces between positively and negatively charged ions. In covalent bonding, which occurs in compounds such as H2O and NH3, there are attractive forces be-tween electrons and nuclei on adjacent atoms within a molecule. In metallic bonding, at-tractive forces exist between the electrons and nuclei in metal atoms such as Cu and Fe. Attractive forces are responsible for more than chemical bonding. There are forces that exist between molecules, called intermolecular forces, which will be discussed in more detail in Chapter 11.

OpeningExploration8.1

Coulomb’s Law

Char

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QuickCheck8.1.1


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Chapter8 Covalent Bonding and Molecular Structure 231

8.1b FundamentalsofCovalentBonding

A covalent bond is characterized by the sharing of valence electrons by two adjacent atoms. This type of bonding occurs most typically between nonmetal elements such as carbon, hydrogen, oxygen, and nitrogen.

For example, consider a simple covalently bonded molecule, H2 (Interactive Figure 8.1.1). When two isolated H atoms are at a great distance from one another, they feel no attractive or repulsive forces. However, as the atoms approach more closely, the attractive and repulsive forces between the two atoms become important. At very short distances, repulsive forces become more important than attractive forces, and the atoms repel.

Attractive forces between the hydrogen atoms result from the interaction between the positively charged nucleus (represented by the element symbol) on one hydrogen atom and the negatively charged electron (represented by a dot) on the other hydrogen atom. Repulsive forces are the result of both the like-charged nuclei on adjacent atoms and the electrons on the two hydrogen atoms.

InteractiveFigure8.1.1

Explore the relationship between potential energy and interatomic distance.

Too close together;repulsive forces dominate

74 pm

–436 kJ/mol

Too far apart; weakattractive force; no bondAtoms are at right

distance for stable bond0

Incr

easi

ng p

oten

tial e

nerg

y

Increasing internuclear distance

H2 molecule

H H

H

H H

Changing the distance between H atoms affects potential energy.


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H H

Electron-electron repulsion Electron-nucleus attractionNucleus-nucleus repulsion

H H H H

When two atoms approach each other, these repulsive and attractive forces always occur. When the attractive forces are greater than the repulsive forces, a covalent bond forms.

H H

Attraction is greater than repulsion

� �H H H H

The balance between the attractive and repulsive forces in H2 is related to the distance between H atoms, as shown in Interactive Figure 8.1.1. At large distances, neither attractive nor repulsive forces are important and no bond forms between H atoms. At short distances, repulsive forces are stronger than attractive forces and no bond forms. At an internuclear distance where the attractive forces are stronger than the repulsive forces, a bond forms between the H atoms. The two valence electrons “pair up” and are shared between the two hydrogen nuclei in a covalent bond that is represented by a single line connecting the H atoms. ( Flashback to Section 7.3a The Pauli Exclusion Principle)

HHH � H

The single line between H atoms in H2 is a very useful representation of a chemical bond, but it does not give an accurate picture of the distribution of bonding electrons in the H2 molecule. More sophisticated descriptions of chemical bonding will be discussed in Chapter 9. ( Flashforward to Section 9.1 Valence Bond Theory)

8.2 LewisStructuresOne of the most important tools chemists use to predict the properties of a chemical spe-cies is the Lewis structure. A Lewis structure shows the arrangement of valence electrons and nuclei in covalently bonded molecules and ions. In this section, we explore how to draw Lewis structures for molecules and ions.

8.2a LewisSymbolsandLewisStructures

A Lewis structure (also called a Lewis dot structure or Lewis diagram) shows the arrange-ment of valence electrons (both bonding and nonbonding) and nuclei in covalently bonded

Section8.1Mastery


Lewis Structures

C

CN

N

H

HH

C

C

N C C O

O

H

H

H

HH

H


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molecules and ions. The simplest Lewis structure is the Lewis symbol for an element, where the element symbol represents the nucleus and core (non valence) electrons and dots represent valence electrons.

Lewis symbols have the following characteristics, as shown by the examples in Figure 8.2.1:

• in a Lewis symbol, electrons are arranged around the four sides of the element symbol;

• a Lewis symbol shows the total number of valence electrons for an element; and ( Flashback to Section 7.3 Electron Configuration of Elements)

• Lewis symbols can be drawn to reflect the electron configuration of the element (the number of paired and unpaired electrons in the ground-state electron configuration of the element), but this is not an absolute rule (for example, both :Be and Be are ac-cepted Lewis symbols for beryllium).

The Lewis symbols for the second-period elements in Figure 8.2.1 also show the relationship between the number of valence electrons and group number for the A group (main-group) elements. Recall that the number of valence electrons for any main-group element is equal to the group number for that element.

ExampleProblem8.2.1 InterpretLewissymbols.

a. Draw the Lewis symbol for Te, tellurium. b. The following Lewis diagram represents the valence electron configuration of a main-group

elementX

Te

Identify the element in the fifth period that has this valence electron configuration.

[He] 2s1 [He] 2s2 [He] 2s2 2p1 [He] 2s2 2p2 [He] 2s2 2p3 [He] 2s2 2p4 [He] 2s2 2p5 [He] 2s2 2p6

Group

Number of valence electrons

1 2 3 4 5 6 7 8

1A 2 A 3A 4A 5A 6A 7A 8A

NeFONCBBeLi

Figure8.2.1 Lewis symbols for the second-period elements


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Solution:You are asked to draw a Lewis symbol for an element or to identify an element from a Lewis symbol.

You are given the identity of an element or a Lewis symbol.

a.

X

Te Tellurium is a Group 6A element and has six valence electrons. b. Rubidium: This element has one valence electron, so it is a Group 1A element. Rubidium is

the Group 1A element in the fifth period.

The representation of H2 shown in the previous section where the bonding electrons are represented with a line, H3H, is the Lewis structure of H2. In a Lewis structure, bond-ing pairs of electrons are represented as lines connecting atom symbols, and nonbonding electrons are shown as dots (Interactive Figure 8.2.2). Nuclei and core electrons are repre-sented by element symbols. Notice in Interactive Figure 8.2.2 that there can be more than one bonding pair between atoms and that nonbonding electrons usually appear in pairs (called lone electron pairs or lone pairs). A bond consisting of two electrons (one line) is called a single bond, a bond made up of four electrons (two pairs, two lines) is called a double bond, and a bond with six electrons (three pairs, three lines) is called a triple bond.

Lewis structures are very useful for visualizing the physical and chemical properties of compounds made up of nonmetal elements. We will begin by learning how to create Lewis dot structures; in the following sections, we will use Lewis structures to explore bond prop-

Video Solution

Tutorial 8.2.1

Practice Problem 8.2.1


Interpret Lewis structures.

HH

HH

C C I Cl

Central atoms

Terminal atom

Lone pairs

Shared or bondingelectron pair

Lone pairs

Terminal atom

Two bond pairs(a double bond)

One bond pair(a single bond)

One bond pair(a single bond)

Lewis structures for C2H4 and ICl

ExampleProblem8.2.1 (continued)


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erties (bond order, bond length, bond energy, and bond polarity), the shapes of molecules, molecular polarity, and how the shape and polarity of molecules influence chemical proper-ties (Figure 8.2.3).

8.2b DrawingLewisStructures

An important guideline to follow when drawing Lewis structures is the octet rule. The octet rule states that most atoms in a Lewis structure are surrounded by no more than eight electrons (shared bonding electrons and unshared nonbonding electrons). The octet rule is related to the fact that valence shells contain a single s orbital and three p orbitals that can accommodate up to eight electrons, and it is these orbitals that are most often involved in forming covalent bonds between nonmetals in covalent compounds.

