Chemical Bonding—The Formation of Materials

C H A P T E R

3 Chemical Bonding—The Formation of Materials O U T L I N E 3.1 Atoms and Ions

75

3.7 Molecular Polarity

105

3.2 Ionic Bonding

82

3.8 Intermolecular Forces

107

3.3 Covalent Bonding

86

Important Terms

113

3.4 Mixed Covalent/Ionic Bonding

92

Study Questions

114

3.5 Molecular Orbitals

95

Problems

115

3.6 Molecular Geometry

100

3.1 ATOMS AND IONS A neutral atom that loses one or more electrons becomes a positively charged ion. This positively charged ion is known as a cation (from the Greek word kata´, meaning “down”). A neutral atom that gains one or more electrons has a negative charge and is known as an anion (from the Greek word a´no¯, meaning “up”). The number of electrons an element will gain or lose is also a periodic property and can generally be predicted from its position in the periodic table as shown in Fig. 3.1. Atoms will gain or lose electrons to form ions that have electronic configurations which are more stable than the electronic configurations of the parent atoms. For most elements, this means that they will either gain or lose the number of electrons needed to achieve a closed valence shell. Remember from Table 2.9 of Chapter 2 that the number of electrons in an atom’s valence shell can be determined from its group number. Since the noble gases in group 18 already have a closed valence shell with eight valence electrons (ns2np6), they do not form ions. Other elements (except for those in groups 8 through

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3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

FIG. 3.1 The Periodic Table of the Elements showing the common ions formed by the elements in each group. Elements indicated by a * have more than one ionic form.

12) tend to gain or lose electrons to achieve the ns2np6 closed valence shell of a noble gas. Most of the elements can easily achieve this by losing the extra electrons in their valence shell and become cations with the new valence shell of ns2np6. However, elements in groups 15 through 17 have valence shells that are nearly full and so can complete the ns2np6 closed valence shells by gaining the missing electrons and become anions. The alkali metals in group 1 have one electron in their valence shell (ns1). The loss of this electron forms a cation with a stable electronic configuration of the noble gas in the period previous to it. For example, sodium has the electronic configuration 1s22s22p63s1. By losing the electron from the 3s valence orbital, sodium acquires the stable electronic configuration of the noble gas neon (1s22s22p6) with a new closed valence shell of 2s22p6. So, the alkali metals will always lose the ns electron to form 1+ cations. Although hydrogen is normally placed in group 1, it is unusual in that it is the only element in the periodic table with only one electron. However, like the alkali metals, hydrogen will also lose this 1s electron to form a 1+ cation, even though it is now only a single proton with no electrons. The alkaline earth metals in group 2 have two electrons in their valence shell (ns2). They can achieve a closed valence shell with the electronic configuration of the noble gas in the period just above them by losing both valence electrons. The valence shell then becomes ns2np6.The alkaline earth metals always form 2+ cations. The transition metals in group 3 have three valence electrons [ns2(n
1)d1] and will lose these three electrons to achieve the closed valence shell of a noble gas and become 3+ cations. The transition metals in groups 4 through 7 can also lose their valence electrons as indicated by their group numbers, to get to the electronic configuration of the noble gas just before them in the periodic table. However, many transition metals can also form cations with other charges as shown in Table 3.1. For example, all the transition metals in group 4 form

77

3.1 ATOMS AND IONS

TABLE 3.1 Elements With Multiple Ionic Forms Element

Group

Ionic Forms

Titanium

4

4+, 3+, 2+

Vanadium

5

5+, 4+, 3+, 2+

Niobium

5

5+, 3+

Chromium

6

6,+ 3+, 2+

Manganese

7

7+, 4+, 3+, 2+

Technetium

7

7+, 6+, 4+

Rhenium

7

7+, 6+, 4+

Iron

8

3+, 2+

Osmium

8

3+, 4+

Cobalt

9

3+, 2+

Iridium

9

4+, 3+

Nickel

10

2+, 3+

Palladium

10

2+, 3+

Platinum

10

2+, 4+

Copper

11

1+, 2+

Gold

11

1+, 3+

Mercury

12

2+, 1+

Thallium

13

3+, 1+

Germanium

14

4+, 2+

Tin

14

4+, 2+

Lead

14

4+, 2+

Arsenic

15

5+, 3+, 3


Antimony

15

5+, 3+, 3


Bismuth

15

5+, 3+

Tellurium

16

6+, 4+, 2


Polonium

16

6+, 4+, 2+

4+ cations, but titanium can also form a 3+ cation and a 2+ cation. Similarly, the transition metals in group 5 all form 5+ cations, but vanadium can also form a 4+ cation, a 3+ cation, and a 2+ cation. Niobium can also form a 3+ cation. This variability in the ionic forms of many of the transition metals is because the removal of all the valence electrons to get to the noble gas configuration would require

78

3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

a great deal of energy for transition metals with many valence electrons. The additional ionic forms are achieved by losing a smaller number of electrons, which is more energy-efficient. Although this does not give the transition metal a closed valence shell, the resulting electronic configuration is still more stable than that of the parent atom. Elements in groups 8 through 12 are unable to lose all their valence electrons and are restricted to cations with lower charges. Looking at Table 3.1, the most common cations for the transition metals are 2+ and 3+. The valence electrons of the transition elements are in the ns and the (n
1)d subshells. The orbitals in these two subshells are very close in energies and the electrons in both subshells can be used in bond formation. The 2+ cation is common among the transition metals because the two electrons in ns subshell are lost first, before the (n
1)d electrons. The 3+ and 4+ cations are also common because there is a tendency for the transition metals to lose unpaired d electrons since unpaired electrons are less stable than paired electrons. These trends in the d-block elements lead to lower ionic charges than expected from their position in the periodic table. They also contribute to the multiple ionic forms of many of the transition metals. The elements in groups 13 and 14 in the p-block of the periodic table have three (ns2np1) and four (ns2np2) electrons in their valence shells. They will lose these valence electrons to achieve the valence shell of the noble gases and become 3+ and 4+ cations, respectively. The exceptions in these two groups are boron, carbon, and silicon, which do not form ions. These elements prefer to gain a closed shell by sharing electrons with another atom rather than losing them entirely. The sharing of electrons will be covered in Section 3.3. Thallium in group 13 can form a 1+ cation by losing the single unpaired p electron and leaving the filled ns2 subshell. Similarly, germanium, tin, and lead in group 14 can form 2+ cations by losing their two p electrons leaving the filled ns2 subshell. The elements in groups 15 (ns2np3), 16 (ns2np4), and 17 (ns2np5) have five, six, and seven valence electrons and so require three, two, and one electrons to achieve the closed shell of eight electrons. Because they can reach the stable configuration of eight electrons more easily by gaining electrons than by losing them, they have a high electron affinity (see Fig. 2.16). They will gain the required electrons to achieve the closed valence shell of eight. So, elements in group 15 will form 3
anions, those in group 16 will form 2
anions, and those in group 17 will form 1
anions. Notice from Fig. 2.16 that the exceptions to this pattern are the elements in the higher periods which have lower electron affinities. It is easier for these elements to lose electrons than to gain them because the outer shell is so far from the nucleus. So, arsenic and antimony in group 15 can lose all their valence electrons to form 5+ cations or they can lose only the three p electrons to form 3+ cations. Similarly, tellurium in group 16 can form 6+ and 4+ cations. Bismuth and polonium in period 6 have such low electron affinities that they cannot form anions at all, but are restricted to the cationic forms. The chemical symbol for an ion consists of the symbol for element it is derived from followed by a sign showing the number of electrons it has lost or gained. Cations are designated by a plus sign, while anions are designated by a minus sign. The charge is written in superscript immediately after the atomic symbol. For ions with charges >1, the magnitude of the charge is written before the sign. For singly charged ions, the magnitude of the charge is omitted. For example, the sodium cation is written as Na+ (not Na1+), while the calcium cation is Ca2+.

79

3.1 ATOMS AND IONS

EXAMPLE 3.1: DETERMINING THE ELECTRONIC CONFIGURATION OF AN ION What is the electronic configuration of O2
? 1. Determine the electronic configuration of oxygen. Oxygen is in group 16 of period 2. The noble gas in period 1 is helium, so the electronic configuration of oxygen in noble gas notation is: [He]2s22p4. 2. Determine the electronic configuration of O2
. Since O2
has a 2
charge it has gained two electrons. So, the electronic configuration of O2
will be that for oxygen with two electrons added to the p subshell: [He]2s22p6. Notice that this is also the electronic configuration for the noble gas neon.

Anions are named by adding the suffix “ide” to the root of the name of the parent element. So, Cl
is the chloride ion, N3
is the nitride ion, O2
is the oxide ion, and so on. The names of all the anions are listed in Table 3.2. Cations of elements that have only one ionic form are named by simply adding the word “ion” after the element name. For example, Na+ is called the sodium ion and Zn2+ is called the zinc ion. Cations of elements that have multiple ionic forms start with the name of the element followed immediately by a Roman numeral in parentheses, called the Stock number, to indicate the charge of the ion. For example, Fe2+ is iron (II) and Fe3+ is iron(III). TABLE 3.2 The Names of the Anions Symbol 3


N P

3


O

Arsenide ion Antimonide ion

2


S

Selenide ion Telluride ion




Br I

Sulfide ion

2





Cl

Oxide ion

2


Te F

Phosphide ion

3


2


Se

Nitride ion

3


As Sb

Name







Fluoride ion Chloride ion Bromide ion Iodide ion




At

Astatide ion

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3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

The use of Roman numerals to denote the charge of the cation is the method in use today. However, an older, and possibly more confusing, system of naming cations with multiple charges may be found that appends the suffixes “ous” and “ic” to the root name of the element to denote the charge. The ion with the lesser charge ends with “ous” and the one with greater charge ends with “ic.” For example, in this system Fe2+ is called the ferrous ion while Fe3+ is called the ferric ion, Cu+ is called the cuprous ion while Cu2+ is the cupric ion, and Sn2+ is called the stannous ion while Sn4+ is called the stannic ion. Although this naming system is outdated, it can still be found in older textbooks. The gain or loss of electrons by an atom to form an ion has a very large effect on the chemical and physical properties of the atom. Since the electronic configurations of the ions are more stable than that of the parent atom, ions are less reactive than neutral atoms. For example, sodium is a soft metal which reacts rapidly and explosively with water. In Fig. 3.2, the reaction of sodium metal with water is shown to be so violent that it breaks the glass container. In contrast, the sodium cation dissolves readily in water without any reaction. Chlorine is a greenish yellow gas that is so reactive it corrodes every metal and is toxic to all living things. It reacts with almost all elements including other chlorine atoms to form a diatomic chlorine molecule. On the other hand, chlorine anions are colorless and also dissolve readily in water without reaction. Both sodium and chlorine ions are so unreactive that they are found in most food products in the form of table salt and are an essential ingredient for life. As with the atomic radius, the trend in changing ionic radius (the distance from the nucleus to the outermost occupied electron orbital in an ion) is also a periodic property. A comparison between atomic radius and ionic radius for the most common ions of the elements is shown in Fig. 3.3. Since anions have more electrons than the parent atom and more electrons than protons in the nucleus, the attraction between the valence electrons and the nucleus is weaker resulting in a larger ionic radius than the parent atom. This can be seen in Fig. 3.3 for elements in groups 15 through 17 just before the noble gases. Cations have fewer electrons than protons in the nucleus causing the attraction between the valence electrons and the nucleus to become stronger, pulling the valence shell closer to the nucleus. So, cations have smaller radii than the parent atom. The cations also have smaller radii than most of the anions. Notice in Fig. 3.3 that the ionic radius of the transition metals is more variable than the atomic radius of the neutral atoms. This is because ionic charge also affects the ionic radius. The higher the ionic charge, the stronger the nuclear attraction and the smaller the ionic radius. Since the transition metals have multiple ionic states that vary within a group, the ionic radius FIG. 3.2 Right: Sodium metal reacting with water. Left: Sodium and chloride ions dissolving in water. Photographs by Naatriumi and Chris 73, Wikimedia Commons.