When determining whether elements have satisfied octets, sum the number of lone pair electrons and the number of bonding electrons assigned to an atom.

In addition to the octet rule, it is useful to remember that only certain elements (C, N, O, P, and S) form multiple (double and triple) bonds due to their size and elec-tronic properties. Note that this does not mean that no other elements form multiple bonds; however, it is more likely for these elements to do so. Some ele ments rarely form multiple bonds, notably fluorine because of its high affinity for electrons.

Lewis structures are drawn by following the five steps shown in Table 8.2.1.

Electron-pairgeometry

Shape

Molecularpolarity

Number of bonds

Bond order

Resonancestructures

Electrondistribution

Chemicalreactivity

Physical properties vapor pressure solubility boiling and melting points

LewisStructure

Figure8.2.3 Relationship between Lewis structure and physical and chemical properties

Table8.2.1 HowtoDrawaLewisStructure

Example: PF3 Example: CO2

Step 1: Count valence electrons.Count the total number of valence electrons in the molecule or ion. Anions have extra electrons, so add 1 electron for each negative charge. Cations have a deficiency of electrons, so subtract 1 electron for each positive charge.

Phosphorus has 5 valence electrons and each fluorine has 7 valence electrons.

5 + (3 × 7) = 26 electrons (or 13 electron pairs)

Carbon has 4 valence electrons and each oxygen has 6 valence electrons.

4 + (2 × 6) = 16 electrons (or 8 electron pairs)

Step 2: Arrange atoms.The central atom is usually the one with the lowest affinity for electrons (the one farthest from fluorine on the periodic table). Exception: H is never a central atom. Certain elements are found more frequently as central atoms (C, N, S, P) or terminal atoms (halogens, O) but there are, of course, exceptions. Electronegativity (Section 8.4b) can also be used to choose the central atom in a Lewis structure.

F

P FF C OO

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Table8.2.1 (continued)

The steps in Table 8.2.1 can also be applied to the Lewis structures of ionic species. When the Lewis structure for an ion is drawn, the structure is placed within square brackets and the ion charge is shown outside the brackets. For example, the steps required to draw the Lewis structure for SO3

2− are as follows:

Step 1: Sulfur has 6 valence electrons, each oxygen has 6 valence electrons, and the 2− charge on the ion adds 2 more electrons:

6 + (3 × 6) + 2 = 26 valence electrons (or 13 pairs)

Example: PF3 Example: CO2

Step 3: Add single bonds.Add one bond (using a line) between each terminal atom and the central atom. Each bond represents 2 electrons. F

P FF

26 electrons − 6 bonding electrons = 20 electrons remaining

C OO

16 electrons − 4 bonding electrons = 12 electrons remaining

Step 4: Add remaining electrons.Assign any remaining electrons to the terminal atoms, in pairs, until the octet rule is satisfied for each terminal atom (except hydrogen). If additional electrons remain, add them to the central atom.

F

P FF

Each F needs 3 pairs to satisfy the octet rule, and the 1 remaining pair is assigned to P.

C OO

Each O needs 3 pairs to satisfy the octet rule. No other electrons re-main to satisfy the octet rule for C.

Step 5: Check octet rule.Use the octet rule to determine whether multiple bonds are necessary between atoms. If there is an electron deficiency for an element, change a nonbonding electron pair (lone pair) on an adjacent atom into a bonding pair. Continue only until the octet rule is satisfied for all elements (other than the known exceptions described in Section 8.2c).

F

P FF

All elements have complete octets.

C OO

C OO

The central atom is sharing only 4 electrons. Use one lone pair on each oxygen to make a second bond to carbon, satisfying the octet rule.

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Steps 2 and 3:

S O

O

O

Steps 4 and 5:

S O

O

O

2�

ExampleProblem8.2.2 DrawLewisstructures.

Draw the Lewis structure for

a. SCl2 b. CN−

Solution:You are asked to draw the Lewis structure for a molecule or ion.

You are given the chemical formula for a molecule or ion.

a. Step 1: 6 + (2 × 7) = 20 valence electrons (or 10 pairs)

Steps 2 and 3:S ClCl

Sulfur has a lower affinity for electrons than Cl, so it is the central atom.

Steps 4 and 5:S ClCl

All atoms have an octet of electrons, so it is not necessary to create multiple bonds.

b. Step 1: 4 + 5 + 1 = 10 valence electrons (or 5 pairs)

Steps 2 and 3:NC

Step 4:NC

Step 5:NC �

A triple bond between carbon and nitrogen results in a satisfied octet for both atoms.

Is your answer reasonable? As a final check, always count the number of valence electrons in your Lewis structure and confirm that it matches the number of valence electrons from Step 1.

Video Solution

Tutorial 8.2.2



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8.2c ExceptionstotheOctetRule

Although many Lewis structures follow the octet rule, there are exceptions.Electron-deficient compounds are compounds in which an element has an incomplete

octet. Some elements, notably H, Be, and B, often have fewer than eight electrons in Lewis structures. Hydrogen has a single valence electron in a 1s orbital and therefore accommo-dates only two electrons when it forms covalent bonds. Therefore, it almost always forms only one chemical bond to another atom and does not accommodate lone pairs of electrons. Beryllium (two valence electrons) and boron (three valence electrons) often accommodate only four or six electrons, respectively, in Lewis structures.

For example, BF3 is an electron-deficient compound.

F

BF F

Each fluorine has a complete octet (six nonbonding electrons plus two bonding electrons), but boron has only six electrons (six bonding electrons and no lone pairs). Changing a fluo-rine lone pair to a bonding pair would alleviate the electron deficiency, but fluorine’s high affinity for electrons means this element is unlikely to share its nonbonding electrons with boron. The electron deficiency means that BF3 is a highly reactive compound. For example, it reacts readily with NH3.

F

F

B HNF �

F

F

B HN

H

H

H

H

F

In this reaction, the lone pair on N forms a new covalent bond between the compounds. In the new compound, both N and B have full octets and neither compound is electron deficient.

Free radicals are compounds with at least one unpaired electron. Free radicals can also be electron-deficient compounds. Nitrogen monoxide (nitric oxide, NO) is a free-radi-cal compound because it is an odd-electron molecule with 11 valence electrons and 1 un-paired electron.

ON

Notice that the unpaired electron is placed on the nitrogen atom. In general, the odd electron in free radicals is not located on oxygen because of its high affinity for elec-trons. Free radicals are highly reactive species because the unpaired electrons react


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with other molecules. Pure NO, for example, reacts readily with halogens, O2, and other free radicals.

Elements with an expanded valence (also called an expanded octet) have more than 8 electrons (often 10 or 12) in a Lewis structure. Elements in the third period and below, such as phosphorus, sulfur, and bromine, often have an expanded valence because of their larger radii (when compared to the second-row elements) and the availability of empty d orbitals in the valence shell.

Consider the Lewis structure of SF4.

F

F

SF F

Each fluorine has a satisfied octet (6 nonbonding electrons plus 2 bonding electrons), but the central sulfur atom has an expanded octet with 10 electrons around it (8 bonding elec-trons and 2 nonbonding electrons).

ExampleProblem8.2.3 DrawLewisstructures(octetruleexceptions).

Draw the Lewis structure for

a. ClO b. IBr3

Solution:You are asked to draw the Lewis structure for a molecule or ion that contains at least one atom that does not follow the octet rule.

You are given the chemical formula for a molecule or ion.

a. Step 1: 7 + 6 = 13 valence electrons (or 6 pairs and 1 unpaired electron)

Steps 2 and 3:OCl

Steps 4 and 5:OCl

This is an odd-electron molecule (a free radical). The unpaired electron is placed on chlorine because oxygen has a high affinity for electrons.


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b. Step 1: 7 + (3 × 7) = 28 valence electrons (or 14 pairs)

Steps 2 and 3:

Br

I BrBr

Iodine has a lower affinity for electrons than bromine, so it is the central atom.

Steps 4 and 5:

Br

I BrBr

Iodine is in the fifth period and therefore can have an expanded valence.

8.2d ResonanceStructures

Some molecules have more than one valid Lewis structure. Two or more valid Lewis struc-tures for a species that differ only in the arrangement of electrons, not the arrangement of atoms, are called resonance structures. A resonance hybrid is the actual electron ar-rangement for the molecule or ion, and it is intermediate between the resonance structures but not represented by any of the individual resonance structures. There is a great deal of experimental evidence to support resonance, including bond distances and angles that can-not be explained by the existence of a single Lewis structure for a molecule or ion.

Consider the case of ozone, O3. Completing the first four steps of drawing its Lewis structure results in the following structure for ozone.

O OO

To complete the Lewis structure, the central oxygen needs one more pair of electrons. Both terminal oxygens have lone pairs that can be changed to shared bonding pairs, completing the octet for the central oxygen. There are therefore two possible Lewis structures for O3, and they are drawn separated by a double-headed arrow.

O OO O OO

The two resonance structures for ozone suggest that the oxygen–oxygen bonds in this molecule are not single bonds or double bonds, but something in between. The resonance hybrid, which is not represented by either resonance structure, has oxygen–oxygen bonds that have equivalent properties such as length and energy.

Video Solution

Tutorial 8.2.3




Shape

Molecularpolarity

Number of bonds

Bond order

Resonancestructures


Chemicalreactivity


LewisStructure

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The ozone resonance structures are equivalent to one another because they contain the same number and type of chemical bonds. Not all resonance structures are equivalent, however. For example, carbon dioxide has three resonance structures, and they are not all equivalent.

C OO C OO C OO

The first and third resonance structures are equivalent because each contains one carbon–oxygen triple bond and one carbon–oxygen single bond. The middle resonance structure is unique because it has two carbon–oxygen double bonds. Later in this chapter we will look more closely at the electron distribution in molecules and will see how to use that informa-tion to determine the most likely resonance structure for a molecule or ion. ( Flashforward to Section 8.4c Resonance Structures, Formal Charge, and Electronegativity)

ExampleProblem8.2.4 Drawresonancestructures.

Draw all resonance structures for the carbonate ion, CO32−.

Solution:

You are asked to draw all resonance structures for a molecule or ion.

You are given the chemical formula for the molecule or ion.

The incomplete Lewis structure (octet rule not satisfied for carbon) is

OC

O

O

2�

The electron deficiency for carbon is corrected by changing a lone pair on an adjacent oxygen into a bonding pair. There are three oxygen atoms with lone pairs that can correct the carbon electron deficiency, so there are three equivalent resonance structures for the carbonate ion.

OC

O

O

2�

OC

O

O

2�

OC

O

O

2�

Video Solution

Tutorial 8.2.4


Section8.2Mastery


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8.3 BondPropertiesThe properties of the chemical bonds in a molecule affect its chemical and physical proper-ties. For example, nitrogen, N2, is very unreactive because of the strong triple bond between nitrogen atoms. Hydrazine, N2H4, has a weaker nitrogen–nitrogen single bond that contributes to its high reactivity and its use as a rocket fuel.

8.3a BondOrder,BondLength,andBondEnergy

Lewis structures show the arrangement of valence electrons in covalently bonded molecules and ions. We can use Lewis structures to predict the properties of the bonds in molecules and ions, such as the properties of bond length and bond energy, and use these bond properties to predict physical and chemical properties of molecules and ions.

Bond OrderOne factor that has a great influence on bond properties is bond order, the number of bond-ing electron pairs between two bonded atoms. The bond order of the carbon– carbon single bond in acetone is 1, for example, whereas the carbon–oxygen double bond in acetone has a bond order of 2. The carbon–nitrogen triple bond in the cyanide ion has a bond order of 3.

C CH3

O

H3C

Bond order = 2

Bond order = 1 Bond order = 3

NC �

Bond LengthAs we saw earlier, chemical bonds form when attractive forces between atoms are stronger than repulsive forces. The distance between the atomic nuclei when energy is minimized is the bond length.

Accurate bond distances are determined from careful measurements using techniques such as x-ray crystallography. Bond lengths between two different elements vary slightly between compounds. For that reason, average bond lengths are reported in tables, such as Interactive Table 8.3.1.

The bond lengths in Interactive Table 8.3.1 have units of picometers (1 pm = 10−12 m). Other common units for bond lengths are nanometers (1 nm = 10−9 nm) and Ångstroms (1 Å = 10−10 m). The data in Interactive Table 8.3.1 demonstrate two general trends in bond lengths. First, bond lengths increase with increasing atom size. Consider the trend in H3X bond lengths (where X is a halogen). Atomic radii increase as you move


Bond Energy

Char

les

D. W

inte

rs


Shape

Molecularpolarity

Number of bonds

Bond order

Resonancestructures


Chemicalreactivity


LewisStructure


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down the periodic table (F < Cl < Br < I), and therefore the H3X bond lengths increase as the halogen radius increases. ( Flashback to Section 7.4 Properties of Atoms)

F H Cl H Br H I H

92 pm < < <127 pm 142 pm 161 pm

The second trend demonstrated in Interactive Table 8.3.1 is the relationship between bond length and bond order. As bond order increases, there is an increase in electron den-sity between two nuclei. This results in stronger attractive forces between electrons and

InteractiveTable8.3.1

Some Average Bond Lengths (pm)

Single Bonds

H C N O F Si P S Cl Br I

H 74 110 98 94 92 145 138 132 127 142 161

C 154 147 143 141 194 187 181 176 191 210

N 140 136 134 187 180 174 169 184 203

O 132 130 183 176 170 165 180 199

F 128 181 174 168 163 178 197

Si 234 227 221 216 231 250

P 220 214 209 224 243

S 208 203 218 237

Cl 200 213 232

Br 228 247

I 226

Multiple Bonds

C5C 134 O5O 112

C9C 121 C5O 122

N5N 120 N5O 108

N9N 110 C5N 127


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nuclei, decreasing the distance between the nuclei. A carbon–carbon single bond has a bond order of 1 and is longer than a carbon–carbon double bond with a bond order of 2. In general, for a series of bonds that differ only in bond order, an increase in bond order results in a decrease in bond length.

C3O 143 pm > C5O 122 pm > C9O 113 pm

Bond EnergyAs shown previously in Interactive Figure 8.1.1, a chemical bond forms when the attractive and repulsive forces between atoms result in an energy minimum. Bond energy is the energy required to break a chemical bond in a gas-phase molecule. For example, the bond energy of an H3H bond is 436 kJ/mol (at 298 K). This means that 436 kJ of energy is re-quired to break 1 mol of H3H bonds, forming 2 mol of H atoms.

H3H(g) S H(g) + H(g) ∆Hº = +436 kJ/mol

Breaking bonds is an endothermic process; therefore, bond energies are always posi-tive values. Conversely, bond formation is an exothermic process that always releases en-ergy. Just as bond lengths vary between compounds, so do bond energies. Some average bond energies are shown in Interactive Table 8.3.2.