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3.1 ATOMS AND IONS

FIG. 3.3 Atomic radius (blue) and ionic radius (green) in picometers as a function of atomic number for elements 1 through 95.

also varies, although it is consistently smaller than the parent atom and also smaller than the anions. Overall, the ionic radius follows the same general periodic trends as the atomic radius and for the same reasons. Both the atomic radius and the ionic radius increase going down a group as long as the charge on the ions remains the same. This is due to the addition of an extra principal electron shell with each increasing period. Also, like the atomic radius, the ionic radius generally decreases going across a period for ions of the same charge due to the stronger nuclear attraction with the increasing number of protons. This decreasing trend across a period is not as apparent for some transition metals due to the large variation in ionic charge in the d-block. In summary: • • • • • •

Cations are smaller than their parent atoms. Anions are larger than their parent atoms. Anions are generally larger than cations. Increasing charge leads to decreasing ionic radius. Ionic radius increases going down a group. Ionic radius generally decreases going across a period.

EXAMPLE 3.2: DETERMINING THE RELATIVE SIZE OF IONS List the following ions in order of increasing size: Cs+, K+, F
, and Cl
. 1. Determine the position of the ions in the periodic table. Cs+ and K+ are both in group 1; K+ is in period 4 and Cs+ is in period 6. F
and Cl
are both in group 17; F
is in period 1 and Cl
is in period 2. 2. Determine how the position of the ions is related to their size. Since ionic radius increases going down a group: Cs+ > K+ and Cl
> F
. Cs+ and K+ in periods 4 and 6 have more electronic shells than F
and Cl
in period 1 and 2. 3. Determine how the ionic charge is related to their size. Anions are smaller than cations: F
< Cl
< K+ < Cs+.

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3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

3.2 IONIC BONDING When a chemical reaction occurs between two atoms, their valence electrons are rearranged to achieve a more stable electronic configuration for both of them. The simplest way to accomplish this is to completely transfer one or more electrons from one atom to another. This creates two oppositely charged ions, a cation that has lost the electrons and an anion that has accepted the electrons. The electrostatic attractions between the oppositely charged positive and negative ions create an ionic bond which holds the atoms together forming an ionic compound. The force (F) acting between two charged particles with charges q1 and q2 is described by Coulomb’s law as; F¼k

q1 q2 d2

(1)

where “d” is the distance between the two charged particles and “k” is a constant with the value of 9  109 N • m2 • C
2. Chemists use a modified version of this law to describe the potential energy (E) between two ions, with charges q1 and q2. E¼k

q1 q2 d

(2)

A negative potential energy (E ¼
) means that the ions will attract each other, while a positive potential energy (E ¼ +) means that the ions will repel each other. If one ion is a cation (q1 ¼ +) and the other ion is an anion (q2 ¼
), the energy of their interaction will be negative and the ions will attract each other. The potential energy (E) as a function of the distance (d) between two oppositely charged ions is shown in Fig. 3.4. When the ions are very far apart, there is a very small energy of attraction between the two ions. But as they get closer to each other (d decreases), the energy between them decreases. So, the two ions of opposite charge will have a lower energy and be more stable when they are close together than when they are far apart. An energy minimum is reached at the ionic bond FIG. 3.4

Potential energy (E) as a function of the distance (d) between two oppositely charged ions. The values of the ionic bond length and the ionic bond strength are shown by dotted lines.

3.2 IONIC BONDING

83

length of the resulting ionic compound. If the ions move closer than the bond length, they will repel each other and the energy increases rapidly. This happens because of the repulsion between the positively charged nuclei at very small distances. The bond length represents the distance where the attractive and repulsive forces between the two oppositely charged ions are balanced. The magnitude of the energy minimum in Fig. 3.4 gives a measure of the ionic bond strength between the two ions and the distance at which the energy minimum occurs is the bond length. So, the strength of an ionic bond can be predicted by using Coulomb’s law where the distance between the two ions in an ionic compound is equal to the sum of the two ionic radii (d ¼ r1 + r2). From Eq. (2), the magnitude of the bond strength depends on the magnitude of the product of the charges (q1  q2) and the bond length (d) where the energy is at a minimum. Larger charges will have stronger interactions and result in lower potential energies and a stronger bond. Also, smaller ions will be able to get closer together and have smaller bond lengths. They will also have lower potential energies and form stronger bonds. In summary: • The smaller the ionic radius, the shorter the bond length and the stronger the ionic bond. • The larger the ionic radius, the longer the bond length and the weaker the ionic bond. • The larger the ionic charge, the stronger the ionic bond.

EXAMPLE 3.3: DETERMINING THE RELATIVE STRENGTH OF IONIC BONDS List the following ionic bonds in the order of increasing bond strength: NadF, NadCl, CadF, NadI, and ScdF. 1. Determine the product of the ionic charges for each ion pair. NadF ¼ +1 
1 ¼
1. NadCl ¼ + 1 
1 ¼
1. CadF ¼ +2 
1 ¼
2. NadI ¼ +1 
1 ¼
1. ScdF ¼ +3 
1 ¼
3. According to the charges of the ions: ScdF > CadF, > NadI, NadF, NadCl. 2. Determine the remaining order of increasing bond strength by comparing the size of the ions. NadF, NadCl, and NadI have the same ionic charge product and the same cation, The size of the anion is: I
> Cl
> F
. 3. The order of increasing bond strength: NadI < NadCl < NadF < CadF < ScdF.

Since there are few elements in the periodic table that form anions, ionic bonds are restricted to the anions of the nonmetals in groups 15, 16, and 17 binding with the cations of metals. Most ionic bonds occur between elements with very different electronegativities (Fig. 2.17). The further they are apart in the periodic table, the more different their electronegativities and the more likely they are to form ionic bonds. One simple ionic compound formed from the elements in groups 1 and 17 is sodium chloride. When sodium and chlorine react, the 3s valence electron of sodium is transferred to the 3p valence orbital of chlorine. Sodium has

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3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

the electronic configuration [Ne]3s1. By losing the electron from the 3s valence orbital, sodium acquires the stable electronic configuration of the noble gas neon (1s22s2sp6). By gaining the electron, chlorine ([Ne]3s23p5) will complete its valence shell and acquire the electronic configuration of the noble gas argon (1s22s2sp63s23p6).

Na 1s2 2s2 sp6 3s1
1e
! Na + 1s2 2s2 sp6

Cl 1s2 2s2 sp6 3s2 3p5
1e
! Cl
1s2 2s2 sp6 3s2 3p6 This tendency for atoms in the s- and p-blocks to combine in such a way that each atom acquires eight electrons in its valence shell is known as the octet rule. Since the formation of chemical bonds involves the rearrangement of the valence electrons of the atoms, it can be represented by electron dot structures. The electron dot structures of the formation of an ionic bond between a metal and a nonmetal shows the transfer of electrons from the metal to the nonmetal to form a stable electronic configuration for both. The electron dot representation of the formation of the ionic compound sodium chloride from the elements sodium and chlorine would be; Na

+

Cl

[Na] + [ Cl ] −

The electron dot structure of the ionic compound is written with the dot structures of the ions in brackets. The charge of the ions is placed in the upper right hand corner outside the brackets. The anion is shown with the stable configuration of eight valence electrons. Although the cation now also has eight valence electrons in the new outermost electronic shell, it is shown with an empty valence shell to indicate the loss of its old valence electrons to the anion.

EXAMPLE 3.4: DETERMINING THE ELECTRON DOT REPRESENTATION OF AND IONIC COMPOUND Write the ionic reaction of magnesium and oxygen to form magnesium oxide using electron dot representations. 1. Determine the electron dot representations for magnesium and oxygen. Magnesium is in group 2 of the periodic table with two valence electrons. Mg

Oxygen is in group 16 of the periodic table with six valence electrons. O

2. Determine the number of electrons gained and lost in the reaction. In order for oxygen ([He]2s22p4) to achieve the noble gas valence shell of eight electrons, it must gain two electrons. Similarly, in order for magnesium ([Ne]3s2) to achieve a noble gas electronic configuration, it must lose two electrons. 3. The electron dot representation of this reaction would be: Mg

+

O

[Mg]2+ [ O ]2−

3.2 IONIC BONDING

85

Electron dot representations can also be used to predict the chemical formula of an ionic compound. A chemical formula is a way of expressing the bonding between atoms and ions in a compound using a single line of the element symbols along with numeric subscripts to indicate the number of atoms of each element in the compound. For the reaction between calcium ([Ar]4s2) and chlorine ([Ne]3s23p5), the electron dot structures for the neutral atoms are; Ca

+

Cl

Calcium needs to lose its two 4s valence electrons to achieve the stable noble gas electronic configuration, but chlorine only needs one electron to complete the octet. So the ionic compound that forms between calcium and chlorine will need two chlorine atoms for every one calcium atom in order for calcium to lose both valence electrons. The electron dot representation for the ionic compound is; [ Cl ]− [Ca]2+ [ Cl ]−

When writing the chemical formula for the ionic compound, the atomic symbol of the cation is always written first followed by the atomic symbol for the anion. Numeric subscripts are used to indicate the number of atoms of each ion in the compound. The charges of the ions are not included in the chemical formulas of ionic compounds since the overall charge of the compound is zero. The chemical formula for the ionic compound formed between calcium and chlorine is CaCl2.

EXAMPLE 3.5: DETERMINING THE CHEMICAL FORMULA OF AN IONIC COMPOUND USING ELECTRON DOT REPRESENTATIONS What is the chemical formula of the ionic compound formed from the reaction between sodium and sulfur? 1. Determine the electron configurations of the neutral atoms. sodium ¼ [Ne]3 s1. sulfur ¼ [Ne]3s23p4. 2. Determine the electron dot representations for the neutral atoms. S

and

Na

3. Determine the combination of atoms that will result in a closed valence shell. Sulfur needs two electrons to complete the valence octet. This requires two sodium atoms. 4. Write the chemical formula. Na2S.

To determine the chemical formula for ionic compounds that have more complicated valence configurations, such as the transition metals, the ions must be combined so that the resulting compound is electrically neutral. That is, the total positive charge of the cations must equal the total negative charge of the anions. For the compound formed by a combination of Zn2+ and Cl
, there must be two chloride ions for every zinc ion in order for the positive and negative charges to balance and to achieve a total charge of zero. So, the

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3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

chemical formula is ZnCl2. Similarly, for the compound formed from Al3+ and O2
, there must be three oxygen anions for every two aluminum cations for the compound to be electrically neutral. The aluminum contributes a 6+ charge and the oxygen contributes a 6
charge resulting in a total charge of zero and the chemical formula for the ionic compound is Al2O3. Ionic compounds are named by simply combining the names of the ions without using the term “ion.” As with the chemical formula, the name of the cation is first followed by the name of the anion. For example, NaCl is sodium chloride, MgO is magnesium oxide, Na2S is sodium sulfide, and CaCl2 is calcium chloride. For compounds containing metals with multiple ionic states such as iron, the charge on the cation can be determined from the chemical formula. For example, the iron cation in FeCl2 must have a 2+ charge in order to balance out the two negative charges of the chlorine atoms. So, FeCl2 is iron(II) chloride. In the same way, FeCl3 is iron(III) chloride.

3.3 COVALENT BONDING Two atoms with very different electronegativities (those far apart on the periodic table) will form an ionic compound since the atom with a high electronegativity has the ability to capture electrons from the atom with low electronegativity. But, elements with similar electronegativities (those closer together in the periodic table) cannot completely transfer electrons from one atom to another. They can still achieve a closed valence shell by sharing their electrons. For example, two hydrogen atoms have the same electronegativity and cannot transfer electrons from one hydrogen atom to the other to form an ionic bond. But they can both achieve the closed valence shell of a helium atom (1s2) if both atoms share their single valence electron to form a shared electron pair. This can be represented by an electron dot structure as; H

+

H

H H or

H−H

The pair of electrons that is shared between the two hydrogen atoms forms a covalent bond between them resulting in a diatomic molecule of hydrogen with the formula H2. Similarly, two fluorine atoms ([He]2s22p5) can both achieve the closed valence shell of neon ([He]2s22p6) by sharing one valence electron each. F

+

F

F F

or

F

F

The shared electron pair, which forms the covalent bond between the two fluorine atoms, is known as bonding pair electrons. The three pairs of valence electrons around each fluorine atom that are not shared are known as lone pair electrons. Covalent bonds are formed when two or more valence electrons are attracted by the positively charged nuclei of both atoms and so are shared between the two atoms. This description of covalent bonds as involving shared pairs of valence electrons that are localized in a bond between two atoms is known as valence bond theory. Fig. 3.5 shows the potential energy between two atoms of hydrogen as they approach each other. In a similar manner

87

3.3 COVALENT BONDING

FIG. 3.5 Potential energy change during HdH covalent bond formation from isolated hydrogen atoms. A representation of the two atoms with their 1s electron shell is shown above the graph.

as in the formation of an ionic bond (Fig. 3.4), the potential energy decreases as the hydrogen atoms get closer together and the attraction between the valence electrons and the nuclei of each atom becomes stronger. The covalent bond is formed when the two hydrogen atoms reach the lowest potential energy, which is the covalent bond length. The bond length is determined by the sum of the atomic radii of the two atoms. For hydrogen, this occurs at a distance of 74 pm. At this point, the overlap of the 1s orbitals of the two hydrogen atoms concentrates the electron density between the two nuclei and the attractive and repulsive forces are balanced. If the nuclei get closer together than the bond length, the repulsive forces become dominant and the potential energy increases. If the formation of a single bonding electron pair between two atoms does not result in each atom achieving the stable valence octet, it is possible for two atoms to share more than one electron pair. For example, oxygen has six valence electrons and needs two electrons to achieve the stable valence octet of neon ([He]2s22p6). If two oxygen atoms ([He]2s22p4) shared one electron pair, they would each only gain one electron. But if they shared two electron pairs, each oxygen atom would then have eight valence electrons resulting in a diatomic oxygen molecule with the formula O2. +

O

O

O

O

or

O

O

Similarly, if two atoms share two electron pairs and still do not have eight valence electrons, they can share three electron pairs. An example of this is the formation of N2. Each atom of nitrogen has five valence electrons and needs three more electrons to get to the stable valence octet of neon ([He]2s22p6). This can be achieved if each nitrogen atom shares three electron pairs. N

+

N

N

N

or

N

N

The covalent bond that results when two atoms share one electron pair is called a single bond. The bond resulting from sharing two electron pairs is a double bond and that resulting

88

3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

from sharing three electron pairs is a triple bond. Double bonds are shorter and stronger than single bonds and triple bonds are shorter and stronger than double bonds. The triple bond in N2 is very strong and requires a lot of energy to break it. In fact, diatomic nitrogen is so stable it is considered to be chemically inert. The only elements that normally exist in nature as stable diatomic molecules are the gases H2, N2, O2, F2, Cl2, Br2, and I2. Since a compound must contain at least two different elements and these molecules are only composed of a single element, these diatomic gases are not considered to be chemical compounds. Instead, they are known as diatomic elements.

EXAMPLE 3.6: DETERMINING THE ELECTRON DOT STRUCTURES OF COVALENT COMPOUNDS What is the electron dot structure for CO2? 1. Determine the number of valence electrons for carbon and oxygen. Carbon is in period 2, group 14 with four valence electrons. Oxygen is in period 2, group 16 with six valence electrons. 2. Draw the electron dot structures for both atoms. C

O

3. Determine the number of electrons each atom needs to achieve a stable valence configuration. Carbon needs four electrons and each oxygen atom needs two electrons. In order for carbon to obtain four electrons, it would have to share four electron pairs. Since there are two oxygen atoms in CO2, this could be achieved by sharing two electron pairs from each oxygen atom. 4. The electron dot structure would then be: O

C

O

or

O

C

O

When two bonded atoms have the same electronegativities, they will share the electrons equally. The bonds between atoms where electrons are shared equally are known as nonpolar covalent bonds. In molecules where two bonded atoms have different electronegativities, the electrons are shared unequally. This difference in electronegativities between the two atoms results in the electron density being shifted towards the more electronegative atom giving it a partial negative charge, while the less electronegative atom acquires a partial positive charge. This type of bond where the electrons are unequally shared between two atoms is called a polar covalent bond. For example, in the molecule HF, hydrogen and fluorine share a pair of valence electrons. However, the fluorine atom has a much higher electronegativity (3.98 on the Pauling scale) than the hydrogen atom (2.20 on the Pauling scale). So the fluorine atom attracts the shared electrons more than the hydrogen atom. Since the hydrogen atom has its single valence electron pulled away from it, it has a partial positive charge while the fluorine atom has a partial negative charge. A bond (or molecule) that has a partial positive charge on one end and a partial negative charge on the other end is called a dipole. In molecular

89

3.3 COVALENT BONDING

structures, the bond polarity is indicated by a “δ+” written by the less electronegative atom and a “δ
” written by the more electronegative atom as; δ−

δ+

F

H

The larger the difference in electronegativities of the two atoms, the more polar the bond will be. For example, as shown in Fig. 3.6, the halogens have electronegativities on the Pauling scale of: F ¼ 3.98, Cl ¼ 3.16, Br ¼ 2.96, I ¼ 2.66, At¼ 2.20. If each of the halides is bonded to hydrogen (2.20), the differences in electronegativities between the halogen and hydrogen, shown in Table 3.3, decrease from a value of 1.78 for HdF to 0.46 for HdI. Consequently, the hydrogendhalogen bond polarity decreases in the order of HdF > HdCl > HdBr > HdI. In addition, since hydrogen and astatine have the same electronegativity (2.20), the HdAt bond will be nonpolar. The measure of the bond polarity is the dipole moment of the bond. The bond dipole is modeled as two partial opposite charges δ+ and δ
that are equal in magnitude and separated Period

Group

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

1

H 2.20

2

Be Li 0.98 1.57

3

P S Cl Al Si Na Mg Ar 1.61 1.90 2.19 2.58 3.16 0.93 1.31 As Se Br Kr Co Ni Cu Zn Ga Ge Ti V Cr Mn Fe K Ca Sc 0.82 1.00 1.36 1.54 1.63 1.66 1.55 1.83 1.88 1.91 1.90 1.65 1.81 2.01 2.18 2.55 2.96 3.00

4

He N O F B C 2.04 2.55 3.04 3.44 3.98

Ne

5

Sb Te I Xe Tc Ru Rh Pd Ag Cd In Sn Sr Y Zr Nb Mo Rb 0.82 0.95 1.22 1.33 1.60 2.16 1.90 2.20 2.28 2.02 1.93 1.69 1.78 1.96 2.05 2.10 2.66 2.60

6

Bi Po At Rn Re Os Ir Pt Au Hg Tl Pb Ba La Hf Ta W Cs 0.79 0.89 1.10 1.30 1.50 2.36 1.90 2.20 2.20 2.28 2.54 2.00 1.62 2.33 2.02 2.00 2.20 2.20

7

Ra Ac Fr 0.70 0.90 1.10

<1

Rf

Db

Sg

Bh

Hs

Mt

Ds

Rg

Cn

Fl

2.0−2.9

1−1.9

Lv

3.0−3.9

FIG. 3.6 Electronegativities of the elements on the Pauling scale. TABLE 3.3

Properties of the Hydrogen Halide Bonds

Molecule

Electronegativity Difference

Dipole Moment (D)

˚) Bond Length (A

HF

1.78

1.82

0.92

HCl

0.96

1.08

1.27

HBr

0.76

0.82

1.41

HI

0.46

0.44

1.61

HAt

0.0

0.0

1.72

90

3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

δ+

d

δ−

The model for a covalent bond dipole where δ+ and δ
are the partial charges on the bonded atoms and d is the bond length.

FIG. 3.7

FIG. 3.8 Electron density surfaces for the covalent bonds between hydrogen and the halogens. The bar and circle inside each figure represents the molecule with the hydrogen atom shown in blue and the halogens in orange (F), green (Cl), red (Br), and purple (I). The outer shape describes the extent of the electron density in each molecule. The red color represents the partial negatively charged regions (δ
) and the blue color represents the partial positively charged regions (δ+). Ben Mills, Wikimedia Commons.

HF

HCl

HBr

HI

by a distance (d) as shown in Fig. 3.7. The dipole moment (μ) of the bond is given by the product of the magnitude of the charge on either atom (δ) and the bond length (d) as; μ¼δd

(3)

The SI unit for a dipole moment is the coulomb-meter (C • m). However, a more convenient unit for covalent bond polarities is the debye (D), which is defined as 1D ¼ 3.34  10
30C • m. The dipole moments for the hydrogendhalide bonds in Table 3.3 decrease from 1.82D for ˚ for HdF HdF to 0.44D for HdI. At the same time, the bond length increases from 0.92 A ˚ ˚ to 1.61 A for HdI and 1.72 A for the nonpolar HdAt. So, the bond length increases with decreasing bond polarity. The bond polarity trend for the polar hydrogendhalide bonds is demonstrated in Fig. 3.8. The bar and circle shape inside each figure represents the center of the HdF, HdCl, HdBr, and HdI molecules. The electron density around the atoms is shown as the outer shape. The red color represents the partial negatively charged regions (δ
) caused by the electrons spending more time near the halogen atoms in each bond. The blue color represents the partial positively charged regions (δ+) surrounding the hydrogen atoms. The colors are strongest for HdF and progressively weaker for each halogen because the HdF bond is strongest and more polar, while the HdI bond is weakest and less polar. The bond length also increases as the bond polarity decreases. As shown in Table 3.3, it is the electronegativity differences between atoms that control the dipole moment and the polarity of the bond. For bonds where the electronegativity differences are nonzero but very small, they can be considered as virtually nonpolar for purposes of determining the chemical reactivity of the bond. One such bond that receives much attention in chemistry is the CdH bond in organic molecules. Carbon has an electronegativity of 2.55 on the Pauling scale and hydrogen has an electronegativity of 2.20. So, the electronegativity difference for a CdH bond is 0.35, which is very small. The bond would therefore have a small dipole moment (0.3D) and could be considered as virtually nonpolar for the purpose of determining its chemical reactivity. This will become very important in Chapter 13.