Some Average Bond Energies (kJ/mol)

Single Bonds

H C N O F Si P S Cl Br I

H 436 413 391 463 565 318 322 347 432 366 299

C 346 305 358 485 3 3 272 339 285 213

N 163 201 283 3 3 3 192 243 3

O 146 184 452 335 3 218 201 201

F 155 565 490 284 253 249 278

Si 222 3 293 381 310 234

P 201 3 326 3 184

S 226 255 213 3

Cl 242 216 208

Br 193 175

I 151


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A clear trend that can be observed from the data in Interactive Table 8.3.2 is the rela-tionship between bond energy and bond order. Bond energy increases with increasing bond order:

C3O 358 kJ/mol < C5O 732 kJ/mol < C9O 1072 kJ/mol

As bond order increases, the stronger attractive forces between bonding electrons and nuclei mean that more and more energy is required to separate the bonded nuclei.

ExampleProblem8.3.1 Relatebondorder,bondlength,andbondenergy.

a. What is the bond order of the boron–oxygen bonds in the borate ion, BO33−?

b. Which molecule has the shortest carbon–carbon bond: C2H4, C2H2, or C2H6? c. Which molecule has the weakest carbon–carbon bond: C2H4, C2H2, or C2H6?

Solution:You are asked to identify the bond order in a molecule or ion and to use bond order to make predictions about relative bond length or bond energy in a series of molecules or ions.

You are given the chemical formula of a molecule or ion, or a series of molecules or ions.

a. The Lewis structure for the borate ion shows three boron–oxygen single bonds. Each B3O bond has a bond order of 1.

OB

O

O

3�

Multiple Bonds

C5C 602 O5O 498

C9C 835 C5O 732

N5N 418 N5O 607

N9N 945 C5N 615

Table8.3.2 (continued)


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b. Bond length decreases with increasing bond order. C2H2 has the highest carbon–carbon bond order and the shortest carbon–carbon bond.

HH

HH

C C CH C HCH C H

HH

HH

CC bond order: 1 2 3

c. Bond energy decreases with decreasing bond order. C2H6 has the lowest carbon– carbon bond order and the weakest carbon–carbon bond.

8.3b ResonanceStructures,BondOrder,BondLength,andBondEnergy

As shown earlier, compounds with resonance structures often have chemical bonds that are not easily described as single, double, or triple bonds. To describe the bond order, bond length, and bond energy of these bonds, the number of resonance structures and bonding pairs must be taken into account. Consider the nitrite ion, NO2

−, which has two equivalent resonance structures.

ONO�

ONO�

Because neither resonance structure represents the actual electron arrangement, the nitrogen–oxygen bonds in this ion are not single bonds (bond order = 1) or double bonds (bond order = 2). Instead, NO2

− has two equivalent NO bonds where three pairs of bonding electrons are distributed over two equivalent NO bond locations. The best way to describe the bonding in the resonance hybrid is with a fractional bond order:

each NO bond order in NO22 5

total number of NO bonding pairsnumber of NO bond locations

5 32

5 1.5

The NO bonds in the nitrite ion have a bond order that is intermediate between a single and a double bond. The bond length of the NO bonds in the nitrite ion are also intermediate between average NO single and double bond lengths.

Video Solution

Tutorial 8.3.1




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Bond Bond Length (pm)

N3O 136

NO in NO2− 125

N5O 115

ExampleProblem8.3.2 Relatebondorder,bondlength,andbondenergy(resonancestructures).

a. What is the bond order of the nitrogen–oxygen bonds in the nitrate (NO3−) ion?

b. In which ion (NO2− or NO3

−) are the nitrogen–oxygen bonds longer? c. In which ion (NO2

− or NO3−) are the nitrogen–oxygen bonds stronger?

Solution:You are asked to identify the bond order in a molecule or ion that has resonance structures and to use bond order to make predictions about relative bond length or bond order in a series of molecules or ions that have resonance structures.

You are given the chemical formula of a molecule or ion, or a series of molecules or ions.

a. The nitrate ion has three equivalent resonance structures.

ON

O

O

�

ON

O

O

�

ON

O

O

�

There are four NO bonding pairs distributed over three NO bonding locations.

each NO bond order in NO32 5

total number of NO bonding pairsnumber of NO bond locations

5 43

5 1.3

b. Bond length increases with decreasing bond order. The nitrogen–oxygen bond order in NO3

− is less than the nitrogen–oxygen bond order in NO2− (1.3 versus 1.5, respectively).

Therefore, NO3− has longer nitrogen–oxygen bonds than does NO2

−. c. Bond energy increases with increasing bond order. The nitrogen–oxygen bond order in

NO2− is greater than the nitrogen–oxygen bond order in NO3

− (1.5 versus 1.3, respectively). Therefore, NO2

− has stronger nitrogen–oxygen bonds than does NO3−.

Video Solution

Tutorial 8.3.2



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8.3c BondEnergyandEnthalpyofReaction

Bond energy values can be used to calculate the enthalpy change for gas-phase reactions. First, assume all chemical bonds are broken in reactant molecules, creating isolated atoms. Next, rearrange the atoms to form products and new chemical bonds. The first step involves breaking bonds and is an endothermic process; the second step involves forming bonds and is an exothermic process. The bond energies are summed as shown in Equation 8.2.

∆Hº = ∑(energies of bonds broken) − ∑(energies of bonds formed) (8.2)

ExampleProblem8.3.3 Calculateenthalpyofreactionusingbondenergies.

Calculate the enthalpy change for the following gas-phase reaction.

C2H6(g) + Cl2(g) S C2H5Cl(g) + HCl(g)

Solution:You are asked to calculate the enthalpy change for a reaction using bond energies.

You are given a chemical equation.

Draw Lewis structures for reactants and products and use them to list all reactant bonds broken and product bonds formed, along with bond energies from Interactive Table 8.3.2.

Reactants: Products:

CH C H

HH

HH

ClCl

CH C H

HH

HH

ClCl

Bonds broken Bonds formed

6 mol C3H 6 × 413 kJ/mol 5 mol C3H 5 × 413 kJ/mol

1 mol C3C 346 kJ/mol 1 mol C3C 346 kJ/mol

1 mol Cl3Cl 242 kJ/mol 1 mol C3Cl 339 kJ/mol

1 mol H3Cl 432 kJ/mol

Use Equation 8.2 to calculate ∆Hº for the reaction.

∆Hº = [6 mol(413 kJ/mol) + 1 mol(346 kJ/mol) + 1 mol(242 kJ/mol)]− [5 mol(413 kJ/mol) + 1 mol(346 kJ/mol) + 1 mol(339 kJ/mol) + 1 mol(432 kJ/mol)]

= −116 kJ


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Notice that five of the C3H bonds and the C3C bond in C2H6 are unchanged in the reaction. The enthalpy of reaction can also be calculated using only the energies of the bonds that are broken (1 mol C3H and 1 mol Cl3Cl) and the bonds that are formed (1 mol C3Cl and 1 mol H3Cl).

∆Hº = [1 mol(413 kJ/mol) + 1 mol(242 kJ/mol)] − [1 mol(339 kJ/mol) + 1 mol(432 kJ/mol)]

= −116 kJ

8.4 ElectronDistributioninMoleculesLewis structures give chemists one method for visualizing the valence electron arrangement in molecules and ions. However, these structures do not fully represent the way electrons are dis-tributed. Calculated formal charge and electronegativity are two tools chemists use, in addition to a Lewis structure, to more accurately describe the electron distribution in a molecule.