3.3 COVALENT BONDING

91

A “rule of thumb” for determining how a bond will behave in chemical reactions is: • If the electronegativity difference between the two bonded atoms is >0.4, the bond will behave as polar. • If the electronegativity difference is 0.4 or less, the bond will behave as nonpolar. • If the electronegativity difference is >2, the bond will behave as ionic. All the examples given above have used electron dot structures to determine the number of electrons shared in covalent bonds. Since electron dot formulas can only be used to show eight valence electrons per atom, all the examples have followed the octet rule of acquiring eight valence electrons to form a stable molecule (two for hydrogen). However, the octet rule only holds for elements in the s- and p-blocks of the periodic table with a few other exceptions. Elements in periods 3 and higher can have more than eight valence electrons when bonding to fluorine, chlorine, or oxygen. This is because the electron shells with n ¼ 3 and higher can also have empty d orbitals, which can accommodate additional valence electrons. Some examples are: SF6 where sulfur has 12 valence electrons, PF5 where phosphorous has 10 valence electrons, ClF3 where chlorine has 10 valence electrons including two lone pairs, and BrF5 where bromine has 10 valence electrons. Another exception to the octet rule is boron, which can form compounds with other nonmetals with three covalent bonds giving boron six valence electrons, two short of the octet. However, these compounds are very reactive and often react with other molecules or ions that can provide the missing electron pair. A more general notation for representing covalent bonds in a molecule is bonding notation where the lone pair electrons are omitted and the bonding electrons are represented by lines. In this notation, the molecular structure for F2, O2, and N2 then becomes FdF, O]O, and N^N. In addition to being simpler than electron dot structures, bonding notation can be used for all molecules including those with more than eight valence electrons. SF6 could be represented in bonding notation as; F F

F

S F

F F

The chemical formula for a covalent compound is called a molecular formula because, unlike ionic compounds, covalent compounds can exist as separate, distinct molecules. The molecular formula is written with the least electronegative element (the one further to the left on the periodic table) placed first followed by the more electronegative element. One important exception to this order is when the compound contains oxygen bonded to a halogen. For these compounds, the halogen is written first. In naming covalent compounds, the first element in the molecular formula is named first using the neutral element name. The last element is named as an anion with the suffix “ide.” A Greek prefix is used in front of each element name to indicate how many atoms of each element are in the compound. The most common prefixes are: “mono” (one), “di” (two), “tri” (three), “tetra” (four), “penta” (five), and “hexa” (six). For example, N2O3 is dinitrogen trioxide. Some exceptions are that the “mono” prefix is not used for the first element in the formula as in carbon dioxide (CO2) or silicon tetrafluoride (SiF4). Also, if the use of the prefix

92

3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

places two vowels next to each other, the “a” or “o” of the prefix is dropped. For example, NO is nitrogen monoxide, N2O is dinitrogen monoxide, and N2O5 is dinitrogen pentoxide. But, the “i” of “di” and “tri” are never dropped. Some simple covalent compounds have common names rather than systematic names. The most often encountered are water (H2O), ammonia (NH3), and methane (CH4). Methane is an organic compound. The naming of organic compounds will be covered in Chapter 13.

3.4 MIXED COVALENT/IONIC BONDING Polyatomic ions, also called molecular ions, are ions that are made up of two or more different atoms covalently bonded tightly together so that they can behave as a single unit. Polyatomic ions have a charge because the group of atoms making up the molecule has either gained or lost electrons. So, the polyatomic ion is a covalently bonded molecule that behaves like an ion in forming ionic compounds since it has a charge. Some common polyatomic ions are listed in Table 3.4. TABLE 3.4 Common Polyatomic Ions With Their Chemical Formulas. The Ions are Listed in Groups or Families Depending on the Parent Element. Although Not Listed in the Table, Bromine and Iodine Form the Same Four Polyatomic Ions as Chlorine Parent Element

Polyatomic Ion

Formula

Hydrogen

Hydroxide

OH


Hydronium

H3O+

Carbonate

CO32


Hydrogen carbonate (bicarbonate)

HCO3


Cyanate

CNO


Thiocyanate

CNS


Cyanide

CN


Acetate

H3C2O2


Oxalate

C2O4


Nitrate

NO3


Nitrite

NO2


Ammonium

NH4+

Sulfate

SO42


Hydrogen sulfate

HSO4


Thiosulfate

S2O32


Sulfite

SO32


Hydrogen sulfite

HSO3


Carbon

Nitrogen

Sulfur

93

3.4 MIXED COVALENT/IONIC BONDING

TABLE 3.4 Common Polyatomic Ions With Their Chemical Formulas. The Ions are Listed in Groups or Families Depending on the Parent Element. Although Not Listed in the Table, Bromine and Iodine Form the Same Four Polyatomic Ions as Chlorine—cont’d Parent Element

Phosphorous

Chlorine

Metals

Polyatomic Ion

Formula

Thiosulfite

S2O22


Phosphate

PO43


Hydrogen phosphate

HPO42


Dihydrogen phosphate

H2PO4


Phosphite

PO33


Hypophosphite

PO23


Hydrogen phosphite

HPO32


Dihydrogen phosphite

H2PO3


Chlorate

ClO3


Perchlorate

ClO4


Chlorite

ClO2


Hypochlorite

ClO


Aluminate

AlO2


Arsenate

AsO43


Arsenite

AsO33


Chromate

CrO42


Chromite

CrO2


Dichromate

Cr2O72


Permanganate

MnO4


The names of the polyatomic ions follow some general, although sometimes confusing, conventions. Most of the common polyatomic ions are anions. There are only two cations listed in Table 3.4. These cations are H3O+ (hydronium ion) and NH4+ (ammonium ion), both of which end in the suffix “ium.” For the polyatomic anions, the names of the ions containing one or more oxygen atoms (oxyanions) are determined by the number of oxygens in the ion. The name ending in the suffix “ate” is considered to be the base name for the polyatomic ions containing oxygen. If there are only two possible polyatomic ions in a group that contain oxygen atoms, the ion containing the most oxygens ends with the suffix “ate,” such as nitrate (NO3
). The ion that has one less oxygen atom than the “ate” form ends with the suffix “ite,” such as nitrite (NO2
). For groups with more than two ions containing oxygen atoms, the ions with a prefix of “per” combined with a suffix of “ate” have one more oxygen atom than the “ate” form. Ions with a prefix of “hypo” and a suffix of “ite” have one less oxygen atom than the “ite” form. For example, the chlorine group of polyatomic ions has four forms containing oxygen: perchlorate (ClO4
) with four oxygen atoms, chlorate (ClO3
) with three oxygen

94

3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

atoms, chlorite (ClO2
) with two oxygen atoms, and hypochlorite (ClO
) with one oxygen atom. The phosphorous group only has three forms containing oxygen. The form containing the most oxygen atoms (PO4 3
) is named phosphate. Then the last two ions in the series are named phosphite (PO3 3
) and hypophosphite (PO2 3
). Notice that in all cases, the charge on the oxyanions remains the same. In addition to the naming conventions for the oxyanions, the prefix “thio” indicates that one oxygen atom has been replaced with a sulfur atom. For example, in thiosulfate (S2 O3 2
) the prefix “thio” indicates that it is a sulfate ion (SO4 2
) with one oxygen atom replaced by sulfur. Again, the charge on the ion is unchanged. Also, some polyatomic oxyanions can add hydrogen ions (H+). These are named simply by adding the name “hydrogen” to that of the oxyanion as in hydrogen carbonate (HCO3
). An older convention indicates the addition of a hydrogen atom by using the prefix “bi” naming HCO3
bicarbonate instead of hydrogen carbonate. For the polyatomic ions containing hydrogen, each added hydrogen ion neutralizes one negative charge on the parent anion. So, carbonate has a 2
charge while hydrogen carbonate has a 1
charge. There are only a few exceptions to these naming conventions. For example, the names of the hydroxide (OH
) and cyanide (CN
) ions have the “ide” suffix because they were once thought to be monatomic ions.

EXAMPLE 3.7: DETERMINING THE ELECTRON DOT STRUCTURES OF POLYATOMIC IONS What are the electron dot structure for NO3
? 1. Determine the number of valence electrons in the group. Nitrogen has five valence electrons, each oxygen atom has six valence electrons. Since the charge on the group is 1
, there is one extra electron. The number of valence electrons is: 5 + (3  6) + 1 ¼ 24. 2. Determine the central atom in the structure. Almost always the central atom will be the least electronegative atom. It is also the atom that will require the most bonds to achieve a closed valence shell. Nitrogen will need to share three electron pairs, while each oxygen will share only one electron pair. Nitrogen is also less electronegative than oxygen. Nitrogen will be the central atom. 3. Determine the bonding to the central atom. In order for nitrogen to achieve a valence shell of eight electrons, it must share four electron pairs with each of the three oxygen atoms. 4 bonds ¼ two single bonds and one double bond. 4. Determine the electron placement in the electron dot structure. 24 electrons
8 bonding electrons ¼ 16 electrons ¼ 8 lone pair electrons. The remaining 16 electrons are placed as lone pairs around the oxygen atoms. As with the monatomic ions, the electron dot structure is written in brackets with the charge of the polyatomic ion written outside the brackets in the upper left corner. The electron dot structure for NO3
is: −

− O

N O O

or

O

N O

O

95

3.5 MOLECULAR ORBITALS

While the structure for the nitrate ion given in Example 3.7 is correct, it is not the only correct structure. Because of the symmetry of the NO3
ion, it does not matter which of the oxygen atoms receives the double bond. Since there are three different oxygen atoms that could form the double bond to nitrogen, there will be three different correct electron dot structures, called resonance structures. Each resonance structure shows a different oxygen atom with a double bond to the nitrogen atom. It is conventional to use double-headed arrows placed between the multiple resonance structures to indicate that the structures are equivalent. − O

N O

O

− O

N

O

− O

O

N

O

O

Resonance structures are two or more equivalent structures which differ only in the position of their electrons (not the position of the atoms). This does not imply that the structure of the ion (or molecule) switches between these different forms. In reality, the ion exists as an average of these structures where the bonding electrons are delocalized between the oxygens. This electron delocalization makes the ion more stable than if it existed as any of the single resonance structures. Resonance can often exist when multiple atoms of the same type surround a central atom. Electron dot representations as well as the chemical formulas of ionic compounds containing polyatomic ions are much the same as for ionic compounds containing only monoatomic ions. In determining the chemical formula, the ions must be combined so that the resulting compound is electrically neutral. That is, the total positive charge of the cations must equal the total negative charge of the anions. For the compound formed by a combination of Na+ and SO4 2
, there must be two sodium ions for every sulfate ion in order for the positive and negative charges to balance and achieve a total charge of zero. So, the chemical formula is Na2SO4. Similarly, for the compound formed from Al3+ and SO4 2
, there must be three sulfate anions for every two aluminum cations in order for the compound to be electrically neutral. The aluminum contributes a 6+ charge and the sulfate contributes a 6
charge resulting in a total charge of zero for the ionic compound. Parentheses are used in the chemical formula to separate the numeric subscripts used to indicate the number of atoms in the ion from the subscript used to indicate the number of ions in the compound. So, the chemical formula for aluminum sulfate is Al2(SO4)3.

3.5 MOLECULAR ORBITALS When atoms share electrons in covalent bonds, the electrons no longer reside in the atomic orbitals. Instead, they occupy molecular orbitals that are formed when the atomic orbitals overlap. The total number of molecular orbitals is equal to the total number of atomic orbitals involved in bonding. So, when the 1s orbitals of two hydrogen atoms overlap to form the covalent bond in an H2 molecule, two molecular orbitals are formed. One of these molecular orbitals is lower in energy than the 1s atomic orbitals and is called a bonding molecular orbital. The other molecular orbital is higher in energy than the 1s atomic orbitals and is called an antibonding molecular orbital. Bonding molecular orbitals are formed when the atomic orbitals combine in phase. Filled bonding orbitals result in an increase in the electron density

96

3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

between the atoms. The electrons in these bonding orbitals stabilize the bonded atoms since the orbitals are of less energy than the atomic orbitals. Antibonding molecular orbitals are formed when the atomic orbitals combine out of phase. Filled antibonding orbitals result in a decrease in the electron density between the atoms. The electrons in the antibonding orbitals destabilize the molecule since they are higher in energy than the electrons in the atomic orbitals. The valence electrons of the two atoms are assigned to molecular orbitals of increasing energy according to the Aufbau principle, the Pauli Exclusion Principle, and Hund’s Rule in the same way that electrons are assigned to atomic orbitals. As with atomic orbitals, each molecular orbital can have only two electrons, each with an opposite spin. Fig. 3.9 shows a schematic diagram of the molecular orbitals (molecular orbital diagram) for the diatomic H2. The diagram shows the two 1s atomic orbitals which combine to form one bonding orbital and one antibonding orbital. The two paired valence electrons are placed in the bonding molecular orbital, which is lower in energy than the atomic orbitals. This stabilizes the molecule. The higher energy antibonding molecular orbital remains empty. There are two types of molecular orbitals. These are sigma orbitals and pi orbitals as shown in Fig. 3.10. Molecular orbitals that are symmetrical about the axis of the bond are called sigma molecular orbitals, denoted by the Greek letter “σ.” They lie between the nuclei of two atoms where there is an increase in electron density along the bond axis. This increase in electron density causes the nuclei of the two atoms to be drawn closer together. In sigma antibonding orbitals (σ*), there is a low electron density between the nuclei of the two atoms, which destabilizes the bond. Sigma molecular orbitals can be formed from the combination of two s atomic orbitals, as in H2, or from the combination of two p atomic orbitals that lie along the axis of the bond (pz). Pi orbitals are formed from the combination of two atomic orbitals that lie outside of the bond axis (px, py). This results in a side to side overlap of the atomic orbitals. The pi bonding orbital, denoted by the Greek letter “π,” thus has no electron density along the bond axis. Instead, the electron density lies above and below the bond axis. The electron density in the pi antibonding orbital (π*) lies entirely outside the bond axis.

FIG. 3.9 A molecular orbital diagram for the H2 molecule. The combination of two 1s atomic orbitals results in one bonding molecular orbital (σ) and one antibonding molecular orbital (σ*).

3.5 MOLECULAR ORBITALS

Atomic orbitals

Molecular orbitals Bonding

Antibonding

s

s

s∗

pz

s

s∗

py

p

97

FIG. 3.10 The shapes of bonding and antibonding molecular orbitals formed from the combinaton of two of the atomic orbitals shown at left. The black dots indicate the location of the nuclei.

p∗

Single covalent bonds consist of one sigma molecular orbital. Double bonds consist of one sigma molecular orbital and one pi molecular orbital. Triple bonds are made up of one sigma molecular orbital and two pi molecular orbitals. The number of bonds between two atoms is called the bond order. The bond order can be calculated from a molecular orbital diagram as; Bond order ¼ ½ ðb
aÞ m

(4)

where “b” is the number of electrons in bonding molecular orbitals and “a” is the number of electrons in antibonding molecular orbitals. If the bond order is zero, no bonds are produced and the molecule is not stable. If the Bond Order is equal to 1, the molecule contains a single covalent bond. If the bond order is equal to 2, the molecule contains a double bond and if the bond order is equal to 3 the molecule contains a triple bond. So, the bond order also indicates the strength of the bond. The greater the bond order, the stronger the bond. A bond order that is not a whole number indicates that resonance is present and the bond order is an average of the possible resonance structures. The bond order of H2 calculated from Fig. 3.9 is ½ (2
0) ¼ 1, indicating a single bond between the two hydrogen atoms. Compare this to the molecular orbital diagram for the He2 molecule shown in Fig. 3.11. The molecular orbitals formed from the combination of the two 1s atomic orbitals are the same as for H2. However, each He atom has two valence electrons (1s2) giving the molecule four valence electrons. These four electrons fill both the bonding and the antibonding molecular orbitals, which destabilizes the bond. The bond order for He2 calculated from the molecular orbital diagram is ½ (2
2) ¼ 0. This indicates that no stable bonds are formed between the two helium atoms and He2 does not occur in nature. Fig. 3.12 shows the molecular orbital diagrams for the diatomic oxygen (O2) and nitrogen (N2) molecules. Both oxygen and nitrogen have valence electrons in the 2s, 2px, 2py, and 2pz atomic orbitals. The combination of these four atomic orbitals on one atom with the same set of four atomic orbitals on a second atom leads to the formation of a total of eight molecular orbitals: two σ orbitals, two σ* orbitals, two π orbitals, and two π* orbitals. The σ2s molecular orbitals are formed from the atomic 2s orbitals. The σ2p and π2p molecular orbitals are formed from the atomic 2p orbitals. Since the 2s atomic orbitals are lower energy than the 2p orbitals, the σ2s and σ*2s molecular orbitals both lie at lower energies than the molecular orbitals

98

FIG. 3.11

3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

The molecular orbital diagram for the He2 molecule.

FIG. 3.12 The molecular orbital diagram for diatomic oxygen and nitrogen. The subscripts on the molecular orbital designations indicate the atomic orbitals that formed each molecular bond.

formed from the combination of the 2p atomic orbitals. Of the three 2p atomic orbitals, the 2pz orbitals lie in the bond axis, while the 2px and 2py orbitals lie outside the bond axis (see Fig. 3.10). So, the interaction between the two 2pz orbitals is stronger than the interaction between the 2px or 2py orbitals. This normally results in the molecular σ2p orbital, formed from the combination of the atomic 2pz orbitals, being at a lower energy than the π2p orbitals, formed from the 2px and 2py orbitals. Also, the σ2p* orbital is higher energy than the π2p* orbitals. This trend is shown in Fig. 3.12 for diatomic oxygen. Diatomic nitrogen has a slightly different molecular orbital sequence than diatomic oxygen. This is because the 2s and the 2p atomic orbitals are close in energy, making it possible for them to interact. This interaction results in s-p atomic orbital mixing when the molecular orbitals are formed. This orbital mixing is called hybridization and is very important to the understanding of the chemistry of carbon covered in Chapter 13. The result of this orbital hybridization is a slight change in the relative energies of the molecular orbitals and the

3.5 MOLECULAR ORBITALS

99

π2p orbitals become of lower energy than the σ2p orbitals. Notice from Fig. 3.12 that this orbital mixing only affects the order of the bonding orbitals and the order of the antibonding orbitals remains the same. Each nitrogen atom has five valence electrons (2s22p3) giving 10 valence electrons in the N2 molecule. When placed in the molecular orbitals, the σ2s, σ*2s, σ2p, and the two π2p orbitals are completely filled. There is no net bonding from the σ2s orbitals, because the number of bonding electrons equals the number of antibonding electrons. Since none of the σ*2p or π*2p antibonding orbitals are filled, this leaves six total bonding electrons. For N2, the bond order is ½ (8
2) ¼ 3. The bond order of 3 indicates a triple bond with one sigma bond (σ2p) and two pi bonds (π2p). Each oxygen atom has six valence electrons (2s22p4) with a total of 12 valence electrons in the O2 molecule. When placed in the molecular orbitals, the σ2s, σ*2s, σ2p, and the two π2p orbitals are completely filled and the two π*2p orbitals are half filled with one electron each. There is also no net bonding in the σ2s orbitals for O2 because the number of bonding electrons equals the number of antibonding electrons. Also, the two unpaired electrons in the π*2p orbital cancels one additional pair of bonding electrons in the π2p orbitals, leaving a total of four electrons in bonding orbitals and two bonds between the two oxygen atoms. The bond order is ½ (8
4) ¼ 2 indicating a double bond. The number of unpaired electrons in the molecular orbitals determines the magnetic properties of the molecule. Molecules which have all electrons paired, such as N2, are diamagnetic, meaning that they are weakly repelled by a magnetic field. Molecules that have one or more unpaired electrons, like O2, are paramagnetic. They are strongly attracted to a magnetic field. Liquid oxygen, with its two unpaired electrons in the π*2p orbitals, is attracted to a magnetic field as shown in Fig. 3.13. The valence electron configuration for molecules can be written in the same way that electron configurations are written for atoms, by listing the molecular orbitals and the number of electrons in them. The valence electron configuration for the H2 molecule would be simply

FIG. 3.13 A stream of liquid O2 is deflected in a magnetic field. Photograph by Pieter Kuiper, Wikimedia Commons.

100

3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

TABLE 3.5 Electron Configurations and Predicted and Observed Properties of Diatomic Molecules Formed From the Elements in the Second Period of the Periodic Table Electron Configuration

Bond Order

Bond Energy (kJ)

Bond Length (pm)

Unpaired Electrons

Li2

(σ2s)2

1

105

267

0

d

Be2

2

2

0

―

―

0

―

2

2

1

1

1

289

159

2

p

2

2

2

2

2

598

131

0

d

2

2

2

2

2

3

946

110

0

d

2

2

2

2

2

1

1

2

498

121

2

p

2

2

2

2

2

2

2

1

158

143

0

d

2

2

2

2

2

2

2

0

―

―

0

―

B2 C2 N2 O2 F2 Ne2

(σ2s) (σ*2s)

(σ2s) (σ*2s) (π2p) (π2p) (σ2s) (σ*2s) (π2p) (π2p)

(σ2s) (σ*2s) (π2p) (π2p) (σ2p)

(σ2s) (σ*2s) (π2p) (π2p) (σ2p) (π*2p) (π*2p) (σ2s) (σ*2s) (π2p) (π2p) (σ2p) (π*2p) (π*2p)

(σ2s) (σ*2s) (π2p) (π2p) (σ2p) (π*2p) (π*2p) (σ*2p)

2

d ¼ diamagnetic while; p ¼ paramagnetic.

(σ1s)2 with the 2 superscript indicating the number of electrons in the molecular orbital. Similarly, the valence electron configuration for N2 and O2 are:
2
2
2 N2 : ðσ2s Þ2 ðσ∗ 2s Þ2 π2p
π2p
σ2p

1
1 2 2 2 O2 : ðσ2s Þ2 ðσ∗ 2s Þ2 π2p π2p σ2p π∗ 2p π∗ 2p The order of molecular orbitals is important in molecular orbital diagrams because it denotes the order of increasing energies of the molecular orbitals. However, it is not important in electron configurations since the lower energy orbitals are completely filled. The electron configuration of molecules can be used to predict molecular properties. For example, the number of unpaired electrons determines magnetic properties and bond order determines bond strength, bond length, molecular stability, and in some cases the presence of resonance structures. Some examples from the possible diatomic elements in period 2 are shown in Table 3.5. Of the eight possible diatomic molecules listed in the table, two have a bond order of 0 indicating that no bonds are formed and so the molecules do not exist. Those with bond orders from 1 to 3 have increasing bond energies and decreasing bond length. Only two of the molecules listed have unpaired electrons, predicting that they will be paramagnetic.

3.6 MOLECULAR GEOMETRY Molecules are three-dimensional groups of atoms. The chemical formulas or electron dot structures of the molecules can tell us about the arrangement and bonding of the atoms, but they tell us nothing about their three-dimensional shapes. The shape of a molecule is important because it determines several molecular properties including: chemical reactivity, polarity, physical state, boiling point, melting point, and many more. The molecular shape

3.6 MOLECULAR GEOMETRY

101

depends on the bond lengths, the angles between the bonds, and the positioning of the electron pairs. The repulsions of electron pairs held in the molecular bonds or as lone pairs control the angles between bonds and the positions of the atoms in the molecule. Both the electrons held in covalent bonds, regardless of the bond order, and those as lone pairs are considered as electron groups. Since electrons repel each other, the electron groups will seek to be as far apart as possible. So, a molecule will have a geometry that minimizes the repulsion between its electron groups. The prediction of molecular shape from the repulsion between bonding and nonbonding electron groups is known as the valence shell electron pair repulsion (VSEPR) model of molecular geometry. There are five basic arrangements of electron groups around a central atom that is surrounded by two to six electron groups shown in Fig. 3.14. When a molecule has two electron groups around a central atom, they will occupy positions opposite each other in order to minimize the repulsion between the electron groups. The resulting geometry is linear with the bond angles of 180 degrees. When three electron groups surround a central atom, the most stable geometry will be in the shape of a triangle with the bond angles of 120 degrees. This geometry is called trigonal planar since all atoms lie in the same plane. With four electron groups around the central atom, the most stable geometry will be in the shape of a tetrahedron with the bond angles of 109.5 degrees. With five electron groups surrounding a central atom, the electron groups will be in the shape of two tetrahedra connected at the bases with the central atom positioned in the center of the base. This geometry is called trigonal bipyramidal. The atoms that lie along the vertical axis of the molecule are known as the axial positions and those that lie in the horizontal plane of the molecule, perpendicular to the vertical axis, are known as the equatorial positions. The bond angles between the axial atoms are 90 degrees, while the bond angles between the equatorial atoms are 120 degrees. With six electron groups around a central atom, the most stable geometry will be in the shape of two square base pyramids connected at the bases with the central atom at the center of the base. This geometry is called octahedral because the resulting figure has eight sides. The bond angles in an octahedral geometry are all 90 degrees. These electron group geometries cannot easily be explained by simple overlap of s and p atomic orbitals to form molecular orbitals. They can, however, be explained by including orbital hybridization. The hybrid orbitals, formed by mixing of s and p atomic orbitals, which

Linear

109.5 degrees

120 degrees

180 degrees

Trigonal planar

Tetrahedral 90 degrees

90 degrees

120 degrees Trigonal bipyramidal

Octahedral

FIG. 3.14 The electron group geometries predicted by the VSEPR model for a central atom that is surrounded by two to six electron groups.