8.4a FormalCharge

The formal charge of an atom in a molecule or ion is the charge it would have if all bonding electrons were shared equally. Formal charge is a “bookkeeping” method of showing elec-tron distribution in a Lewis structure, and although it does not give a completely accurate picture of charge distribution, it is helpful in identifying regions with a large positive or negative charge buildup. Consider the Lewis structure for BCl3, and in particular the elec-trons represented by the B3Cl bonds.

B Cl

Cl

Cl

The formal charge on the chlorine atom in the B3Cl bond is a measure of the relation-ship between the chlorine valence electrons (equal to its group number) and the number of bonding and nonbonding electrons assigned to chlorine in the Lewis structure. In calcu-lating formal charge, we assume that all bonding electrons are shared equally between the atoms in the bond and therefore that each atom gets half of them (Equation 8.3). ( Flashback to Section 4.4 Oxidation–Reduction Reactions)

formal charge 5 q number ofvalence electrons

r 2 £q number ofnonbonding electrons

r 112q number of

bonding electronsr§ (8.3)

Video Solution

Tutorial 8.3.3


Section8.3Mastery



Charge Distribution in Molecules

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As shown in Interactive Figure 8.4.1, all of the atoms in BCl3 have a formal charge of zero and we predict that there is no buildup of positive or negative charge in the molecule. Formal charge, however, assumes all bonding electrons are shared equally. As you will see in the following section, other methods that take into account the unequal sharing of bond-ing electrons can give a more accurate picture of electron distribution in a molecule.

The sum of the formal charges for all atoms in a molecule or ion is equal to the charge on the molecule or ion, as shown in the following example.

ExampleProblem8.4.1 Calculateformalcharge.

Use the formal charge for each atom in the cyanide ion, CN−, to predict whether H+ is more likely to attach to carbon or nitrogen when forming hydrocyanic acid.

Solution:You are asked to identify the formal charge for every atom in a polyatomic ion and to use formal charge to predict the attachment site of H+.

You are given the chemical formula for the polyatomic ion.

First draw the Lewis structure of CN−.

NC �

Use Equation 8.3 to calculate the formal charge for carbon and nitrogen.

C formal charge = (4) − [2 + ½(6)] = −1

N formal charge = (5) − [2 + ½(6)] = 0

When the positively charged H+ ion attaches to CN−, it is more likely to attach to the atom with the negative formal charge, forming H3C9N.

Is your answer reasonable? Notice that the sum of the formal charges is equal to the overall charge on the ion (−1).

Video Solution

Tutorial 8.4.1



Determine formal charge.

B Cl

Cl

Cl B Cl

Cl

Cl

B � 3 � [0 � 1/2(6)] � 0

Cl � 7 � [6 � 1/2(2)] � 0

Formal charges in BCl3


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8.4b BondPolarity

In a covalent bond, electrons are attracted to two nuclei, but sometimes one nucleus attracts the electrons more strongly than the other. When one nucleus attracts the electrons more strongly, the bonding electrons are located closer to one nucleus than the other. This creates an uneven distribution of bond electron density and a polar bond (or polar covalent bond). When electrons experience the same attractive force to both nuclei, the bond is nonpolar.

The term polar refers to the existence of a dipole, a separation of partial positive (symbolized δ+) and partial negative (symbolized δ−) charge within a bond or a molecule. The partial charges in a dipole are due to an uneven distribution of electron density, not a transfer of electrons between atoms to form ions.

A dipole is characterized by its dipole moment, the measurement of the strength or polarity of the dipole. Dipole moments, which are reported in units of debyes (D), are pro-portional to the sizes of the charges and their distance apart. Dipoles are commonly indi-cated by use of an arrow that points at the negative end of the dipole and has a cross to indicate the positive end of the dipole.

��

X Y

Consider a fluorine–fluorine bond and a carbon–fluorine bond.

��

F CF F

In the fluorine–fluorine bond, the bonding electrons are attracted equally to both fluorine nuclei. The electron density is therefore evenly distributed between the fluorine atoms, and the bond is nonpolar. The carbon–fluorine bond, in contrast, is polar because the bonding electrons are attracted more strongly to fluorine than to carbon. This results in electron density that is closer to fluorine than to carbon. Recall that fluorine has a higher effective nuclear charge than carbon and its valence atomic orbitals are lower in energy than those of carbon. ( Flashback to Section 7.4 Properties of Atoms) A partial negative charge oc-curs at fluorine because of this uneven electron density distribution, and a corresponding partial positive charge happens at the electron-deficient carbon.

The ability of an atom in a molecule to attract electrons to itself is referred to as its electronegativity, χ (Interactive Figure 8.4.2). Electronegativity, a concept first pro-posed by Linus Pauling in 1932, is a relative scale where the most electronegative element (fluorine) is assigned a value of 4.0. Notice in Interactive Figure 8.4.2 that

• the noble gases (Group 8A) are not assigned electronegativity values (most of these elements do not form covalent bonds);


Shape

Molecularpolarity

Number of bonds

Bond order

Resonancestructures


Chemicalreactivity


LewisStructure

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• electronegativity values increase as you move left to right across the periodic table and decrease as you move down the periodic table;

• hydrogen does not follow the periodic trend and has an electronegativity similar to that of carbon;

• metals generally have low electronegativity values and nonmetals generally have high electronegativity values; and

• fluorine, oxygen, nitrogen, and chlorine are the most electronegative elements.

The polarity of a chemical bond is related to the difference in electronegativity (∆χ) of the two elements that make up the bond. For covalent bonds between non metals, a ∆χ greater than zero indicates that the bond is polar and a zero ∆χ indicates a nonpolar bond. For example, the C3F bond described earlier has ∆χ = (4.0 − 2.5) = 1.5. It is a polar bond.

When ∆χ is very large, the interaction between elements has more ionic character than covalent character. For example, aluminum and fluorine have very different electronegativi-


Explore electronegativity.

Li1.0

1A 2A 3A 4A 5A 6A 7A

3B 4B 5B 6B 7B8B

1B 2BNa1.0

K0.9

Rb0.9

Cs0.8

�1.01.0–1.4

1.5–1.92.0–2.4

2.5–2.93.0–3.9

4.0

Be1.5

H2.1

Mg1.2

Ca1.0

Sr1.0

Ba1.0

Sc1.3

Y1.2

La1.1

Ti1.4

Zr1.3

Hf1.3

V1.5

Nb1.6

Ta1.4

Cr1.6

Mo1.6

W1.5

Mn1.6

Tc1.7

Re1.7

Fe1.7

Ru1.8

Os1.9

Co1.7

Rh1.8

Ir1.9

Ni1.8

Pd1.8

Pt1.8

Cu1.8

Ag1.6

Au1.9

Zn1.6

Cd1.6

Hg1.7

B2.0

Al1.5

Ga1.7

In1.6

Tl1.6

C2.5

Si1.8

Ge1.9

Sn1.8

Pb1.7

N3.0

P2.1

As2.1

Sb1.9

Bi1.8

O3.5

S2.5

Se2.4

Te2.1

Po1.9

F4.0

Cl3.0

Br2.8

I2.5

At2.1

Electronegativity values

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ties [∆χ = F(4.0) − Al(1.5) = 2.5], and an Al3F bond has much greater ionic character than a C3F bond.

There is not a defined electronegativity difference that separates ionic from polar bonds. Instead, there is a continuum moving between these two extremes. All polar bonds have some “ionic character” and some “covalent character.”

ExampleProblem8.4.2 Useelectronegativitytodeterminebondpolarity.

a. Which of the following bonds are nonpolar?