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3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

are close in energy, are directed towards the bond axis leading to better overlap and stronger bonds. The number of hybrid orbitals formed will be equal to the number of atomic orbitals that were combined. The types of hybridization for the first three geometries shown in Fig. 3.14 are; • sp. hybridization—The mixing of one s atomic orbital with one p atomic orbital on the central atom to give two hybrid orbitals separated by 180 degrees with a linear geometry. • sp2 hybridization—The mixing of one s atomic orbital with two p atomic orbitals on the central atom to give three sp2 hybrid orbitals separated by 120 degrees with a trigonal planar geometry. • sp3 hybridization—The mixing of one s atomic orbital with three p atomic orbitals on the central atom to give four sp3 hybrid orbitals separated by 109.5 degrees with a tetrahedral geometry. The geometries shown in Fig. 3.14 are for electron groups surrounding a central atom. Since molecular geometry describes the arrangement of atoms around a central atom, the molecular geometry will be the same as the electron group geometry only if all the electron groups are contained in bonds. Although the lone pairs on a central atom occupy space and are part of the electron group geometry, they are not part of the molecular geometry. So, molecules containing lone pairs of electrons on the central atom will not have the same molecular geometry as that of the electron groups. However, the molecular geometry can be derived from one of the five basic shapes.

EXAMPLE 3.8: PREDICTING MOLECULAR GEOMETRIES OF MOLECULES WITH ONLY SINGLE BONDS SURROUNDING A CENTRAL ATOM What is the electron group geometry, molecular geometry, and bond angles of methane (CH4). 1. Draw the electron dot structure of methane. Carbon has four valence electrons and hydrogen has one valence electron. If carbon and hydrogen each share one valance electron, there will be four single bonds to carbon. The electron dot structure of methane is: H H

C

H

H

2. Determine the electron group geometry. Methane has four electron groups surrounding a central carbon atom. The electron group geometry will be tetrahedral. 3. Determine the molecular geometry. Since all the electron pairs are contained in bonds, the molecular geometry will also be tetrahedral with bond angles of 109.5 degrees.

3.6 MOLECULAR GEOMETRY

103

In order to better represent the molecular geometry, a three-dimensional form of bonding notation is used in which the structures are drawn with solid lines representing bonds in the plane of the paper, dotted lines representing bonds extending behind the plane of the paper, and wedge-shaped lines representing bonds extending in front of the plane of the paper. The geometric structure of methane would then be drawn as; H C

H

H

H

For molecules that have one or more lone pair electrons on the central atom, the lone pairs are also considered as an electron group and occupy a position in the electron pair geometry. For example, the ammonia molecule (NH3) has four electron groups surrounding the central nitrogen atom. Three of these are bonding electrons and one is a lone pair. The electron dot structure for ammonia is; H

N

H

H

The predicted electron group geometry for four electron groups would be tetrahedral, similar to methane. However, since lone pairs are not part of the molecular geometry, the electron group geometry and the molecular geometry will not be the same. The atoms in the ammonia molecule form the shape of a pyramid with the hydrogens at the base and the nitrogen at the peak of the pyramid. This molecular geometry is called trigonal pyramidal (half of a trigonal bipyramidal geometry). N

H

H

H

Similarly, the water molecule with the electron dot structure of; H

O

H

has two bonding electron groups and two nonbonding electron groups. With four electron groups surrounding the central oxygen atom, the electron group geometry is tetrahedral, but the molecular geometry is known as a bent shape represented as; O

H

H

Since the electron group geometries of both ammonia and water are tetrahedral, it would be expected that the bond angles would still be 109.5 degrees. However, the bond angles in the ammonia molecule are actually 107.5 degrees and those in the water molecule are 104.5 degrees. This is because the lone pairs occupy more space than bonded pairs. This increases

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3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

TABLE 3.6 Predicted Electron Group Geometries and Molecular Geometries for Molecules with Two to Six Electron Groups and a Varying Number of Lone Pairs Surrounding a Central Atom Electron Groups

Lone Pairs

Bonds

Electron Group Geometry

Molecular Geometry

Bond Angle (Degrees)

2

0

2

Linear

Linear

180

3

0

3

Trigonal planar

Trigonal planar

120

3

1

2

Trigonal planar

Bent

<120

4

0

4

Tetrahedral

Tetrahedral

109.5

4

1

3

Tetrahedral

Trigonal pyramidal

<109.5

4

2

2

Tetrahedral

Bent

<109.5

5

0

5

Trigonal bipyramidal

Trigonal bipyramidal

90, 120

5

1

4

Trigonal bipyramidal

See-saw

90, 120

5

2

3

Trigonal bipyramidal

T-shaped

90

5

3

2

Trigonal bipyramidal

Linear

180

6

0

6

Octahedral

Octahedral

90

6

1

5

Octahedral

Square pyramidal

90

6

2

4

Octahedral

Square planar

90

the repulsion between electron groups and forces the atoms closer together than predicted for molecules without lone pairs, resulting in smaller bond angles between the atoms. Table 3.6 describes the difference between the electronic group geometry and molecular geometry for molecules with two to six electron groups surrounding a central atom and a varying number of lone pairs. The shapes that occur in molecular geometries that do not occur in electron group geometries are: bent, trigonal pyramidal, see-saw, T-shaped, square pyramidal, and square planar. The bent and trigonal pyramidal geometries have been described above for water and ammonia; the remaining four are shown in Fig. 3.15. FIG. 3.15

The molecular geometries for a central atom surrounded by five electron groups with one lone pair (seesaw) and two lone pairs (T-shaped) and by six electron groups with one lone pair (square pyramidal) and two lone pairs (square planar).

90 degrees 90 degrees

T-shaped

Square planar 90 degrees 90 degrees 120 degrees

Square pyramidal

See-saw

3.7 MOLECULAR POLARITY

105

3.7 MOLECULAR POLARITY As explained in Section 3.3, polar covalent bonds occur when two bonded atoms have different electronegativities and share the electrons unequally, while nonpolar covalent bonds occur when two bonded atoms have the same electronegativities and share the electrons equally. Molecules can also be polar or nonpolar depending on the overall polarity of the bonds in the molecule. The polarity of the molecule is the sum of all of the individual bond polarities in the molecule. Since the dipole moment of each bond is a vector quantity with both magnitude and direction, the dipole moment of the molecule is determined as the vector sum of the individual bond dipole moments. Also, because the molecular polarity is a vector sum, the polarity of all bonds, however small, must be considered unless they are truly nonpolar with a dipole moment of 0.0D. A molecule that contains no polar covalent bonds (all bonds ¼ 0.0D) will have no charge difference between one part of the molecule and another part and the molecule will be nonpolar. A polar molecule occurs when electron density accumulates in one part of the molecule giving it a partial negative charge (δ
). The other side of the molecule will then have an equally partial positive charge (δ+). Since diatomic molecules have only one bond, if that bond is polar, the molecule will be polar, as in HBr. Or, if the bond is nonpolar the molecule will be nonpolar, as in HAt. In polyatomic molecules, the molecular polarity is determined from the sum of all of the individual bond polarities and how they are oriented in space (molecular geometry). For example, consider CO2 with the electron dot structure; +

O

δ−

δ+

C

+

O

δ−

With two electron groups around the central carbon atom, the electron group geometry will be linear and, since there are no lone pairs on the central atom, the molecular geometry will also be linear. Since carbon and oxygen have different electronegativities, both bonds in the CO2 molecule are polar. However, the molecule is symmetrical and the polarity of the two bonds is identical and oriented in exactly opposite directions. This is shown by arrows signifying the direction and strength of the bond polarities. The “+” sign at the beginning of the arrow indicates that the carbon end of the bond has the partial positive charge. The vector sum of the dipole moments of these two bonds is zero because they are exactly equal, but orientated in exactly opposite directions. So, even though the individual C]O bonds are polar, the CO2 molecule is nonpolar. In contrast, SO2 has three electron groups around the central sulfur atom with a trigonal planar electron group geometry. But, since one of the electron groups is a lone pair, the molecular geometry is bent. In this case, the SdO bond polarities contribute to the molecular polarity because the bent shape of the molecule is not symmetrical. The vector sum of the individual bond dipole moments gives a molecular polarity that is directed from the less electronegative sulfur atom towards the more electronegative oxygen atoms as indicated by the red arrow in the structure;

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3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

S O

O

In summary: • A polyatomic molecule is nonpolar if all of its terminal atoms have the same electronegativities and they are arranged symmetrically around the central atom. • A polyatomic molecule is polar if its terminal atoms have different electronegativities or they have the same electronegativities, but are not arranged symmetrically around the central atom. • The direction and strength of the polarity of a polyatomic molecule is determined by the vector sum of the dipole moments of all the bonds.

EXAMPLE 3.9: PREDICTING WHETHER A MOLECULE IS POLAR OR NONPOLAR What is the electron group geometry, molecular geometry, and polarity of: H2S, COS, HCN, and CCl4. 1. First write the electron dot structures for each compound. Cl H S H

O

C

S

H C

N

Cl

C

Cl

Cl

2. Determine the electron group geometry for each compound. H2S—with four electron groups is tetrahedral. COS—with two electron groups is linear. HCN—with two electron groups is linear. CCl4—with four electron groups is tetrahedral. 3. Determine the molecular geometry for each compound. H2S—with two lone pairs is bent. COS—with no lone pairs remains linear. HCN—with no lone pairs remains linear. CCl4—with no lone pairs remains tetrahedral. 4. Determine the molecular polarity of each compound. H2S: Sulfur (2.58) is more electronegative than hydrogen (2.20), so the SdH bonds are polar. The vector sum of the two HdS bond dipole moments results in a molecular dipole moment directed from the less electronegative hydrogens towards more electronegative sulfur. The H2S molecule will be polar with the partial negative charge on the sulfur. S H

H

COS: Sulfur (2.58) has very similar electronegativity as carbon (2.55), so the C]S bond has a dipole moment 0.0 and is nonpolar. Oxygen (3.44) is more electronegative than carbon, so the C]O bond is polar. The COS molecule will be polar with the partial negative charge on oxygen.

3.8 INTERMOLECULAR FORCES

107

EXAMPLE 3.9: PREDICTING WHETHER A MOLECULE IS POLAR OR NONPOLAR— CONT’D O

C

S

HCN: Carbon (2.55) is more electronegative than hydrogen (2.20). The CdH bond is polar with the partial negative charge on carbon. Nitrogen (3.04) is also more electronegative than carbon. The vector sum of both bond dipole moments results in a molecular dipole moment that is directed from the less electronegative hydrogen to the most electronegative nitrogen. H

C

N

CCl4: Chlorine (3.16) is more electronegative than carbon (2.55), so each CdCl bond will be polar. However, the tetrahedral geometry of the molecule is symmetrical. Since CCl4 has a symmetric charge distribution around the central carbon atom, the polar CdCl bonds all have dipole moments of equal magnitude with each pair directed opposite each other. The vector addition of all the CdCl dipole moments will be zero and the CCl4 molecule will be nonpolar. Cl C Cl

Cl

Cl

3.8 INTERMOLECULAR FORCES Molecular polarity is the source of interactions between molecules, which are important in the determination of many of the compound’s physical properties. The forces of attraction and repulsion between molecules are known as intermolecular forces. The attractive forces are known as van der Waals forces, named after the Dutch scientist Johannes Diderik van der Waals. These van der Waals forces are weak compared to the forces that hold the atoms of a molecule together, such as covalent or ionic bonding. However, they still can affect boiling point, freezing point, vapor pressure, evaporation rate, viscosity, surface tension, solubility, and other molecular properties. What determines the physical state of a substance, whether it exists as a solid, liquid, or gas, is based on both the strength of the van der Waals forces and the thermal energy of the system. At a given temperature, substances that contain strong van der Waals forces are more likely to be solids or liquids, while those with weak van der Waals forces will tend to be gases. There are two types of van der Waals forces: dipole-dipole forces and London dispersion forces. Dipole-dipole forces are the strongest type of van der Waals forces. A dipole-dipole force is an attractive force that occurs between molecules with permanent dipoles. Polar molecules, which have permanent dipole moments, will attract each other when the partially positive region of one molecule is near the partially negative region of another molecule.

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3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

FIG. 3.16

An example of a dipole-dipole interaction in liquid HCl where the partially positive hydrogen attracts the partially negative chlorine resulting in the alignment of the HCl molecules.

An example of a dipole-dipole interaction is seen in HCl shown in Fig. 3.16. Since chlorine is more electronegative than hydrogen and the molecular geometry is linear, the HdCl bond is polar and so has a permanent dipole moment. The positive region of the molecule will attract the negative region of a neighboring molecule and affect its position. This attraction results in all the molecules aligning so that the attractions between molecules are maximized and the repulsions are minimized. A very special type of dipole-dipole interaction is hydrogen bonding. This force is referred to as bonding because it is the strongest type of van der Waals force. It occurs when the permanent dipole in a molecule results from a covalent bond between a hydrogen atom and one of the very small, highly electronegative atoms: fluorine, oxygen, or nitrogen. The very large difference in electronegativities between hydrogen (2.20) and fluorine (3.98), oxygen (3.44), and nitrogen (3.04) causes the bond between them to be extremely polar. The electronegative atom attracts the bonding electrons towards itself and away from the hydrogen so strongly that that the hydrogen atom essentially becomes an exposed proton. An attractive force then forms between the hydrogen atom of one molecule and a lone pair of electrons on the electronegative atom of another molecule. The hydrogen becomes the “hydrogen bond donor” and the lone pair becomes the “hydrogen bond acceptor” forming a bridge between the hydrogen and the highly electronegative element. This can occur between molecules of the same kind, between molecules of different kinds, or between different sites on the same molecule if the molecule is very large. This bridging between hydrogen and a lone pair on oxygen or nitrogen is responsible for the folding of protein molecules giving them their three-dimensional structures.

CASE STUDY: WATER Water (H2O) is the most abundant molecular compound found on Earth. It covers 70% of the Earth’s surface and is essential for all life, making up 65% of the human body. Water is the only substance found naturally in all three of the common states of matter: solid, liquid, and gas. The gas form is found in the atmosphere as water vapor or on the Earth’s surface as steam from hydrothermal vents. Liquid water is in the atmosphere as clouds and also in precipitation as rain. It is found on the surface as both fresh and salt water and also in groundwater aquifers. Ice, the solid form, is seen as snow or hail in precipitation, as icebergs in the polar oceans, and as glaciers in higher elevations. As described in Section 3.6, the water molecule has two bonding electron groups and two nonbonding electron groups. With four electron groups surrounding the central oxygen atom, the electron group geometry is tetrahedral but the molecular geometry is bent. With a difference in electronegativity between oxygen (3.44) and hydrogen (2.20) and with two lone pairs on the oxygen atom, water is a very polar molecule with a dipole moment of 1.85D. O H

H

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3.8 INTERMOLECULAR FORCES

Water has many unusual properties including its boiling point, freezing point, surface tension, viscosity, and cohesion. Table 3.7 lists the boiling and freezing points of the compounds formed from the elements in group 16 of the periodic table bonded to hydrogen. Going down the group from hydrogen sulfide (H2S) to hydrogen telluride (H2Te), the boiling points increase from
60°C to
2°C as the molecular size increases. But water, the smallest of the group, has a boiling point of 100°C, which is very high for its molecular size. The same trend is seen in the freezing points of this group. Going down the group from H2S to H2Te, the freezing points increase from
82°C to
49°C as the molecular size increases, but water has a very high freezing point of 0°C. These inconsistent boiling and freezing points of water are due to the fact that water forms very strong hydrogen bonds. In liquid water, a lone pair on the oxygen of one water molecule can form a hydrogen bond with a hydrogen atom on another water molecule. In liquid water, this hydrogen bonding is repeated until every water molecule in the liquid is bonded to four other water molecules, two through the two lone pairs on the oxygen atom and two through the two hydrogen atoms as shown in Fig. 3.17. Water is unique in that it can form such a large number of hydrogen bonds per molecule. This is because the number of lone pairs and hydrogen atoms in each molecule are equal. In contrast, hydrogen fluoride has three lone pairs on the fluorine atom, but only one hydrogen atom. So there are three times as many lone pairs as there are hydrogen atoms in liquid HF and the number of hydrogen bonds it can form is limited to the number of hydrogen atoms. Each HF molecule can only form two hydrogen bonds, one with the hydrogen atom and one with one of the lone pairs on the fluorine atom. The other two lone pairs remain unbonded due to the lack of hydrogen atoms. Similarly, ammonia has only one lone pair on nitrogen and three hydrogen atoms. This time the number of hydrogen bonds formed in liquid NH3 is limited by the number of lone pairs. So, each Boiling and Freezing Points in °C of the Hydrides of Group 16 Elements

TABLE 3.7 Compound

Molecular Formula

Boiling Point

Water

H2O

100

0

Hydrogen sulfide

H2S


60


82

Hydrogen selenide

H2Se


41


66

Hydrogen telluride

H2Te


2


49

FIG. 3.17 δ− δ+ δ+

δ− δ+

Hydrogen bonds H O

δ−

H δ+

δ−

Freezing Point

Hydrogen bonding in liquid water where each water molecule forms hydrogen bonds with four other water molecules, two through the two lone pairs on the oxygen atom and two through the two hydrogen atoms. Modified from Qwerter, Wikimedia Commons.

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3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

ammonia molecule can also only form two hydrogen bonds, one with the lone pair and one with one of the hydrogen atoms. The unusually high boiling point of water is due to the high number of hydrogen bonds each molecule can form relative to its small size. This extensive hydrogen bonding prevents water molecules from being easily released from the surface of the liquid, so a higher temperature is required to achieve vaporization. The large number of hydrogen bonds in water also leads to the unusually high freezing point. Although the liquid water molecules are mobile and the hydrogen bonds are in flux, the hydrogen-bonded structure approximates an extended tetrahedral arrangement as shown in Fig. 3.17. Since the molecules are already in an extended regular structure in liquid water, the transition from a liquid to a solid does not require a large drop in temperature as with similar molecules that are not so strongly hydrogen-bonded. The hydrogen-bonded structures of liquid water and ice are compared in Fig. 3.18. Liquid water has a partially ordered tetrahedral structure in which the hydrogen bonds are constantly being formed and broken. On the other hand, ice has a rigid structure where each water molecule remains hydrogen-bonded to the same four water molecules. So, when water becomes a solid at the freezing point, the water molecules transition into a crystalline structure which has an open cage-like form that contains a lot of empty space. Because of this, ice increases in volume by about 9% over liquid water. Water is the only known chemical compound that expands when it freezes and since water is ubiquitous in nature, the effects of this behavior can be powerful. The expansion of ice as water freezes is the basic cause of water pipes bursting from the pressure of the expanding ice inside the pipes. It is also the major cause of damage to building foundations and roadways. Liquid water can seep into cracks in building materials, expanding and widening the cracks when the temperature drops to the freezing point at night. The subsequent rise in temperatures during the day can result in an expansion-contraction cycle during winter months, widening cracks and increasing damage. This freeze-thaw cycle is also responsible for the natural weathering of rocks. Along with the increasing volume when water freezes, the density of ice also decreases over that of the liquid water phase. All substances become less dense when they are heated and denser when they are cooled. So, when liquid water is cooled its density increases. The density continues to increase until it reaches a maximum density at 4°C (1.00 g/cm3) as shown in Fig. 3.19. This is the point where molecular motion is significantly decreased and the extended tetrahedral structure of liquid water becomes most compact. As water is cooled below 4°C, it becomes less dense as it begins to freeze and transition into the open cage-like structure of the solid form. The density of ice is 0.917 g/cm3 at 0°C, while the density FIG. 3.18 The structures of liquid water and ice. P99am, Wikimedia Commons.

Liquid water

Ice

111

3.8 INTERMOLECULAR FORCES

FIG. 3.19

The temperature dependence of the densities of ice and water.

1.01 1

Maximum density = 4 °C

0.99

Density (g/cm3)

0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 –100

–50

0

50

100

150

Temperature (°C)

of liquid water is 0.9998 g/cm3 at 0°C. So, the density of ice is approximately 8.3% less than the density of water at the same temperature. The density of ice increases slightly with decreasing temperature and has a value of 0.927 g/cm3 at
80°C. Since the water molecules are more tightly packed in the liquid state than in the solid state, this explains why ice floats on liquid water.

The weakest type of van der Waals forces is the London dispersion force named after the German American physicist Fritz London. The London dispersion force is a weak van der Waals force arising from the formation of an induced polarization in molecules that do not have a permanent dipole moment. As two nonpolar molecules approach each other, the repulsion between their electrons leads to a distortion of the electron clouds. This distortion results in a temporary polarization of the molecules, creating a temporary dipole in each molecule. These temporary dipoles can cause a temporary dipole to form in nearby molecules due to the attraction between their partially positive regions and the electron clouds of other molecules. The temporary attractions between the partially positive region of one dipole with the partially negative region of another dipole causes the molecules to line up as shown in Fig. 3.20, stabilizing the system. This stabilization also affects chemical properties such as boiling points, freezing points, and solubilities. However, since London dispersion forces are much weaker than dipole-dipole interactions, the effects are not as strong. London dispersion forces are the only van der Waals forces that act on nonpolar molecules including the diatomic elements (N2, O2, and the halogens) as well as nonpolar hydrocarbons such as methane. London forces can cause nonpolar substances to condense into liquids and to freeze into solids when the temperature is lowered sufficiently. The strength of the London dispersion force depends on how easily the electrons in a molecule can be polarized, called the polarizability of a molecule. In general, London forces increase with an increasing

112

3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

FIG. 3.20 The formation of an induced dipole in a nonpolar diatomic molecule. The temporary distortion of the electron cloud results in induced temporary dipoles in neighboring molecules, resulting in weak attractive forces called London dispersion forces.