C3Cl H3Cl H3H F3F P3H S3O B3F

b. Which of the following bonds is most polar?

C3Cl H3Cl H3H F3F P3H S3O B3F

Solution:You are asked to identify bonds as polar or nonpolar and to identify the most polar bond in a series of bonded atoms.

You are given a series of bonded atoms.

a. The H3H, F3F, and P3H bonds are nonpolar. Any bond between two like atoms is non-polar because ∆χ = 0. The P3H bond is nonpolar by the coincidence that both P and H have the same electronegativity value of 2.1. The C3Cl, H3Cl, S3O, and B3F bonds are polar because when two different elements are bonded, the bond is almost always polar.

b. The B3F bond has the greatest ∆χ (4.0 − 2.0 = 2.0), so it is the most polar bond.

8.4c ResonanceStructures,FormalCharge,andElectronegativity

When nonequivalent resonance structures exist, the most likely resonance structure is the one with formal charges closest to zero. A general rule of chemical stability is that the localization of positive or negative charges within a molecule is destabilizing. Consider the following two possible inequivalent resonance structures for BCl3 shown here with calculated formal charges.

B Cl

Cl

Cl

(0)

(0)

(0)(0)

B Cl

Cl

Cl

(–1)

(+1)

(0)(0)

The resonance structure on the right is less likely than the one on the left because it has localized formal charges of +1 and −1. In addition, chlorine (χ = 3.0) is more electro-

Video Solution

Tutorial 8.4.2



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negative than boron (χ = 2.0), so a resonance structure that has a positive formal charge on the more electronegative element (and a negative formal charge on the less electronega-tive element) is probably not stable.

The three nonequivalent resonance structures of CO2 are shown here with calculated formal charges.

(0) (–1)(+1) (+1)(0) (0)(0) (–1) (0)

C OO C OO C OO

The central structure is the most likely resonance structure for CO2 because it has formal charges of zero on each atom, whereas both of the other resonance structures have formal charges of +1 and −1 on the O atoms.

The cyanate ion, OCN−, has three nonequivalent resonance structures.

(0) (–2)(+1) (–1)(0)(0) (–1) (0) (0)

CO CO CON N N� � �

None of the three resonance structures have formal charges of zero on all atoms. The first resonance structure is not very likely because of the large formal charges (+1 and −2). The other two resonance structures, however, each have small formal charges. In this case, electronegativity can help determine the best resonance structure. The electronegativity of oxygen (3.5) is greater than that of nitrogen (3.0). Therefore, oxygen is more likely to carry a negative formal charge in a Lewis structure, and according to formal charges, the reso-nance structure on the right is most likely.

ExampleProblem8.4.3 Useformalchargeandelectronegativitytoidentifybestresonancestructure.

Three nonequivalent resonance structures for the chlorate ion are shown here. Assign formal charges to all atoms in the resonance structures and identify the more likely resonance structure.

OCl

O

O

�

OCl

O

O

�

OCl

O

O

�

A B C


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Solution:You are asked to use formal charge to identify the most likely resonance structure of those given for a polyatomic ion.

You are given three valid resonance structures.

Formal charges:

(0)(+2) (0)(–1)(–1)(–1) (–1)

(0)(0)(–1)

(0)(0)

OCl

O

O

�

OCl

O

O

�

OCl

O

O

�

Structure B is the most likely resonance structure. The formal charges in B are close to zero, and the highly electronegative oxygen atom carries a −1 formal charge. Structure A is unlikely because of the large positive formal charge on chlorine. Structure C is unlikely because the least electronegative element in the ion (chlorine) has a negative formal charge while the most electronegative element in the ion (oxygen) has a formal charge of zero.

8.4d PartialCharge

Calculated formal charges and relative electronegativities are useful tools for assigning charge distribution in a Lewis structure because they help identify likely resonance struc-tures and regions with a buildup of positive or negative charge in molecules and ions. They do not, however, give an accurate picture of the actual electron distribution in molecules. Computer modeling programs calculate partial charges on atoms that give a more accu-rate picture of electron distribution. For example, the calculated partial charges on the atoms in carbon dioxide and the cyanate ion are shown in the following figure. Red spheres indicate positive partial charge, and yellow spheres indicate negative partial charge. The size of the sphere is proportional to the magnitude of the partial charge. As was true with formal charge, the sum of partial charges is equal to the charge on the molecule or ion.

(–0.26) (+0.52) (–0.26) (–0.54) (+0.16) (–0.62)

O C O O C N�

Video Solution

Tutorial 8.4.3




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In CO2, each oxygen carries a negative partial charge and the carbon has a positive partial charge. This reflects the fact that oxygen is more electronegative than carbon but does not reflect the calculated formal charges of zero in the most likely resonance structure for CO2. However, the fact that both oxygen atoms have negative calculated partial charges suggests that the two resonance structures that have a positive formal charge on oxygen are very un-likely. The calculated partial charges also show that the CO bonds are polar, results that are supported by electronegativity values but not by formal charge calculations.

In the cyanate structure, both oxygen and nitrogen carry approximately the same negative partial charge and carbon has a slightly positive partial charge. None of the three OCN− resonance structures shows a negative formal charge on both nitrogen and oxygen, but two of the resonance structures have a −1 formal charge on either nitrogen or oxygen. The calculated partial charges for OCN− suggest that both of the resonance structures with −1 formal charges on nitrogen and oxygen are important and both contribute to the reso-nance hybrid for OCN−.


The shape of a molecule or ion is one of its most important characteristics because it controls many other properties of a compound, such as melting and boiling points and chemical reac-tivity. A variety of experimental techniques such as x-ray crystallography and spectroscopy

Section8.4Mastery

QuickCheck8.4.1


Exploring Shapes of Molecules

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are used to determine precise atom distances, bond angles, and the shape of a molecule. However, the Lewis structure, which can be used to predict the shape of a molecule or ion, is one of the most useful tools a chemist has.

8.5a VSEPRandElectron-PairGeometry

Lewis structures show the atom connectivity and number of bonds and lone pairs in a mole-cule or ion but do not provide information about the three- dimensional shapes of molecules. For example, numerous experiments have shown that water, H2O, has a bent (nonlinear) shape. The Lewis structure, however, can be drawn to show a linear arrangement of atoms.

H O H

The valence shell electron-pair repulsion (VSEPR) theory allows chemists to eas-ily predict the shapes of molecules and ions made up of nonmetals.

According to VSEPR theory,

• positions around a central atom are occupied by structural electron pairs, nonbond-ing or bonding electrons that repel one another and are arranged so as to avoid one another as best as possible;

• structural electron pairs can be nonbonding electrons, where each pair of electrons (or single electrons, in free radicals) is counted as one structural electron pair on a central atom;

• structural electron pairs can be bonding electrons, where each bond (single or multi-ple) is counted as one structural electron pair on a central atom;

• the electron-pair geometry is the arrangement of the structural electron pairs around the central atom; and

• the shape (also called molecular geometry) is the arrangement of atoms around the central atom.

The electron-pair geometry is defined by the arrangement of structural electron pairs around the central atom. In large molecules with multiple central atoms, we will describe the electron-pair geometry around each central atom. When a central atom is surrounded by two, three, four, five, or six structural pairs of electrons, they are arranged in one of the following ideal electron-pair geometries (Interactive Table 8.5.1).