δ−

δ+

δ−

δ+

δ−

δ+

TABLE 3.8 Boiling Points (°C) and Number of Electrons in the Diatomic Elements. The Boiling Point of At2 Has Not Been Measured and is Predicted From Chemical Properties Element

Electrons

Boiling Point (°C)

N2

14


196

O2

16


183

F2

18


188

Cl2

34


34

Br2

70

59

I2

106

184

At2

170

337

number of electrons. The larger the atoms, the more electrons in the molecule, the more easily they can be polarized, and the stronger the London dispersion force. Also, in a larger atom, the electrons occupy higher electron shells that are farther away from the nucleus, so the electrons will be less tightly held by the nuclear attractive forces and are able to move more freely. This is why the London dispersion force increases with increasing atomic mass. London dispersion forces affect boiling points of nonpolar substances. Table 3.8 lists the boiling points of the diatomic elements. It is clear from the trend of the halogens that the boiling point increases as the number of electrons increases. For example, Cl2 with 34 electrons has a higher boiling point than F2 with 18 electrons due to the higher polarizability, and thus, the stronger London dispersion forces between the larger Cl2 molecules than for the smaller F2 molecules. This trend continues down the group from F2 to I2. Although the boiling point of the last member of the group has not been measured directly due to the very high radioactivity of At2, it has been predicted from other observed chemical properties to be very high (337°C). The first three diatomic elements shown in Table 3.8 (N2, O2, and F2) are all in period 2 of the periodic table. They have very similar boiling points ranging from d196°C for N2 to
183°C for O2, a difference of only 13°C compared to a difference of 247°C for F2 (
188°C) and Br2 (59°C). Since N2, O2, and F2 are in adjacent groups (15 through 17) in the same period, they each have a very similar number of electrons (14 to 18) and also their electron configurations are similar with all the electrons occupying the same electron shells. So, it is expected that they would have very similar polarizabilities and very similar London dispersion forces leading to their similarity in boiling points.

IMPORTANT TERMS

113

IMPORTANT TERMS Anion a negatively charged ion. Antibonding molecular orbital a molecular orbital resulting from the combination of atomic orbitals out of phase. Axial the atoms that lie along the vertical axis of a molecule. Bond order the number of bonds between two atoms. Bonding pair electrons the shared electron pair that forms a covalent bond between two atoms. Bonding molecular orbital a molecular orbital resulting from the combination of atomic orbitals in phase. Bonding notation a representation of the structure of a molecule using element symbols connected by lines to represent bonding electrons. Cation a positively charged ion. Chemical formula a way of expressing the bonding between atoms and ions in a compound using a single line of element symbols along with numeric subscripts to indicate the number of atoms of each element. Coulomb’s Law the force of the electrostatic interaction between two charged particles is proportional to the product of the charges divided by the square of the distance between them. Covalent bond sharing of a pair of electrons between two atoms which holds them together. Diatomic molecule a molecule made up of two atoms. Diamagnetic having the property of being weakly repelled by a magnetic field. Dipole a bond (or molecule) that has a partial positive charge on one end and partial negative charge on the other. Dipole-dipole forces an attractive force between molecules with permanent dipole moments. Dipole moment a measure of the polarity of a covalent bond. Double bond a covalent bond that results from the sharing of two electron pairs between two atoms. Equatorial the atoms that lie along the horizontal plane of a molecule. Hybridization a mixing of s and p atomic orbitals when molecular orbitals are formed. Hydrogen bonding a type of dipole-dipole force that occurs between molecules containing a covalent bond between a hydrogen atom and a very electronegative atom with at least one lone pair of electrons, usually fluorine, oxygen, or nitrogen. Intermolecular forces the forces of attraction and repulsion between molecules. Ionic bond electrostatic attractions between oppositely charged positive and negative ions which holds the atoms together to form an ionic compound. Ionic radius the distance from the nucleus to the outermost occupied electron orbital in an ion. London dispersion force a weak attractive force arising from the formation of an induced instantaneous polarization in molecules that do not have a permanent dipole moment. Lone pair electrons a pair of electrons surrounding an atom in a molecule that is not shared with another atom. Molecular formula the chemical formula for a covalent compound. Molecular orbitals orbitals formed when the atomic orbitals overlap during covalent bonding. Nonpolar covalent bond a covalent bond where electrons are shared equally between two atoms. Octet rule atoms in the s- and p-blocks of the periodic table tend to combine in such a way that each atom acquires eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. Paramagnetic having the property of being strongly attracted by a magnetic field. Polar covalent bond a covalent bond where electrons are shared unequally between two atoms. Polarizability the ability for a molecule to be polarized. Resonance structures two or more equivalent chemical structures which differ only in the position of their electrons (not the position of the atoms). Single bond a covalent bond that results from the sharing of one electron pair between two atoms. Stock number a system of naming cations that uses the name of the element followed by a Roman numeral in parentheses to indicate the charge of the ion. Triple bond a covalent bond that results from the sharing of three electron pairs between two atoms. Valence bond theory the description of covalent bonds as involving shared pairs of electrons which are localized in a bond between two atoms. van der Waals forces the forces of attraction between molecules.

114

3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

STUDY QUESTIONS 3.1 What is the difference between a cation and an anion? 3.2 What determines the number of electrons an atom will gain or lose? 3.3 Which group in the periodic table does not form ions? Give the group number and its name. 3.4 Which group in the periodic table forms 1+ ions? Give the group number and its name. 3.5 Which group in the periodic table forms 1
ions? Give the group number and its name. 3.6 Which group in the periodic table forms 2+ ions? Give the group number and its name. 3.7 What is the common name for the groups in the periodic table that contain elements which can have multiple ionic forms? 3.8 What are the most common cations for the transition metals? 3.9 What is an ionic radius? 3.10 Which ion has a larger radius than the parent atom; anion or cation? Why? 3.11 Which ion has a smaller radius than the parent atom? Why? 3.12 Which ion has the larger radius; anion or cation? 3.13 How does ionic charge affect ionic radius? 3.14 How does ionic radius vary within a group? 3.15 How does ionic radius vary within a period? 3.16 What creates an ionic bond? 3.17 What does Coulomb’s Law describe? 3.18 The potential energy between two charged particles is directly proportional to what? Inversely proportional to what? 3.19 How does ionic radius affect ionic bond strength? 3.20 How does ionic charge affect ionic bond strength? 3.21 Ionic bonds generally occur between which anions and cations? 3.22 What is the octet rule? 3.23 What is a chemical formula? 3.24 (a) What is a covalent bond? (b) How is it different from an ionic bond? 3.25 (a) What is a lone pair of electrons? (b) What is a bonding pair? 3.26 What is valence bond theory? 3.27 (a) What is a single bond? (b) Double bond? (c) Triple bond? 3.28 What makes a covalent bond polar? 3.29 What is a dipole? 3.30 What is the dipole moment of a bond or molecule? 3.31 What electronegativity difference between two bonded atoms will result in the bond behaving as: (a) polar, (b) nonpolar, and (c) ionic? 3.32 What is bonding notation? Why is it used? 3.33 Why is the chemical formula of a covalent compound called a molecular formula? 3.34 What is a polyatomic ion? 3.35 What is a resonance structure? 3.36 How are molecular orbitals formed? 3.37 How are bonding molecular orbitals formed? 3.38 How are antibonding molecular orbitals formed? 3.39 What are the two types of bonding molecular orbitals? How do they differ?

PROBLEMS

3.40 3.41 3.42 3.43 3.44 3.45 3.46 3.47 3.48 3.49 3.50 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.58 3.59

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What is the bond order of two bonded atoms? What determines the magnetic properties of a molecule? What causes molecules to be diamagnetic? paramagnetic? What is bond hybridization? What are the three types of bond hybridization? How is each formed? What are the five possible electron group geometries? What determines the direction and strength of the polarity of a polyatomic molecule? What are intermolecular forces? What are van der Waals forces? What are two types of van der Waals forces? What is a hydrogen bond? Which van der Waals force is the strongest? What property of water is responsible for its unusual boiling point? How many hydrogen bonds can a single water molecule form? Why does water expand when freezing? At what temperature is water at its maximum density? What is the weakest van der Waals force? What is the only van der Waals force that acts on nonpolar molecules? What are London dispersion forces? What is polarizability?

PROBLEMS 3.60 What are the charges of the ions formed from the following elements: (a) Na, (b) F, (c) Ca, (d) Br, and (e) Cs? 3.61 What are the electronic configurations in noble gas notation for the following ions: (a) Mg2+, (b) N3
, (c) Al3+, and (d) S2
? 3.62 Name the following anions: (a) P
, (b) O2
, (c) Cl
, (d) S2
, and (e) I
. 3.63 Name the following cations: (a) Al3+, (b) As3+, (c) Cd2+, (d) Cr6+, and (e) Cu1+. 3.64 List the following ions in the order of increasing radius: As3
, N3
, Sb3
, N3
, Sb3+. 3.65 List the following ions in the order of decreasing radius: Sc3+, V3+, K+, V5+, Cr6+. 3.66 List the following ions in the order of increasing size: S 2
, Sr2+, Te2
, Be2
. 3.67 Name the following ionic compounds: (a) CrF2, (b) FeCl3, (c) Al2S3, (d) PbO, (e) Mg3P2, and (f) TiI4. 3.68 Give the chemical formulas for the following ionic compounds: (a) silver cyanide, (b) iron(II) oxide, (c) calcium oxide, (d) sodium bromide, (e) copper(I) arsenide, and (f) beryllium chloride. 3.69 List the following ionic bonds in the order of increasing bond strength: KdBr, KdI, MgdCl, ZrdCl, KdF. 3.70 List the ionic bonds in Problem 3.69 in the order of increasing bond length. 3.71 Write the following ionic reactions using electron dot representations: (a) lithium + chlorine, (b) calcium + sulfur, (c) magnesium + bromine, (d) barium + oxygen and (e) strontium + iodine.

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3. CHEMICAL BONDING—THE FORMATION OF MATERIALS

3.72 Write the chemical formula of the ionic compounds formed from each reaction in Problem 3.71. 3.73 List the following ionic compounds in the order of increasing melting points: KBr, MgCl2, TiCl4, KF, KI. 3.74 Name the following covalent compounds: (a) SbBr3, (b) ClO2, (c) N2O3, (d) PI3, (e) CCl4, and (f) CH4. 3.75 Give the molecular formulas for the following covalent compounds: (a) nitrogen trifluoride, (b) dinitrogen pentoxide, (c) hydrogen sulfide, (d) sulfur hexafluoride, (e) nitrogen dioxide, and (f) carbon disulfide. 3.76 Draw the electron dot structures for the following molecules: (a) BF3, (b) CS2, (c) PCl3, (d) NO2, and (e) CHCl3. 3.77 Which molecules in Problem 3.76 contain double bonds? 3.78 What are the electron group geometries of the molecules listed in Problem 3.76? 3.79 What are the molecular geometries of the molecules listed in Problem 3.76? 3.80 Are the molecules listed in Problem 3.76 polar or nonpolar? 3.81 Write the molecular formulas in Problem 3.76 in three-dimensional bonding notation. 3.82 Name the following polyatomic ions: (a) OH
, (b) CNS
, (c) SO4
, (d) ClO4
, and (e) CrO4
. 3.83 Write the chemical formulas for the following polyatomic ions: (a) hydronium, (b) carbonate, (c) nitrate, (d) phosphate, and (e) nitrite. 3.84 Write the electron dot structure for the following polyatomic ions: (a) CO32
, (b) OH
, (c) NO2
, and (d) H3O+. 3.85 Which polyatomic ions in Problem 3.84 have resonance structures? Draw the resonance structures. 3.86 In the molecular orbital diagram for Li2: (a) How many electrons occupy the bonding molecular orbitals? (b) How many electrons occupy the antibonding molecular orbitals? (c) What is the bond order for Li2? and (d) Is Li2 a stable molecule? 3.87 In the molecular orbital diagram for Be2: (a) How many electrons occupy the bonding molecular orbitals? (b) How many electrons occupy the antibonding molecular orbitals? (c) What is the bond order for Be2? and (d) Is Be2 a stable molecule? 3.88 List the following molecules in order of increasing boiling points: CH4, HCl, N2, NH3, H2, H2O.