Interactive Table 8.5.1 also shows the bond angles that are characteristic for each ideal electron-pair geometry. Bond angle is the angle formed by the nuclei of two atoms with a central atom at the vertex. The bond angles shown in Interactive Table 8.5.1 are ideal


Shape

Molecularpolarity

Number of bonds

Bond order

Resonancestructures


Chemicalreactivity


LewisStructure


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Number of Structural Pairs

Species Type (A = central atom, X = terminal atom)

Electron-Pair Geometry Example X3A3X Bond Angles

2 AX2 Linear CO2 180°

3 AX3 Trigonal planar BF3

120°

4 AX4 Tetrahedral CH4

109.5°

5 AX5 Trigonal bipyramidal

PCl5

120°

90°

6 AX6 Octahedral SF6

90°


Ideal Electron-Pair Geometries

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angles, and most molecules with these ideal electron-pair geometries have bond angles that are very close to these values.

Notice that of all the electron-pair geometries in Interactive Table 8.5.1, only one has two different bond angles. In a trigonal bipyramidal geometry, terminal atoms can occupy either an axial or an equatorial position. As shown in Figure 8.5.1, equatorial positions are arranged in a trigonal planar geometry, 120º from each other, whereas axial positions are 90º from the equatorial (trigonal planar) plane.

Follow these steps to predict the electron-pair geometry of a molecule with a single central atom:

1. Draw the Lewis structure. 2. Sum the number of structural electron pairs around the central atom. 3. Use the number of structural electron pairs to identify the electron-pair geometry us-

ing the ideal geometries shown in Interactive Table 8.5.1.

ExampleProblem8.5.1 Identifyelectron-pairgeometry.

Determine the electron-pair geometry of

a. the carbon atoms in acetic acid, CH3CO2H b. SF4

Solution:You are asked to determine the electron-pair geometry for a molecule or for specific atoms in a complex molecule.

You are given the chemical formula for the molecule.

Draw the Lewis structure of each species, sum the number of structural electron pairs around the central atom, and use Interactive Table 8.5.1 to determine the electron-pair geometry.

a. The Lewis structure of acetic acid shows that there are four structural electron pairs (four single bonds) around the carbon on the left and three structural electron pairs (two single bonds and one double bond) around the carbon on the right.

C C O

O

H

H

H

H

The electron-pair geometry is tetrahedral around the carbon on the left (bond angles of 109.5º) and trigonal planar around the carbon on the right (bond angles of 120º).

b. There are five structural electron pairs around the central atom in SF4: four single bonds and one lone pair of electrons.

axial

axial

equatorial

equatorial

equatorial90°

120°

Figure8.5.1 Equatorial and axial positions in a trigonal bipyramid


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F

F

SF F

The electron-pair geometry of SF4 is trigonal bipyramidal.

8.5b Shape(MolecularGeometry)

The shape of a molecule (its molecular geometry) is defined by the atom positions in a molecule. The shape is the same as the electron-pair geometry when none of the structural electron pairs are nonbonding electrons.

For example, boron trichloride, BCl3, has a trigonal planar electron-pair geometry and a trigonal planar shape. There are three structural electron pairs around the central boron atom, and all are bonding electrons. Notice that a Lewis structure is not always drawn to show the shape of the molecule or the correct bond angles.

B ClCl

Cl

Carbon dioxide, CO2, has a linear electron-pair geometry and a linear shape. There are two structural electron pairs around the central carbon atom, and both are bonding electrons.

O C O

There are many molecules for which the shape is not the same as the electron-pair geometry. For example, ozone, O3, has a trigonal planar electron-pair geometry and a bent shape. There are three structural electron pairs around the central oxygen atom, but only two are bonding electrons. Because shape is defined by the positions of the atoms in a molecule, not the electrons, ozone has a bent shape rather than a trigonal planar shape.

O O O

Video Solution

Tutorial 8.5.1




Shape

Molecularpolarity

Number of bonds

Bond order

Resonancestructures


Chemicalreactivity


LewisStructure


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Interactive Table 8.5.2 shows the shapes for molecules with three to six structural electron pairs and varying numbers of nonbonding electron pairs on the central atom.


Shapes of Molecules with Three to Six Structural Electron Pairs

Number of Nonbonding Structural Pairs

0 1 2 3

Num

ber

of S

truc

tura

l Ele

ctro

n P

airs

3 Trigonal planarBF3

120°

BentO3

4 TetrahedralCF4

109.5°

Trigonal pyramidalNH3

BentH2O

5 Trigonal bipyramidalPF5

120°

90°

SeesawSF4

T-shapedClF3

LinearXeF2

6 OctahedralSF6

90°

Square pyramidalBrF5

Square planarXeF4

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ExampleProblem8.5.2 Identifymoleculargeometry.

Determine the shape of

a. ICl5 b. SO3

2−

Solution:You are asked to determine the shape of a molecule or ion.

You are given the chemical formula for the molecule or ion.

Draw the Lewis structure of each species, sum the number of structural electron pairs around the central atom, and use Interactive Table 8.5.1 to determine the electron-pair geometry. Use the number of bonding and nonbonding structural pairs, along with Interactive Table 8.5.2, to determine the molecular geometry.

a. ICl5 has six structural electron pairs around the central atom. Five are bonding electrons, and one is nonbonding.

ICl

ClCl

Cl

Cl

The electron-pair geometry is octahedral, and the molecular geometry is square pyramidal.

b. SO32− has four structural electron pairs around the central atom. Three are bonding elec-

trons, and one is nonbonding.

O S O

O 2�

The electron-pair geometry is tetrahedral, and the molecular geometry is trigonal pyramidal.

When determining the shape of a molecule with nonbonding electrons (lone pairs) in structural positions, it is important to note the different steric requirements of lone pairs and bonding pairs. Lone pairs are diffuse because they are attracted to a single nucleus; bonding pairs, in contrast, are localized between and attracted to two nuclei. Lone pairs therefore occupy more space around a central atom than do bonding pairs. Consider SF4, which has four structural positions occupied by bonding pairs and one occupied by a lone pair. The five structural positions are arranged in a trigonal bipyramid. The lone pair oc-

Video Solution

Tutorial 8.5.2



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cupies an equatorial position (seesaw shape) because this minimizes repulsive forces be-tween the larger, diffuse lone pair and the bonding pairs (Figure 8.5.2(a)). If the lone pair occupies an axial position (Figure 8.5.2(b)), the close contact (90º angles) between the lone pair and bonding pairs increases repulsive forces, making this configuration less favor-able. Thus, lone pairs occupy equatorial positions in trigonal bipyramidal electron-pair ge-ometries. Similarly, lone pairs occupy positions opposite each other in an octa hedron, be-cause this also minimizes repulsive forces.

Molecular shapes predicted using the VSEPR ideal electron-pair shapes are usually very close to the shapes measured by experiment, especially when all terminal atoms are identical. However, when lone pairs are present on the central atom, bond angles in particular differ from predicted values. Consider the bond angles in CH4, NH3, and H2O (Figure 8.5.3). All molecules have the same electron-pair geometry (tetrahedral), but they differ in the number of lone pairs on the central atom. As the number of lone pairs on the central atom increases, the H3X3H bond angle decreases due to the steric requirements of the lone pairs.

8.6 MolecularPolarityAs we saw earlier, covalent bonds are polar when there is an uneven attraction for elec-trons between the bonded atoms. Polar bonds in a molecule can result in a polar mole-cule, which affects the physical properties of a compound. For example, polar molecules are often very soluble in water, whereas nonpolar molecules are not.

8.6a MolecularPolarity

For a molecule to be polar, it must contain polar bonds and those bonds must be arranged so that there is an uneven charge distribution. The following steps are used to predict whether a molecule is polar.

1. Draw the Lewis structure. 2. Determine the shape.

Section8.5Mastery

QuickCheck8.5.1

FF

FF

SS

FF

FF187°

87°

<90°102°

(b)(a)

Figure8.5.2 SF4 with lone pair in (a) equatorial and (b) axial positions


Polarity of Small Molecules

109.5° 107.5°107.5° 104.5°

Figure8.5.3 Effect of lone pairs on bond angles


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3. If the molecule has polar bonds, indicate them on the molecule. 4. Use the shape and bond dipoles to determine whether there is an uneven distribution

of bond electron density in the molecule.

For example, boron trifluoride, BF3, is a nonpolar molecule that has polar bonds.

��

��

��B

FF

F

The shape of BF3 is trigonal planar and the B3F bonds are polar (fluorine is the nega-tive end of the bond dipole). As shown in the preceding illustration, the three bond dipoles are arranged symmetrically in the molecule and do not result in an uneven distribution of electron density. BF3 is therefore nonpolar.

Trifluoromethane is a polar molecule.

CF F

F

H ��

��

��

��

The shape of CHF3 is tetrahedral, and the C3F and C3H bonds are polar. Carbon is the negative end of the C3H bond dipole, and fluorine is the negative end of each C3F bond dipole. When we draw in the individual bond dipoles, we see that there is a net movement of bond electron density away from hydrogen and toward the fluorine atoms. This uneven electron density distribution means that CHF3 is polar, and the molecule has a net dipole with the positive end near hydrogen and the negative end near the fluorine atoms.

��

��

This method is also useful for larger, more complex molecules. For example, consider acetone, CH3COCH3.


Shape

Molecularpolarity

Number of bonds

Bond order

Resonancestructures


Chemicalreactivity


LewisStructure


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O

CCC

H

H HH H

H

Carbon and hydrogen have very similar electronegativities (∆χ = 0.4), so the bonds in the 3CH3 groups are only slightly polar. The carbon–oxygen bond, however, is very polar (∆χ = 1.0), and oxygen is the negative end of the C3O bond dipole. There is a net shift of electron density toward oxygen, so the molecule is polar. The net molecular dipole is shown here.

��

��

Dipole moments for some common molecules are shown on Table 8.6.1.

ExampleProblem8.6.1 Determinepolarityofmolecules.

Determine whether each of the following is polar.

a. SO3

b. BrF3

Solution:You are asked to determine whether a molecule is polar.

You are given the compound formula.

Draw the Lewis structure for each molecule, determine the shape, and label any polar bonds. Use shape and bond polarity to determine whether the molecule is polar.

a. Nonpolar. SO3 has a trigonal planar shape, and all three SO bonds are polar. The three bond dipoles are arranged symmetrically in the molecule, so the molecule is not polar.

O

S

O

O

Table8.6.1 Dipolemomentsforsomecommonmolecules

Molecule Dipole Moment (debye, D)

BF3 0

NF3 0.23

CH4 0

CH2Cl2 1.60

H2O 1.85

H2S 0.95

HCl 1.07

HI 0.38


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b. Polar. BrF3 is T-shaped, and all three BrF bonds are polar. The three bond dipoles are not ar-ranged symmetrically around the molecule, so the molecule is polar. The bromine is the posi-tive end of the net dipole, and one of the fluorine atoms is the negative end of the bond dipole.

F

Br FF

F

Br FF

ChapterRecap

KeyConcepts

8.1 AnIntroductiontoCovalentBonding

• The force between charged particles is described in Coulomb’s law, which shows that the force is directly related to the magnitude of the charges and inversely related to the distance between the particles (8.1a).

• Forces between the particles that make up matter include ionic bonding, covalent bonding, metallic bonding, and intermolecular forces (8.1a).

• Covalent bonds are characterized by the sharing of valence electrons by two adjacent atoms (8.1b).

8.2 LewisStructures

• A Lewis structure shows the arrangement of valence electrons and nuclei in a cova-lently bonded molecule or ion (8.2a).

• Lewis structures include nonbonding electrons (lone pairs) and bonding electrons (single, double, or triple bonds) (8.2a).

• The octet rule, an important guideline when drawing Lewis structures, states that most atoms in a Lewis structure are surrounded by no more than eight electrons (8.2b).

• Exceptions to the octet rule include electron-deficient compounds, free radicals, and compounds where an atom has an expanded valence (8.2c).

• Resonance structures are two or more valid Lewis structures for a given species that vary only in the arrangement of electrons. The resonance hybrid, the actual electron arrangement, is intermediate between the resonance structures (8.2d).

Video Solution

Tutorial 8.6.1


Section8.6Mastery



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8.3 BondProperties

• Bond order is the number of bonding electron pairs between two bonded atoms (8.3a).

• Bond length is the distance between atomic nuclei when energy is minimized (8.3a).

• Bond energy is the energy required to break a chemical bond in a gas-phase molecule (8.3a).

• For a series of bonds between like atoms, as bond order increases, bond length de-creases and bond energy increases (8.3a).

• Bond energy values can be used to calculate the enthalpy change for gas-phase reac-tions (8.3c).

8.4 ElectronDistributioninMolecules

• Formal charge is the charge an atom in a molecule or ion would have if all bonding electrons were shared equally. The sum of formal charges on all atoms in a molecule or ion is equal to the charge on the molecule or ion (8.4a).

• When bonding electrons are unequally shared between atoms, a polar bond results (8.4b).

• A polar bond has a dipole, a separation of partial positive and negative charges, which is characterized by a dipole moment (8.4b).

• Electronegativity is a measure of the ability of an atom in a molecule to attract elec-trons to itself (8.4b).

• The greater the difference in electronegativity between bonded atoms, the more polar the bond (8.4b).

• Partial charge is a calculated value that gives a more accurate picture of electron dis-tribution in molecules and ions (8.4d).


• Shapes of molecules and ions made up of nonmetals are predicted using VSEPR theory, which states that electron pairs (structural and nonbonding) repel one another and are arranged to avoid one another as best as possible. (8.5a).

• Electron-pair geometry is the arrangement of structural electron pairs around the cen-tral atom, and molecular geometry is the arrangement of atoms around the central atom (8.5a).

8.6 MolecularPolarity

• For a molecule to be polar, it must contain polar bonds that are arranged so that there is an uneven charge distribution (8.6a).


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KeyEquations

Force ~1qA2 1qB2

r2 (8.1)

∆Hº = ∑(energies of bonds broken) − ∑(energies of bonds formed) (8.2)

formal charge 5 q number ofvalence electrons

r 2 £ q number ofnonbonding electrons

r 112q number of

bonding electronsr § (8.3)

Key Terms

8.1 AnIntroductiontoCovalentBondingCoulomb’s lawbondionic bondingcovalent bondingmetallic bondingintermolecular forces

8.2 LewisStructuresLewis structureLewis symbolbonding pairlone (electron) pairssingle bonddouble bond

triple bondoctet ruleelectron deficientfree radicalsexpanded valenceresonance structuresresonance hybrid

8.3 BondPropertiesbond orderbond lengthbond energy

8.4 ElectronDistributioninMoleculesformal chargepolar bond

polar covalent bondnonpolardipoledipole momentelectronegativity, χpartial charges

8.5 Valence-ShellElectron-PairRepulsionTheoryandMolecularShapevalence-shell electron-pair repulsion (VSEPR)structural electron pairselectron-pair geometryshape (molecular geometry)bond angle

Chapter8 ReviewandChallengeProblems


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chemistry owl book chapter 8

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